Daily Papers

Diffusion Transformers (DiTs) have recently gained substantial attention in both industrial and academic fields for their superior visual generation capabilities, outperforming traditional diffusion models that use U-Net. However,the enhanced performance of DiTs also comes with high parameter counts and implementation costs, seriously restricting their use on resource-limited devices such as mobile phones. To address these challenges, we introduce the Hybrid Floating-point Quantization for DiT(HQ-DiT), an efficient post-training quantization method that utilizes 4-bit floating-point (FP) precision on both weights and activations for DiT inference. Compared to fixed-point quantization (e.g., INT8), FP quantization, complemented by our proposed clipping range selection mechanism, naturally aligns with the data distribution within DiT, resulting in a minimal quantization error. Furthermore, HQ-DiT also implements a universal identity mathematical transform to mitigate the serious quantization error caused by the outliers. The experimental results demonstrate that DiT can achieve extremely low-precision quantization (i.e., 4 bits) with negligible impact on performance. Our approach marks the first instance where both weights and activations in DiTs are quantized to just 4 bits, with only a 0.12 increase in sFID on ImageNet.

Mathematical formulas are a fundamental and widely used component in various scientific fields, serving as a universal language for expressing complex concepts and relationships. While state-of-the-art transformer models excel in processing and understanding natural language, they encounter challenges with mathematical notation, which involves a complex structure and diverse representations. This study focuses on the development of specialized training datasets to enhance the encoding of mathematical content. We introduce Math Mutator (MAMUT), a framework capable of generating equivalent and falsified versions of a given mathematical formula in LaTeX notation, effectively capturing the mathematical variety in notation of the same concept. Based on MAMUT, we have generated four large mathematical datasets containing diverse notation, which can be used to train language models with enhanced mathematical embeddings.

Power transforms are popular parametric techniques for making data more Gaussian-like, and are widely used as preprocessing steps in statistical analysis and machine learning. However, we find that direct implementations of power transforms suffer from severe numerical instabilities, which can lead to incorrect results or even crashes. In this paper, we provide a comprehensive analysis of the sources of these instabilities and propose effective remedies. We further extend power transforms to the federated learning setting, addressing both numerical and distributional challenges that arise in this context. Experiments on real-world datasets demonstrate that our methods are both effective and robust, substantially improving stability compared to existing approaches.

We propose ID-to-3D, a method to generate identity- and text-guided 3D human heads with disentangled expressions, starting from even a single casually captured in-the-wild image of a subject. The foundation of our approach is anchored in compositionality, alongside the use of task-specific 2D diffusion models as priors for optimization. First, we extend a foundational model with a lightweight expression-aware and ID-aware architecture, and create 2D priors for geometry and texture generation, via fine-tuning only 0.2% of its available training parameters. Then, we jointly leverage a neural parametric representation for the expressions of each subject and a multi-stage generation of highly detailed geometry and albedo texture. This combination of strong face identity embeddings and our neural representation enables accurate reconstruction of not only facial features but also accessories and hair and can be meshed to provide render-ready assets for gaming and telepresence. Our results achieve an unprecedented level of identity-consistent and high-quality texture and geometry generation, generalizing to a ``world'' of unseen 3D identities, without relying on large 3D captured datasets of human assets.

Face swapping is a task that changes a facial identity of a given image to that of another person. In this work, we propose a novel face-swapping framework called Megapixel Facial Identity Manipulation (MFIM). The face-swapping model should achieve two goals. First, it should be able to generate a high-quality image. We argue that a model which is proficient in generating a megapixel image can achieve this goal. However, generating a megapixel image is generally difficult without careful model design. Therefore, our model exploits pretrained StyleGAN in the manner of GAN-inversion to effectively generate a megapixel image. Second, it should be able to effectively transform the identity of a given image. Specifically, it should be able to actively transform ID attributes (e.g., face shape and eyes) of a given image into those of another person, while preserving ID-irrelevant attributes (e.g., pose and expression). To achieve this goal, we exploit 3DMM that can capture various facial attributes. Specifically, we explicitly supervise our model to generate a face-swapped image with the desirable attributes using 3DMM. We show that our model achieves state-of-the-art performance through extensive experiments. Furthermore, we propose a new operation called ID mixing, which creates a new identity by semantically mixing the identities of several people. It allows the user to customize the new identity.

Text-to-image diffusion models have remarkably excelled in producing diverse, high-quality, and photo-realistic images. This advancement has spurred a growing interest in incorporating specific identities into generated content. Most current methods employ an inversion approach to embed a target visual concept into the text embedding space using a single reference image. However, the newly synthesized faces either closely resemble the reference image in terms of facial attributes, such as expression, or exhibit a reduced capacity for identity preservation. Text descriptions intended to guide the facial attributes of the synthesized face may fall short, owing to the intricate entanglement of identity information with identity-irrelevant facial attributes derived from the reference image. To address these issues, we present the novel use of the extended StyleGAN embedding space W_+, to achieve enhanced identity preservation and disentanglement for diffusion models. By aligning this semantically meaningful human face latent space with text-to-image diffusion models, we succeed in maintaining high fidelity in identity preservation, coupled with the capacity for semantic editing. Additionally, we propose new training objectives to balance the influences of both prompt and identity conditions, ensuring that the identity-irrelevant background remains unaffected during facial attribute modifications. Extensive experiments reveal that our method adeptly generates personalized text-to-image outputs that are not only compatible with prompt descriptions but also amenable to common StyleGAN editing directions in diverse settings. Our source code will be available at https://github.com/csxmli2016/w-plus-adapter.

This study investigates identity-preserving image synthesis, an intriguing task in image generation that seeks to maintain a subject's identity while adding a personalized, stylistic touch. Traditional methods, such as Textual Inversion and DreamBooth, have made strides in custom image creation, but they come with significant drawbacks. These include the need for extensive resources and time for fine-tuning, as well as the requirement for multiple reference images. To overcome these challenges, our research introduces a novel approach to identity-preserving synthesis, with a particular focus on human images. Our model leverages a direct feed-forward mechanism, circumventing the need for intensive fine-tuning, thereby facilitating quick and efficient image generation. Central to our innovation is a hybrid guidance framework, which combines stylized images, facial images, and textual prompts to guide the image generation process. This unique combination enables our model to produce a variety of applications, such as artistic portraits and identity-blended images. Our experimental results, including both qualitative and quantitative evaluations, demonstrate the superiority of our method over existing baseline models and previous works, particularly in its remarkable efficiency and ability to preserve the subject's identity with high fidelity.

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent work has explored enlarging the class of transformations used to the case of Lie groups, principally through the use of their Lie algebra, as well as the group exponential and logarithm maps. The applicability of such methods to larger transformation groups is limited by the fact that depending on the group of interest G, the exponential map may not be surjective. Further limitations are encountered when G is neither compact nor abelian. Using the structure and geometry of Lie groups and their homogeneous spaces, we present a framework by which it is possible to work with such groups primarily focusing on the Lie groups G = GL^{+}(n, R) and G = SL(n, R), as well as their representation as affine transformations R^{n} rtimes G. Invariant integration as well as a global parametrization is realized by decomposing the `larger` groups into subgroups and submanifolds which can be handled individually. Under this framework, we show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the standard affine-invariant benchmark classification task, where we outperform all previous equivariant models as well as all Capsule Network proposals.

Recent advances in large pretrained text-to-image models have shown unprecedented capabilities for high-quality human-centric generation, however, customizing face identity is still an intractable problem. Existing methods cannot ensure stable identity preservation and flexible editability, even with several images for each subject during training. In this work, we propose StableIdentity, which allows identity-consistent recontextualization with just one face image. More specifically, we employ a face encoder with an identity prior to encode the input face, and then land the face representation into a space with an editable prior, which is constructed from celeb names. By incorporating identity prior and editability prior, the learned identity can be injected anywhere with various contexts. In addition, we design a masked two-phase diffusion loss to boost the pixel-level perception of the input face and maintain the diversity of generation. Extensive experiments demonstrate our method outperforms previous customization methods. In addition, the learned identity can be flexibly combined with the off-the-shelf modules such as ControlNet. Notably, to the best knowledge, we are the first to directly inject the identity learned from a single image into video/3D generation without finetuning. We believe that the proposed StableIdentity is an important step to unify image, video, and 3D customized generation models.

We investigate the space of weights spanned by a large collection of customized diffusion models. We populate this space by creating a dataset of over 60,000 models, each of which is a base model fine-tuned to insert a different person's visual identity. We model the underlying manifold of these weights as a subspace, which we term weights2weights. We demonstrate three immediate applications of this space -- sampling, editing, and inversion. First, as each point in the space corresponds to an identity, sampling a set of weights from it results in a model encoding a novel identity. Next, we find linear directions in this space corresponding to semantic edits of the identity (e.g., adding a beard). These edits persist in appearance across generated samples. Finally, we show that inverting a single image into this space reconstructs a realistic identity, even if the input image is out of distribution (e.g., a painting). Our results indicate that the weight space of fine-tuned diffusion models behaves as an interpretable latent space of identities.

Recent advancements in text-to-image generation have spurred interest in personalized human image generation, which aims to create novel images featuring specific human identities as reference images indicate. Although existing methods achieve high-fidelity identity preservation, they often struggle with limited multi-ID usability and inadequate facial editability. We present DynamicID, a tuning-free framework supported by a dual-stage training paradigm that inherently facilitates both single-ID and multi-ID personalized generation with high fidelity and flexible facial editability. Our key innovations include: 1) Semantic-Activated Attention (SAA), which employs query-level activation gating to minimize disruption to the original model when injecting ID features and achieve multi-ID personalization without requiring multi-ID samples during training. 2) Identity-Motion Reconfigurator (IMR), which leverages contrastive learning to effectively disentangle and re-entangle facial motion and identity features, thereby enabling flexible facial editing. Additionally, we have developed a curated VariFace-10k facial dataset, comprising 10k unique individuals, each represented by 35 distinct facial images. Experimental results demonstrate that DynamicID outperforms state-of-the-art methods in identity fidelity, facial editability, and multi-ID personalization capability.

While closed-source Large Language Models (LLMs) demonstrate strong mathematical problem-solving abilities, open-source models continue to struggle with such tasks. To bridge this gap, we propose a data augmentation approach and introduce PersonaMathQA, a dataset derived from MATH and GSM8K, on which we train the PersonaMath models. Our approach consists of two stages: the first stage is learning from Persona Diversification, and the second stage is learning from Reflection. In the first stage, we regenerate detailed chain-of-thought (CoT) solutions as instructions using a closed-source LLM and introduce a novel persona-driven data augmentation technique to enhance the dataset's quantity and diversity. In the second stage, we incorporate reflection to fully leverage more challenging and valuable questions. Evaluation of our PersonaMath models on MATH and GSM8K reveals that the PersonaMath-7B model (based on LLaMA-2-7B) achieves an accuracy of 24.2% on MATH and 68.7% on GSM8K, surpassing all baseline methods and achieving state-of-the-art performance. Notably, our dataset contains only 70.3K data points-merely 17.8% of MetaMathQA and 27% of MathInstruct-yet our model outperforms these baselines, demonstrating the high quality and diversity of our dataset, which enables more efficient model training. We open-source the PersonaMathQA dataset, PersonaMath models, and our code for public usage.

Ongoing efforts that span over decades show a rise of AI methods for accelerating scientific discovery, yet accelerating discovery in mathematics remains a persistent challenge for AI. Specifically, AI methods were not effective in creation of formulas for mathematical constants because each such formula must be correct for infinite digits of precision, with "near-true" formulas providing no insight toward the correct ones. Consequently, formula discovery lacks a clear distance metric needed to guide automated discovery in this realm. In this work, we propose a systematic methodology for categorization, characterization, and pattern identification of such formulas. The key to our methodology is introducing metrics based on the convergence dynamics of the formulas, rather than on the numerical value of the formula. These metrics enable the first automated clustering of mathematical formulas. We demonstrate this methodology on Polynomial Continued Fraction formulas, which are ubiquitous in their intrinsic connections to mathematical constants, and generalize many mathematical functions and structures. We test our methodology on a set of 1,768,900 such formulas, identifying many known formulas for mathematical constants, and discover previously unknown formulas for pi, ln(2), Gauss', and Lemniscate's constants. The uncovered patterns enable a direct generalization of individual formulas to infinite families, unveiling rich mathematical structures. This success paves the way towards a generative model that creates formulas fulfilling specified mathematical properties, accelerating the rate of discovery of useful formulas.

This paper presents a powerful framework to customize video creations by incorporating multiple specific identity (ID) photos, with video diffusion Transformers, referred to as Ingredients. Generally, our method consists of three primary modules: (i) a facial extractor that captures versatile and precise facial features for each human ID from both global and local perspectives; (ii) a multi-scale projector that maps face embeddings into the contextual space of image query in video diffusion transformers; (iii) an ID router that dynamically combines and allocates multiple ID embedding to the corresponding space-time regions. Leveraging a meticulously curated text-video dataset and a multi-stage training protocol, Ingredients demonstrates superior performance in turning custom photos into dynamic and personalized video content. Qualitative evaluations highlight the advantages of proposed method, positioning it as a significant advancement toward more effective generative video control tools in Transformer-based architecture, compared to existing methods. The data, code, and model weights are publicly available at: https://github.com/feizc/Ingredients.

While recent works have achieved great success on one-shot 3D common object generation, high quality and fidelity 3D head generation from a single image remains a great challenge. Previous text-based methods for generating 3D heads were limited by text descriptions and image-based methods struggled to produce high-quality head geometry. To handle this challenging problem, we propose a novel framework, Portrait3D, to generate high-quality 3D heads while preserving their identities. Our work incorporates the identity information of the portrait image into three parts: 1) geometry initialization, 2) geometry sculpting, and 3) texture generation stages. Given a reference portrait image, we first align the identity features with text features to realize ID-aware guidance enhancement, which contains the control signals representing the face information. We then use the canny map, ID features of the portrait image, and a pre-trained text-to-normal/depth diffusion model to generate ID-aware geometry supervision, and 3D-GAN inversion is employed to generate ID-aware geometry initialization. Furthermore, with the ability to inject identity information into 3D head generation, we use ID-aware guidance to calculate ID-aware Score Distillation (ISD) for geometry sculpting. For texture generation, we adopt the ID Consistent Texture Inpainting and Refinement which progressively expands the view for texture inpainting to obtain an initialization UV texture map. We then use the id-aware guidance to provide image-level supervision for noisy multi-view images to obtain a refined texture map. Extensive experiments demonstrate that we can generate high-quality 3D heads with accurate geometry and texture from single in-the-wild portrait images. The project page is at https://jinkun-hao.github.io/Portrait3D/.

We present a new direction for increasing the interpretability of deep neural networks (DNNs) by promoting weight-input alignment during training. For this, we propose to replace the linear transforms in DNNs by our B-cos transform. As we show, a sequence (network) of such transforms induces a single linear transform that faithfully summarises the full model computations. Moreover, the B-cos transform introduces alignment pressure on the weights during optimisation. As a result, those induced linear transforms become highly interpretable and align with task-relevant features. Importantly, the B-cos transform is designed to be compatible with existing architectures and we show that it can easily be integrated into common models such as VGGs, ResNets, InceptionNets, and DenseNets, whilst maintaining similar performance on ImageNet. The resulting explanations are of high visual quality and perform well under quantitative metrics for interpretability. Code available at https://www.github.com/moboehle/B-cos.

The current text-to-video (T2V) generation has made significant progress in synthesizing realistic general videos, but it is still under-explored in identity-specific human video generation with customized ID images. The key challenge lies in maintaining high ID fidelity consistently while preserving the original motion dynamic and semantic following after the identity injection. Current video identity customization methods mainly rely on reconstructing given identity images on text-to-image models, which have a divergent distribution with the T2V model. This process introduces a tuning-inference gap, leading to dynamic and semantic degradation. To tackle this problem, we propose a novel framework, dubbed PersonalVideo, that applies direct supervision on videos synthesized by the T2V model to bridge the gap. Specifically, we introduce a learnable Isolated Identity Adapter to customize the specific identity non-intrusively, which does not comprise the original T2V model's abilities (e.g., motion dynamic and semantic following). With the non-reconstructive identity loss, we further employ simulated prompt augmentation to reduce overfitting by supervising generated results in more semantic scenarios, gaining good robustness even with only a single reference image available. Extensive experiments demonstrate our method's superiority in delivering high identity faithfulness while preserving the inherent video generation qualities of the original T2V model, outshining prior approaches. Notably, our PersonalVideo seamlessly integrates with pre-trained SD components, such as ControlNet and style LoRA, requiring no extra tuning overhead.

Drawing on recent advancements in diffusion models for text-to-image generation, identity-preserved personalization has made significant progress in accurately capturing specific identities with just a single reference image. However, existing methods primarily integrate reference images within the text embedding space, leading to a complex entanglement of image and text information, which poses challenges for preserving both identity fidelity and semantic consistency. To tackle this challenge, we propose Infinite-ID, an ID-semantics decoupling paradigm for identity-preserved personalization. Specifically, we introduce identity-enhanced training, incorporating an additional image cross-attention module to capture sufficient ID information while deactivating the original text cross-attention module of the diffusion model. This ensures that the image stream faithfully represents the identity provided by the reference image while mitigating interference from textual input. Additionally, we introduce a feature interaction mechanism that combines a mixed attention module with an AdaIN-mean operation to seamlessly merge the two streams. This mechanism not only enhances the fidelity of identity and semantic consistency but also enables convenient control over the styles of the generated images. Extensive experimental results on both raw photo generation and style image generation demonstrate the superior performance of our proposed method.

There has been significant progress in personalized image synthesis with methods such as Textual Inversion, DreamBooth, and LoRA. Yet, their real-world applicability is hindered by high storage demands, lengthy fine-tuning processes, and the need for multiple reference images. Conversely, existing ID embedding-based methods, while requiring only a single forward inference, face challenges: they either necessitate extensive fine-tuning across numerous model parameters, lack compatibility with community pre-trained models, or fail to maintain high face fidelity. Addressing these limitations, we introduce InstantID, a powerful diffusion model-based solution. Our plug-and-play module adeptly handles image personalization in various styles using just a single facial image, while ensuring high fidelity. To achieve this, we design a novel IdentityNet by imposing strong semantic and weak spatial conditions, integrating facial and landmark images with textual prompts to steer the image generation. InstantID demonstrates exceptional performance and efficiency, proving highly beneficial in real-world applications where identity preservation is paramount. Moreover, our work seamlessly integrates with popular pre-trained text-to-image diffusion models like SD1.5 and SDXL, serving as an adaptable plugin. Our codes and pre-trained checkpoints will be available at https://github.com/InstantID/InstantID.

Conversion of spoken mathematical expressions is a challenging task that involves transcribing speech into a strictly structured symbolic representation while addressing the ambiguity inherent in the pronunciation of equations. Although significant progress has been achieved in automatic speech recognition (ASR) and language models (LM), the problem of converting spoken mathematics into LaTeX remains underexplored. This task directly applies to educational and research domains, such as lecture transcription or note creation. Based on ASR post-correction, prior work requires 2 transcriptions, focuses only on isolated equations, has a limited test set, and provides neither training data nor multilingual coverage. To address these issues, we present the first fully open-source large-scale dataset, comprising over 66,000 human-annotated audio samples of mathematical equations and sentences in both English and Russian, drawn from diverse scientific domains. In addition to the ASR post-correction models and few-shot prompting, we apply audio language models, demonstrating comparable character error rate (CER) results on the MathSpeech benchmark (28% vs. 30%) for the equations conversion. In contrast, on the proposed S2L-equations benchmark, our models outperform the MathSpeech model by a substantial margin of more than 40 percentage points, even after accounting for LaTeX formatting artifacts (27% vs. 64%). We establish the first benchmark for mathematical sentence recognition (S2L-sentences) and achieve an equation CER of 40%. This work lays the groundwork for future advances in multimodal AI, with a particular focus on mathematical content recognition.

Face anti-spoofing techniques based on domain generalization have recently been studied widely. Adversarial learning and meta-learning techniques have been adopted to learn domain-invariant representations. However, prior approaches often consider the dataset gap as the primary factor behind domain shifts. This perspective is not fine-grained enough to reflect the intrinsic gap among the data accurately. In our work, we redefine domains based on identities rather than datasets, aiming to disentangle liveness and identity attributes. We emphasize ignoring the adverse effect of identity shift, focusing on learning identity-invariant liveness representations through orthogonalizing liveness and identity features. To cope with style shifts, we propose Style Cross module to expand the stylistic diversity and Channel-wise Style Attention module to weaken the sensitivity to style shifts, aiming to learn robust liveness representations. Furthermore, acknowledging the asymmetry between live and spoof samples, we introduce a novel contrastive loss, Asymmetric Augmented Instance Contrast. Extensive experiments on four public datasets demonstrate that our method achieves state-of-the-art performance under cross-dataset and limited source dataset scenarios. Additionally, our method has good scalability when expanding diversity of identities. The codes will be released soon.

The great advancements of generative adversarial networks and face recognition models in computer vision have made it possible to swap identities on images from single sources. Although a lot of studies seems to have proposed almost satisfactory solutions, we notice previous methods still suffer from an identity-attribute entanglement that causes undesired attributes swapping because widely used identity encoders, eg, ArcFace, have some crucial attribute biases owing to their pretraining on face recognition tasks. To address this issue, we design BlendFace, a novel identity encoder for face-swapping. The key idea behind BlendFace is training face recognition models on blended images whose attributes are replaced with those of another mitigates inter-personal biases such as hairsyles. BlendFace feeds disentangled identity features into generators and guides generators properly as an identity loss function. Extensive experiments demonstrate that BlendFace improves the identity-attribute disentanglement in face-swapping models, maintaining a comparable quantitative performance to previous methods.

Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages is the lack of parallel datasets that align natural language with formal language proofs. To address this challenge, this paper introduces a novel framework for translating the Mathlib4 corpus (a unified library of mathematics in formal language Lean 4) into natural language. Building upon this, we employ a dual augmentation strategy that combines tactic-based and informal-based approaches, leveraging the Lean-jixia system, a Lean 4 analyzer. We present the results of this pipeline on Mathlib4 as Herald (Hierarchy and Retrieval-based Translated Lean Dataset). We also propose the Herald Translator, which is fine-tuned on Herald. Herald translator achieves a 93.2% accuracy (Pass@128) on formalizing statements in the miniF2F-test and a 22.5% accuracy on our internal graduate-level textbook dataset, outperforming InternLM2-Math-Plus-7B (74.0% and 7.5%) and TheoremLlama (50.1% and 4.0%). Furthermore, we propose a section-level translation framework for real-world applications. As a direct application of Herald translator, we have successfully translated a template section in the Stack project, marking a notable progress in the automatic formalization of graduate-level mathematical literature. Our model, along with the datasets, will be open-sourced to the public soon.

Geometry problem solving is a well-recognized testbed for evaluating the high-level multi-modal reasoning capability of deep models. In most existing works, two main geometry problems: calculation and proving, are usually treated as two specific tasks, hindering a deep model to unify its reasoning capability on multiple math tasks. However, in essence, these two tasks have similar problem representations and overlapped math knowledge which can improve the understanding and reasoning ability of a deep model on both two tasks. Therefore, we construct a large-scale Unified Geometry problem benchmark, UniGeo, which contains 4,998 calculation problems and 9,543 proving problems. Each proving problem is annotated with a multi-step proof with reasons and mathematical expressions. The proof can be easily reformulated as a proving sequence that shares the same formats with the annotated program sequence for calculation problems. Naturally, we also present a unified multi-task Geometric Transformer framework, Geoformer, to tackle calculation and proving problems simultaneously in the form of sequence generation, which finally shows the reasoning ability can be improved on both two tasks by unifying formulation. Furthermore, we propose a Mathematical Expression Pretraining (MEP) method that aims to predict the mathematical expressions in the problem solution, thus improving the Geoformer model. Experiments on the UniGeo demonstrate that our proposed Geoformer obtains state-of-the-art performance by outperforming task-specific model NGS with over 5.6% and 3.2% accuracies on calculation and proving problems, respectively.

Normalization layers and activation functions are fundamental components in deep networks and typically co-locate with each other. Here we propose to design them using an automated approach. Instead of designing them separately, we unify them into a single tensor-to-tensor computation graph, and evolve its structure starting from basic mathematical functions. Examples of such mathematical functions are addition, multiplication and statistical moments. The use of low-level mathematical functions, in contrast to the use of high-level modules in mainstream NAS, leads to a highly sparse and large search space which can be challenging for search methods. To address the challenge, we develop efficient rejection protocols to quickly filter out candidate layers that do not work well. We also use multi-objective evolution to optimize each layer's performance across many architectures to prevent overfitting. Our method leads to the discovery of EvoNorms, a set of new normalization-activation layers with novel, and sometimes surprising structures that go beyond existing design patterns. For example, some EvoNorms do not assume that normalization and activation functions must be applied sequentially, nor need to center the feature maps, nor require explicit activation functions. Our experiments show that EvoNorms work well on image classification models including ResNets, MobileNets and EfficientNets but also transfer well to Mask R-CNN with FPN/SpineNet for instance segmentation and to BigGAN for image synthesis, outperforming BatchNorm and GroupNorm based layers in many cases.

Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are able to increase accuracy on MATH, our results show that accuracy remains relatively low, even with enormous Transformer models. Moreover, we find that simply increasing budgets and model parameter counts will be impractical for achieving strong mathematical reasoning if scaling trends continue. While scaling Transformers is automatically solving most other text-based tasks, scaling is not currently solving MATH. To have more traction on mathematical problem solving we will likely need new algorithmic advancements from the broader research community.

The ability to synthesize personalized group photos and specify the positions of each identity offers immense creative potential. While such imagery can be visually appealing, it presents significant challenges for existing technologies. A persistent issue is identity (ID) leakage, where injected facial features interfere with one another, resulting in low face resemblance, incorrect positioning, and visual artifacts. Existing methods suffer from limitations such as the reliance on segmentation models, increased runtime, or a high probability of ID leakage. To address these challenges, we propose ID-Patch, a novel method that provides robust association between identities and 2D positions. Our approach generates an ID patch and ID embeddings from the same facial features: the ID patch is positioned on the conditional image for precise spatial control, while the ID embeddings integrate with text embeddings to ensure high resemblance. Experimental results demonstrate that ID-Patch surpasses baseline methods across metrics, such as face ID resemblance, ID-position association accuracy, and generation efficiency. Project Page is: https://byteaigc.github.io/ID-Patch/

Text-guided image-to-image diffusion models excel in translating images based on textual prompts, allowing for precise and creative visual modifications. However, such a powerful technique can be misused for spreading misinformation, infringing on copyrights, and evading content tracing. This motivates us to introduce the task of origin IDentification for text-guided Image-to-image Diffusion models (ID^2), aiming to retrieve the original image of a given translated query. A straightforward solution to ID^2 involves training a specialized deep embedding model to extract and compare features from both query and reference images. However, due to visual discrepancy across generations produced by different diffusion models, this similarity-based approach fails when training on images from one model and testing on those from another, limiting its effectiveness in real-world applications. To solve this challenge of the proposed ID^2 task, we contribute the first dataset and a theoretically guaranteed method, both emphasizing generalizability. The curated dataset, OriPID, contains abundant Origins and guided Prompts, which can be used to train and test potential IDentification models across various diffusion models. In the method section, we first prove the existence of a linear transformation that minimizes the distance between the pre-trained Variational Autoencoder (VAE) embeddings of generated samples and their origins. Subsequently, it is demonstrated that such a simple linear transformation can be generalized across different diffusion models. Experimental results show that the proposed method achieves satisfying generalization performance, significantly surpassing similarity-based methods (+31.6% mAP), even those with generalization designs.

There exist a number of well known multiplicative generating functions for series of Schur functions. Amongst these are some related to the dual Cauchy identity whose expansion coefficients are rather simple, and in some cases periodic in parameters specifying the Schur functions. More recently similar identities have been found involving expansions in terms of characters of the symplectic group. Here these results are extended and generalised to all classical Lie groups. This is done through the derivation of explicit recurrence relations for the expansion coefficients based on the action of the Weyl groups of both the symplectic and orthogonal groups. Copious results are tabulated in the form of explicit values of the expansion coefficients as functions of highest weight parameters. An alternative approach is then based on dual pairs of symplectic and/or orthogonal groups. A byproduct of this approach is that expansions in terms of spin orthogonal group characters can always be recovered from non-spin cases.

We propose a novel framework for ID-preserving generation using a multi-modal encoding strategy rather than injecting identity features via adapters into pre-trained models. Our method treats identity and text as a unified conditioning input. To achieve this, we introduce FaceCLIP, a multi-modal encoder that learns a joint embedding space for both identity and textual semantics. Given a reference face and a text prompt, FaceCLIP produces a unified representation that encodes both identity and text, which conditions a base diffusion model to generate images that are identity-consistent and text-aligned. We also present a multi-modal alignment algorithm to train FaceCLIP, using a loss that aligns its joint representation with face, text, and image embedding spaces. We then build FaceCLIP-SDXL, an ID-preserving image synthesis pipeline by integrating FaceCLIP with Stable Diffusion XL (SDXL). Compared to prior methods, FaceCLIP-SDXL enables photorealistic portrait generation with better identity preservation and textual relevance. Extensive experiments demonstrate its quantitative and qualitative superiority.

We present Concat-ID, a unified framework for identity-preserving video generation. Concat-ID employs Variational Autoencoders to extract image features, which are concatenated with video latents along the sequence dimension, leveraging solely 3D self-attention mechanisms without the need for additional modules. A novel cross-video pairing strategy and a multi-stage training regimen are introduced to balance identity consistency and facial editability while enhancing video naturalness. Extensive experiments demonstrate Concat-ID's superiority over existing methods in both single and multi-identity generation, as well as its seamless scalability to multi-subject scenarios, including virtual try-on and background-controllable generation. Concat-ID establishes a new benchmark for identity-preserving video synthesis, providing a versatile and scalable solution for a wide range of applications.

Formulas involving fundamental mathematical constants had a great impact on various fields of science and mathematics, for example aiding in proofs of irrationality of constants. However, the discovery of such formulas has historically remained scarce, often perceived as an act of mathematical genius by great mathematicians such as Ramanujan, Euler, and Gauss. Recent efforts to automate the discovery of formulas for mathematical constants, such as the Ramanujan Machine project, relied on exhaustive search. Despite several successful discoveries, exhaustive search remains limited by the space of options that can be covered and by the need for vast amounts of computational resources. Here we propose a fundamentally different method to search for conjectures on mathematical constants: through analysis of integer sequences. We introduce the Enumerated Signed-continued-fraction Massey Approve (ESMA) algorithm, which builds on the Berlekamp-Massey algorithm to identify patterns in integer sequences that represent mathematical constants. The ESMA algorithm found various known formulas for e, e^2, tan(1), and ratios of values of Bessel functions. The algorithm further discovered a large number of new conjectures for these constants, some providing simpler representations and some providing faster numerical convergence than the corresponding simple continued fractions. Along with the algorithm, we present mathematical tools for manipulating continued fractions. These connections enable us to characterize what space of constants can be found by ESMA and quantify its algorithmic advantage in certain scenarios. Altogether, this work continues in the development of augmenting mathematical intuition by computer algorithms, to help reveal mathematical structures and accelerate mathematical research.

We introduce ProofNet, a benchmark for autoformalization and formal proving of undergraduate-level mathematics. The ProofNet benchmarks consists of 371 examples, each consisting of a formal theorem statement in Lean 3, a natural language theorem statement, and a natural language proof. The problems are primarily drawn from popular undergraduate pure mathematics textbooks and cover topics such as real and complex analysis, linear algebra, abstract algebra, and topology. We intend for ProofNet to be a challenging benchmark that will drive progress in autoformalization and automatic theorem proving. We report baseline results on statement autoformalization via in-context learning. Moreover, we introduce two novel statement autoformalization methods: prompt retrieval and distilled backtranslation.

Recent advancements in image customization exhibit a wide range of application prospects due to stronger customization capabilities. However, since we humans are more sensitive to faces, a significant challenge remains in preserving consistent identity while avoiding identity confusion with multi-reference images, limiting the identity scalability of customization models. To address this, we present UMO, a Unified Multi-identity Optimization framework, designed to maintain high-fidelity identity preservation and alleviate identity confusion with scalability. With "multi-to-multi matching" paradigm, UMO reformulates multi-identity generation as a global assignment optimization problem and unleashes multi-identity consistency for existing image customization methods generally through reinforcement learning on diffusion models. To facilitate the training of UMO, we develop a scalable customization dataset with multi-reference images, consisting of both synthesised and real parts. Additionally, we propose a new metric to measure identity confusion. Extensive experiments demonstrate that UMO not only improves identity consistency significantly, but also reduces identity confusion on several image customization methods, setting a new state-of-the-art among open-source methods along the dimension of identity preserving. Code and model: https://github.com/bytedance/UMO

How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the robustness of models towards pre-defined continuous transformation groups. Through the use of specially-derived canonical coordinate systems, ETs incorporate functions that are equivariant by construction with respect to these transformations. We show empirically that ETs can be flexibly composed to improve model robustness towards more complicated transformation groups in several parameters. On a real-world image classification task, ETs improve the sample efficiency of ResNet classifiers, achieving relative improvements in error rate of up to 15% in the limited data regime while increasing model parameter count by less than 1%.

Large language models (LLMs) are rapidly approaching the level of proficiency in university-level symbolic mathematics required for applications in advanced science and technology. However, existing benchmarks fall short in assessing the core skills of LLMs in symbolic mathematics-such as integration, differential equations, and algebraic simplification. To address this gap, we introduce ASyMOB, a novel assessment framework focused exclusively on symbolic manipulation, featuring 17,092 unique math challenges, organized by similarity and complexity. ASyMOB enables analysis of LLM generalization capabilities by comparing performance in problems that differ by simple numerical or symbolic `perturbations'. Evaluated LLMs exhibit substantial degradation in performance for all perturbation types (up to -70.3%), suggesting reliance on memorized patterns rather than deeper understanding of symbolic math, even among models achieving high baseline accuracy. Comparing LLM performance to computer algebra systems, we identify examples where they fail while LLMs succeed, as well as problems solved only by combining both approaches. Models capable of integrated code execution yielded higher accuracy compared to their performance without code, particularly stabilizing weaker models (up to +33.1% for certain perturbation types). Notably, the most advanced models (o4-mini, Gemini 2.5 Flash) demonstrate not only high symbolic math proficiency (scoring 96.8% and 97.6% on the unperturbed set), but also remarkable robustness against perturbations, (-21.7% and -21.2% vs. average -50.4% for the other models). This may indicate a recent "phase transition" in the generalization capabilities of frontier LLMs. It remains to be seen whether the path forward lies in deeper integration with sophisticated external tools, or in developing models so capable that symbolic math systems like CAS become unnecessary.

Currently, prominent Transformer architectures applied on graphs and meshes for shape analysis tasks employ traditional attention layers that heavily utilize spectral features requiring costly eigenvalue decomposition-based methods. To encode the mesh structure, these methods derive positional embeddings, that heavily rely on eigenvalue decomposition based operations, e.g. on the Laplacian matrix, or on heat-kernel signatures, which are then concatenated to the input features. This paper proposes a novel approach inspired by the explicit construction of the Hodge Laplacian operator in Discrete Exterior Calculus as a product of discrete Hodge operators and exterior derivatives, i.e. (L := star_0^{-1} d_0^T star_1 d_0). We adjust the Transformer architecture in a novel deep learning layer that utilizes the multi-head attention mechanism to approximate Hodge matrices star_0, star_1 and star_2 and learn families of discrete operators L that act on mesh vertices, edges and faces. Our approach results in a computationally-efficient architecture that achieves comparable performance in mesh segmentation and classification tasks, through a direct learning framework, while eliminating the need for costly eigenvalue decomposition operations or complex preprocessing operations.

Identity document (ID) image analysis has become essential for many online services, like bank account opening or insurance subscription. In recent years, much research has been conducted on subjects like document localization, text recognition and fraud detection, to achieve a level of accuracy reliable enough to automatize identity verification. However, there are only a few available datasets to benchmark ID analysis methods, mainly because of privacy restrictions, security requirements and legal reasons. In this paper, we present the DocXPand-25k dataset, which consists of 24,994 richly labeled IDs images, generated using custom-made vectorial templates representing nine fictitious ID designs, including four identity cards, two residence permits and three passports designs. These synthetic IDs feature artificially generated personal information (names, dates, identifiers, faces, barcodes, ...), and present a rich diversity in the visual layouts and textual contents. We collected about 5.8k diverse backgrounds coming from real-world photos, scans and screenshots of IDs to guarantee the variety of the backgrounds. The software we wrote to generate these images has been published (https://github.com/QuickSign/docxpand/) under the terms of the MIT license, and our dataset has been published (https://github.com/QuickSign/docxpand/releases/tag/v1.0.0) under the terms of the CC-BY-NC-SA 4.0 License.

Text-to-image (T2I) models have significantly advanced the development of artificial intelligence, enabling the generation of high-quality images in diverse contexts based on specific text prompts. However, existing T2I-based methods often struggle to accurately reproduce the appearance of individuals from a reference image and to create novel representations of those individuals in various settings. To address this, we leverage the pre-trained UNet from Stable Diffusion to incorporate the target face image directly into the generation process. Our approach diverges from prior methods that depend on fixed encoders or static face embeddings, which often fail to bridge encoding gaps. Instead, we capitalize on UNet's sophisticated encoding capabilities to process reference images across multiple scales. By innovatively altering the cross-attention layers of the UNet, we effectively fuse individual identities into the generative process. This strategic integration of facial features across various scales not only enhances the robustness and consistency of the generated images but also facilitates efficient multi-reference and multi-identity generation. Our method sets a new benchmark in identity-preserving image generation, delivering state-of-the-art results in similarity metrics while maintaining prompt alignment.

Recent 3D face reconstruction methods have made remarkable advancements, yet there remain huge challenges in monocular high-quality facial reflectance reconstruction. Existing methods rely on a large amount of light-stage captured data to learn facial reflectance models. However, the lack of subject diversity poses challenges in achieving good generalization and widespread applicability. In this paper, we learn the reflectance prior in image space rather than UV space and present a framework named ID2Reflectance. Our framework can directly estimate the reflectance maps of a single image while using limited reflectance data for training. Our key insight is that reflectance data shares facial structures with RGB faces, which enables obtaining expressive facial prior from inexpensive RGB data thus reducing the dependency on reflectance data. We first learn a high-quality prior for facial reflectance. Specifically, we pretrain multi-domain facial feature codebooks and design a codebook fusion method to align the reflectance and RGB domains. Then, we propose an identity-conditioned swapping module that injects facial identity from the target image into the pre-trained autoencoder to modify the identity of the source reflectance image. Finally, we stitch multi-view swapped reflectance images to obtain renderable assets. Extensive experiments demonstrate that our method exhibits excellent generalization capability and achieves state-of-the-art facial reflectance reconstruction results for in-the-wild faces. Our project page is https://xingyuren.github.io/id2reflectance/.

Advancements in LLMs have significantly expanded their capabilities across various domains. However, mathematical reasoning remains a challenging area, prompting the development of math-specific LLMs. These models typically follow a two-stage training paradigm: pre-training with math-related corpora and post-training with problem datasets for SFT. Despite these efforts, the improvements in mathematical reasoning achieved through continued pre-training (CPT) are often less significant compared to those obtained via SFT. This study addresses this discrepancy by exploring alternative strategies during the pre-training phase, focusing on the use of problem-solving data over general mathematical corpora. We investigate three primary research questions: (1) Can problem-solving data enhance the model's mathematical reasoning capabilities more effectively than general mathematical corpora during CPT? (2) Are synthetic data from the same source equally effective, and which synthesis methods are most efficient? (3) How do the capabilities developed from the same problem-solving data differ between the CPT and SFT stages, and what factors contribute to these differences? Our findings indicate that problem-solving data significantly enhances the model's mathematical capabilities compared to general mathematical corpora. We also identify effective data synthesis methods, demonstrating that the tutorship amplification synthesis method achieves the best performance. Furthermore, while SFT facilitates instruction-following abilities, it underperforms compared to CPT with the same data, which can be partially attributed to its poor learning capacity for hard multi-step problem-solving data. These insights provide valuable guidance for optimizing the mathematical reasoning capabilities of LLMs, culminating in our development of a powerful mathematical base model called JiuZhang-8B.

Lara is a key-value algebra that aims at unifying linear and relational algebra with three types of operation abstraction. The study of Lara's expressive ability reports that it can represent relational algebra and most linear algebra operations. However, several essential computations, such as matrix inversion and determinant, cannot be expressed in Lara. Lara cannot represent global and iterative computation, either. This article proposes IterLara, extending Lara with iterative operators, to provide an algebraic model that unifies operations in general-purpose computing, like big data, AI, scientific computing, and database. We study the expressive ability of Lara and IterLara and prove that IterLara with aggregation functions can represent matrix inversion, determinant. Besides, we demonstrate that IterLara with no limitation of function utility is Turing complete. We also propose the Operation Count (OP) as a metric of computation amount for IterLara and ensure that the OP metric is in accordance with the existing computation metrics.

Large language models (LLMs) such as ChatGPT have received immense interest for their general-purpose language understanding and, in particular, their ability to generate high-quality text or computer code. For many professions, LLMs represent an invaluable tool that can speed up and improve the quality of work. In this note, we discuss to what extent they can aid professional mathematicians. We first provide a mathematical description of the transformer model used in all modern language models. Based on recent studies, we then outline best practices and potential issues and report on the mathematical abilities of language models. Finally, we shed light on the potential of LMMs to change how mathematicians work.

Personalized text-to-image generation has emerged as a powerful and sought-after tool, empowering users to create customized images based on their specific concepts and prompts. However, existing approaches to personalization encounter multiple challenges, including long tuning times, large storage requirements, the necessity for multiple input images per identity, and limitations in preserving identity and editability. To address these obstacles, we present PhotoVerse, an innovative methodology that incorporates a dual-branch conditioning mechanism in both text and image domains, providing effective control over the image generation process. Furthermore, we introduce facial identity loss as a novel component to enhance the preservation of identity during training. Remarkably, our proposed PhotoVerse eliminates the need for test time tuning and relies solely on a single facial photo of the target identity, significantly reducing the resource cost associated with image generation. After a single training phase, our approach enables generating high-quality images within only a few seconds. Moreover, our method can produce diverse images that encompass various scenes and styles. The extensive evaluation demonstrates the superior performance of our approach, which achieves the dual objectives of preserving identity and facilitating editability. Project page: https://photoverse2d.github.io/

We present Magic Mirror, a framework for generating identity-preserved videos with cinematic-level quality and dynamic motion. While recent advances in video diffusion models have shown impressive capabilities in text-to-video generation, maintaining consistent identity while producing natural motion remains challenging. Previous methods either require person-specific fine-tuning or struggle to balance identity preservation with motion diversity. Built upon Video Diffusion Transformers, our method introduces three key components: (1) a dual-branch facial feature extractor that captures both identity and structural features, (2) a lightweight cross-modal adapter with Conditioned Adaptive Normalization for efficient identity integration, and (3) a two-stage training strategy combining synthetic identity pairs with video data. Extensive experiments demonstrate that Magic Mirror effectively balances identity consistency with natural motion, outperforming existing methods across multiple metrics while requiring minimal parameters added. The code and model will be made publicly available at: https://github.com/dvlab-research/MagicMirror/

Automatic black-and-white image sequence colorization while preserving character and object identity (ID) is a complex task with significant market demand, such as in cartoon or comic series colorization. Despite advancements in visual colorization using large-scale generative models like diffusion models, challenges with controllability and identity consistency persist, making current solutions unsuitable for industrial application.To address this, we propose ColorFlow, a three-stage diffusion-based framework tailored for image sequence colorization in industrial applications. Unlike existing methods that require per-ID finetuning or explicit ID embedding extraction, we propose a novel robust and generalizable Retrieval Augmented Colorization pipeline for colorizing images with relevant color references. Our pipeline also features a dual-branch design: one branch for color identity extraction and the other for colorization, leveraging the strengths of diffusion models. We utilize the self-attention mechanism in diffusion models for strong in-context learning and color identity matching. To evaluate our model, we introduce ColorFlow-Bench, a comprehensive benchmark for reference-based colorization. Results show that ColorFlow outperforms existing models across multiple metrics, setting a new standard in sequential image colorization and potentially benefiting the art industry. We release our codes and models on our project page: https://zhuang2002.github.io/ColorFlow/.

Understanding sentences that contain mathematical expressions in text form poses significant challenges. To address this, the importance of converting these expressions into formula images has been highlighted. For instance, the expression ``x equals minus b plus or minus the square root of b squared minus four a c, all over two a'' is more readily comprehensible when displayed as an image x = -b pm sqrt{b^2 - 4ac}{2a}. To develop a text-to-image conversion system, we can break down the process into text-to-LaTeX and LaTeX-to-image conversions, with the latter being managed with by existing various LaTeX engines. However, the former approach has been notably hindered by the severe scarcity of text-to-LaTeX paired data, presenting a significant challenge in the field.In this context, we introduce MathBridge, the first extensive dataset for translating mathematical spoken English into LaTeX, which aims to establish a robust baseline for future research in text-to-LaTeX translation. MathBridge comprises approximately 23 million LaTeX formulas paired with corresponding spoken English expressions. Through comprehensive evaluations, including fine-tuning and testing with data, we discovered that MathBridge significantly enhances pre-trained language models' capabilities for text-to-LaTeX translation. Specifically, for the T5-large model, the sacreBLEU score increased from 4.77 to 46.8, demonstrating substantial enhancement. Our findings indicate the necessity for a new metric specifically for text-to-LaTeX conversion evaluation.

How can Transformers model and learn enumerative geometry? What is a robust procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work, we introduce a Transformer-based approach to computational enumerative geometry, specifically targeting the computation of psi-class intersection numbers on the moduli space of curves. By reformulating the problem as a continuous optimization task, we compute intersection numbers across a wide value range from 10^{-45} to 10^{45}. To capture the recursive nature inherent in these intersection numbers, we propose the Dynamic Range Activator (DRA), a new activation function that enhances the Transformer's ability to model recursive patterns and handle severe heteroscedasticity. Given precision requirements for computing the intersections, we quantify the uncertainty of the predictions using Conformal Prediction with a dynamic sliding window adaptive to the partitions of equivalent number of marked points. To the best of our knowledge, there has been no prior work on modeling recursive functions with such a high-variance and factorial growth. Beyond simply computing intersection numbers, we explore the enumerative "world-model" of Transformers. Our interpretability analysis reveals that the network is implicitly modeling the Virasoro constraints in a purely data-driven manner. Moreover, through abductive hypothesis testing, probing, and causal inference, we uncover evidence of an emergent internal representation of the the large-genus asymptotic of psi-class intersection numbers. These findings suggest that the network internalizes the parameters of the asymptotic closed-form and the polynomiality phenomenon of psi-class intersection numbers in a non-linear manner.

Autoformalization, the conversion of natural language mathematics into formal languages, offers significant potential for advancing mathematical reasoning. However, existing efforts are limited to formal languages with substantial online corpora and struggle to keep pace with rapidly evolving languages like Lean 4. To bridge this gap, we propose a new benchmark Formalization for Lean~4 (\name) designed to evaluate the autoformalization capabilities of large language models (LLMs). This benchmark encompasses a comprehensive assessment of questions, answers, formal statements, and proofs. Additionally, we introduce a Process-Supervised Verifier (PSV) model that leverages the precise feedback from Lean 4 compilers to enhance autoformalization. Our experiments demonstrate that the PSV method improves autoformalization, enabling higher accuracy using less filtered training data. Furthermore, when fine-tuned with data containing detailed process information, PSV can leverage the data more effectively, leading to more significant improvements in autoformalization for Lean 4. Our dataset and code are available at https://github.com/rookie-joe/PDA.

Advanced diffusion-based Text-to-Image (T2I) models, such as the Stable Diffusion Model, have made significant progress in generating diverse and high-quality images using text prompts alone. However, T2I models are unable to accurately map identities (IDs) when non-famous users require personalized image generation. The main problem is that existing T2I models do not learn the ID-image alignments of new users. The previous methods either failed to accurately fit the face region or lost the interactive generative ability with other existing concepts in T2I models (i.e., unable to generate other concepts described in given prompts such as scenes, actions, and facial attributes). In this paper, we focus on accurate and semantic-fidelity ID embedding into the Stable Diffusion Model for personalized generation. We address this challenge from two perspectives: face-wise region fitting, and semantic-fidelity token optimization. Specifically, we first visualize the attention overfit problem, and propose a face-wise attention loss to fit the face region instead of the whole target image. This key trick significantly enhances the ID accuracy and interactive generative ability with other existing concepts. Then, we optimize one ID representation as multiple per-stage tokens where each token contains two disentangled features. This expansion of the textual conditioning space enhances semantic-fidelity control. Extensive experiments validate that our results exhibit superior ID accuracy and manipulation ability compared to previous methods.

Evaluating the mathematical capability of Large Language Models (LLMs) is a critical yet challenging frontier. Existing benchmarks fall short, particularly for proof-centric problems, as manual creation is unscalable and costly, leaving the true mathematical abilities of LLMs largely unassessed. To overcome these barriers, we propose Proof2Hybrid, the first fully automated framework that synthesizes high-quality, proof-centric benchmarks from natural language mathematical corpora. The key novelty of our solution is Proof2X, a roadmap of converting mathematical proofs into various kinds of questions that are easy to verify. Instructed by this roadmap, we propose a new type of hybrid-formatted questions, named ``m-out-of-n multiple judge questions'', specifically designed to enable robust, automatic evaluation while being resilient to guessing and superficial pattern matching inherent in traditional formats. As a demonstration of our framework, we introduce AlgGeoTest, a benchmark for algebraic geometry--a frontier domain of modern mathematics--comprising 456 challenging items. Our extensive evaluations on state-of-the-art LLMs using AlgGeoTest reveal profound deficits in their comprehension of algebraic geometry, providing a more precise measure of their true mathematical capabilities. Our framework and benchmark pave the way for a new wave of in-depth research into the mathematical intelligence of AI systems.

Deep neural networks have achieved remarkable accomplishments in practice. The success of these networks hinges on effective initialization methods, which are vital for ensuring stable and rapid convergence during training. Recently, initialization methods that maintain identity transition within layers have shown good efficiency in network training. These techniques (e.g., Fixup) set specific weights to zero to achieve identity control. However, settings of remaining weight (e.g., Fixup uses random values to initialize non-zero weights) will affect the inductive bias that is achieved only by a zero weight, which may be harmful to training. Addressing this concern, we introduce fully identical initialization (IDInit), a novel method that preserves identity in both the main and sub-stem layers of residual networks. IDInit employs a padded identity-like matrix to overcome rank constraints in non-square weight matrices. Furthermore, we show the convergence problem of an identity matrix can be solved by stochastic gradient descent. Additionally, we enhance the universality of IDInit by processing higher-order weights and addressing dead neuron problems. IDInit is a straightforward yet effective initialization method, with improved convergence, stability, and performance across various settings, including large-scale datasets and deep models.

Recent advances in generative modeling have enabled the generation of high-quality synthetic data that is applicable in a variety of domains, including face recognition. Here, state-of-the-art generative models typically rely on conditioning and fine-tuning of powerful pretrained diffusion models to facilitate the synthesis of realistic images of a desired identity. Yet, these models often do not consider the identity of subjects during training, leading to poor consistency between generated and intended identities. In contrast, methods that employ identity-based training objectives tend to overfit on various aspects of the identity, and in turn, lower the diversity of images that can be generated. To address these issues, we present in this paper a novel generative diffusion-based framework, called ID-Booth. ID-Booth consists of a denoising network responsible for data generation, a variational auto-encoder for mapping images to and from a lower-dimensional latent space and a text encoder that allows for prompt-based control over the generation procedure. The framework utilizes a novel triplet identity training objective and enables identity-consistent image generation while retaining the synthesis capabilities of pretrained diffusion models. Experiments with a state-of-the-art latent diffusion model and diverse prompts reveal that our method facilitates better intra-identity consistency and inter-identity separability than competing methods, while achieving higher image diversity. In turn, the produced data allows for effective augmentation of small-scale datasets and training of better-performing recognition models in a privacy-preserving manner. The source code for the ID-Booth framework is publicly available at https://github.com/dariant/ID-Booth.

Identity-invariant facial expression recognition (FER) has been one of the challenging computer vision tasks. Since conventional FER schemes do not explicitly address the inter-identity variation of facial expressions, their neural network models still operate depending on facial identity. This paper proposes to quantify the inter-identity variation by utilizing pairs of similar expressions explored through a specific matching process. We formulate the identity matching process as an Optimal Transport (OT) problem. Specifically, to find pairs of similar expressions from different identities, we define the inter-feature similarity as a transportation cost. Then, optimal identity matching to find the optimal flow with minimum transportation cost is performed by Sinkhorn-Knopp iteration. The proposed matching method is not only easy to plug in to other models, but also requires only acceptable computational overhead. Extensive simulations prove that the proposed FER method improves the PCC/CCC performance by up to 10\% or more compared to the runner-up on wild datasets. The source code and software demo are available at https://github.com/kdhht2334/ELIM_FER.

Recent researches have proven that pre-training on large-scale person images extracted from internet videos is an effective way in learning better representations for person re-identification. However, these researches are mostly confined to pre-training at the instance-level or single-video tracklet-level. They ignore the identity-invariance in images of the same person across different videos, which is a key focus in person re-identification. To address this issue, we propose a Cross-video Identity-cOrrelating pre-traiNing (CION) framework. Defining a noise concept that comprehensively considers both intra-identity consistency and inter-identity discrimination, CION seeks the identity correlation from cross-video images by modeling it as a progressive multi-level denoising problem. Furthermore, an identity-guided self-distillation loss is proposed to implement better large-scale pre-training by mining the identity-invariance within person images. We conduct extensive experiments to verify the superiority of our CION in terms of efficiency and performance. CION achieves significantly leading performance with even fewer training samples. For example, compared with the previous state-of-the-art~ISR, CION with the same ResNet50-IBN achieves higher mAP of 93.3\% and 74.3\% on Market1501 and MSMT17, while only utilizing 8\% training samples. Finally, with CION demonstrating superior model-agnostic ability, we contribute a model zoo named ReIDZoo to meet diverse research and application needs in this field. It contains a series of CION pre-trained models with spanning structures and parameters, totaling 32 models with 10 different structures, including GhostNet, ConvNext, RepViT, FastViT and so on. The code and models will be made publicly available at https://github.com/Zplusdragon/CION_ReIDZoo.

We introduce MIGS (Multi-Identity Gaussian Splatting), a novel method that learns a single neural representation for multiple identities, using only monocular videos. Recent 3D Gaussian Splatting (3DGS) approaches for human avatars require per-identity optimization. However, learning a multi-identity representation presents advantages in robustly animating humans under arbitrary poses. We propose to construct a high-order tensor that combines all the learnable 3DGS parameters for all the training identities. By assuming a low-rank structure and factorizing the tensor, we model the complex rigid and non-rigid deformations of multiple subjects in a unified network, significantly reducing the total number of parameters. Our proposed approach leverages information from all the training identities, enabling robust animation under challenging unseen poses, outperforming existing approaches. We also demonstrate how it can be extended to learn unseen identities.

We study a class of Z^{d}-substitutive subshifts, including a large family of constant-length substitutions, and homomorphisms between them, i.e., factors modulo isomorphisms of Z^{d}. We prove that any measurable factor map and even any homomorphism associated to a matrix commuting with the expansion matrix, induces a continuous one. We also get strong restrictions on the normalizer group, proving that any endomorphism is invertible, the normalizer group is virtually generated by the shift action and the quotient of the normalizer group by the automorphisms is restricted by the digit tile of the substitution.

Natural language image-caption datasets, widely used for training Large Multimodal Models, mainly focus on natural scenarios and overlook the intricate details of mathematical figures that are critical for problem-solving, hindering the advancement of current LMMs in multimodal mathematical reasoning. To this end, we propose leveraging code as supervision for cross-modal alignment, since code inherently encodes all information needed to generate corresponding figures, establishing a precise connection between the two modalities. Specifically, we co-develop our image-to-code model and dataset with model-in-the-loop approach, resulting in an image-to-code model, FigCodifier and ImgCode-8.6M dataset, the largest image-code dataset to date. Furthermore, we utilize FigCodifier to synthesize novel mathematical figures and then construct MM-MathInstruct-3M, a high-quality multimodal math instruction fine-tuning dataset. Finally, we present MathCoder-VL, trained with ImgCode-8.6M for cross-modal alignment and subsequently fine-tuned on MM-MathInstruct-3M for multimodal math problem solving. Our model achieves a new open-source SOTA across all six metrics. Notably, it surpasses GPT-4o and Claude 3.5 Sonnet in the geometry problem-solving subset of MathVista, achieving improvements of 8.9% and 9.2%. The dataset and models will be released at https://github.com/mathllm/MathCoder.

We present Lynx, a high-fidelity model for personalized video synthesis from a single input image. Built on an open-source Diffusion Transformer (DiT) foundation model, Lynx introduces two lightweight adapters to ensure identity fidelity. The ID-adapter employs a Perceiver Resampler to convert ArcFace-derived facial embeddings into compact identity tokens for conditioning, while the Ref-adapter integrates dense VAE features from a frozen reference pathway, injecting fine-grained details across all transformer layers through cross-attention. These modules collectively enable robust identity preservation while maintaining temporal coherence and visual realism. Through evaluation on a curated benchmark of 40 subjects and 20 unbiased prompts, which yielded 800 test cases, Lynx has demonstrated superior face resemblance, competitive prompt following, and strong video quality, thereby advancing the state of personalized video generation.

This paper presents Arc2Face, an identity-conditioned face foundation model, which, given the ArcFace embedding of a person, can generate diverse photo-realistic images with an unparalleled degree of face similarity than existing models. Despite previous attempts to decode face recognition features into detailed images, we find that common high-resolution datasets (e.g. FFHQ) lack sufficient identities to reconstruct any subject. To that end, we meticulously upsample a significant portion of the WebFace42M database, the largest public dataset for face recognition (FR). Arc2Face builds upon a pretrained Stable Diffusion model, yet adapts it to the task of ID-to-face generation, conditioned solely on ID vectors. Deviating from recent works that combine ID with text embeddings for zero-shot personalization of text-to-image models, we emphasize on the compactness of FR features, which can fully capture the essence of the human face, as opposed to hand-crafted prompts. Crucially, text-augmented models struggle to decouple identity and text, usually necessitating some description of the given face to achieve satisfactory similarity. Arc2Face, however, only needs the discriminative features of ArcFace to guide the generation, offering a robust prior for a plethora of tasks where ID consistency is of paramount importance. As an example, we train a FR model on synthetic images from our model and achieve superior performance to existing synthetic datasets.

Person re-identification (ReID) aims to extract accurate identity representation features. However, during feature extraction, individual samples are inevitably affected by noise (background, occlusions, and model limitations). Considering that features from the same identity follow a normal distribution around identity centers after training, we propose a Training-Free Feature Centralization ReID framework (Pose2ID) by aggregating the same identity features to reduce individual noise and enhance the stability of identity representation, which preserves the feature's original distribution for following strategies such as re-ranking. Specifically, to obtain samples of the same identity, we introduce two components:Identity-Guided Pedestrian Generation: by leveraging identity features to guide the generation process, we obtain high-quality images with diverse poses, ensuring identity consistency even in complex scenarios such as infrared, and occlusion.Neighbor Feature Centralization: it explores each sample's potential positive samples from its neighborhood. Experiments demonstrate that our generative model exhibits strong generalization capabilities and maintains high identity consistency. With the Feature Centralization framework, we achieve impressive performance even with an ImageNet pre-trained model without ReID training, reaching mAP/Rank-1 of 52.81/78.92 on Market1501. Moreover, our method sets new state-of-the-art results across standard, cross-modality, and occluded ReID tasks, showcasing strong adaptability.

Autoformalization, which translates natural language mathematics into machine-verifiable formal statements, is critical for using formal mathematical reasoning to solve math problems stated in natural language. While Large Language Models can generate syntactically correct formal statements, they often fail to preserve the original problem's semantic intent. This limitation arises from the LLM approaches' treating autoformalization as a simplistic translation task which lacks mechanisms for self-reflection and iterative refinement that human experts naturally employ. To address these issues, we propose ReForm, a Reflective Autoformalization method that tightly integrates semantic consistency evaluation into the autoformalization process. This enables the model to iteratively generate formal statements, assess its semantic fidelity, and self-correct identified errors through progressive refinement. To effectively train this reflective model, we introduce Prospective Bounded Sequence Optimization (PBSO), which employs different rewards at different sequence positions to ensure that the model develops both accurate autoformalization and correct semantic validations, preventing superficial critiques that would undermine the purpose of reflection. Extensive experiments across four autoformalization benchmarks demonstrate that ReForm achieves an average improvement of 17.2 percentage points over the strongest baselines. To further ensure evaluation reliability, we introduce ConsistencyCheck, a benchmark of 859 expert-annotated items that not only validates LLMs as judges but also reveals that autoformalization is inherently difficult: even human experts produce semantic errors in up to 38.5% of cases.

Recent advances in diffusion models have enabled high-quality generation and manipulation of images guided by texts, as well as concept learning from images. However, naive applications of existing methods to editing tasks that require fine-grained control, e.g., face editing, often lead to suboptimal solutions with identity information and high-frequency details lost during the editing process, or irrelevant image regions altered due to entangled concepts. In this work, we propose S^2Edit, a novel method based on a pre-trained text-to-image diffusion model that enables personalized editing with precise semantic and spatial control. We first fine-tune our model to embed the identity information into a learnable text token. During fine-tuning, we disentangle the learned identity token from attributes to be edited by enforcing an orthogonality constraint in the textual feature space. To ensure that the identity token only affects regions of interest, we apply object masks to guide the cross-attention maps. At inference time, our method performs localized editing while faithfully preserving the original identity with semantically disentangled and spatially focused identity token learned. Extensive experiments demonstrate the superiority of S^2Edit over state-of-the-art methods both quantitatively and qualitatively. Additionally, we showcase several compositional image editing applications of S^2Edit such as makeup transfer.

Fully Homomorphic Encryption (FHE) is an encryption scheme that allows for computation to be performed directly on encrypted data, effectively closing the loop on secure and outsourced computing. Data is encrypted not only during rest and transit, but also during processing. However, FHE provides a limited instruction set: SIMD addition, SIMD multiplication, and cyclic rotation of 1-D vectors. This restriction makes performing multi-dimensional tensor operations challenging. Practitioners must pack these tensors into 1-D vectors and map tensor operations onto this one-dimensional layout rather than their traditional nested structure. And while prior systems have made significant strides in automating this process, they often hide critical packing decisions behind layers of abstraction, making debugging, optimizing, and building on top of these systems difficult. In this work, we approach multi-dimensional tensor operations in FHE through Einstein summation (einsum) notation. Einsum notation explicitly encodes dimensional structure and operations in its syntax, naturally exposing how tensors should be packed and transformed. We decompose einsum expressions into a fixed set of FHE-friendly operations. We implement our design and present EinHops, a minimalist system that factors einsum expressions into a fixed sequence of FHE operations. EinHops enables developers to perform encrypted tensor operations using FHE while maintaining full visibility into the underlying packing strategy. We evaluate EinHops on a range of tensor operations from a simple transpose to complex multi-dimensional contractions. We show that the explicit nature of einsum notation allows us to build an FHE tensor system that is simple, general, and interpretable. We open-source EinHops at the following repository: https://github.com/baahl-nyu/einhops.

We propose a flexible framework that deals with both singer conversion and singers vocal technique conversion. The proposed model is trained on non-parallel corpora, accommodates many-to-many conversion, and leverages recent advances of variational autoencoders. It employs separate encoders to learn disentangled latent representations of singer identity and vocal technique separately, with a joint decoder for reconstruction. Conversion is carried out by simple vector arithmetic in the learned latent spaces. Both a quantitative analysis as well as a visualization of the converted spectrograms show that our model is able to disentangle singer identity and vocal technique and successfully perform conversion of these attributes. To the best of our knowledge, this is the first work to jointly tackle conversion of singer identity and vocal technique based on a deep learning approach.

Current face anonymization techniques often depend on identity loss calculated by face recognition models, which can be inaccurate and unreliable. Additionally, many methods require supplementary data such as facial landmarks and masks to guide the synthesis process. In contrast, our approach uses diffusion models with only a reconstruction loss, eliminating the need for facial landmarks or masks while still producing images with intricate, fine-grained details. We validated our results on two public benchmarks through both quantitative and qualitative evaluations. Our model achieves state-of-the-art performance in three key areas: identity anonymization, facial attribute preservation, and image quality. Beyond its primary function of anonymization, our model can also perform face swapping tasks by incorporating an additional facial image as input, demonstrating its versatility and potential for diverse applications. Our code and models are available at https://github.com/hanweikung/face_anon_simple .

In an unbounded plane, straight lines are used extensively for mathematical analysis. They are tools of convenience. However, those with high slope values become unbounded at a faster rate than the independent variable. So, straight lines, in this work, are made to be bounded by introducing a parametric nonlinear term that is positive. The straight lines are transformed into bounded nonlinear curves that become unbounded at a much slower rate than the independent variable. This transforming equation can be expressed as a continued fraction of straight lines. The continued fraction is real-valued and converges to the solutions of the transforming equation. Following Euler's method, the continued fraction has been reduced into an infinite series. The usefulness of the bounding nature of continued fraction is demonstrated by solving the problem of image classification. Parameters estimated on the Fashion-MNIST dataset of greyscale images using continued fraction of regression lines have less variance, converge quickly and are more accurate than the linear counterpart. Moreover, this multi-dimensional parametric estimation problem can be expressed on xy- plane using the parameters of the continued fraction and patterns emerge on planar plots.

Medical imaging is critical for diagnostics, but clinical adoption of advanced AI-driven imaging faces challenges due to patient variability, image artifacts, and limited model generalization. While deep learning has transformed image analysis, 3D medical imaging still suffers from data scarcity and inconsistencies due to acquisition protocols, scanner differences, and patient motion. Traditional augmentation uses a single pipeline for all transformations, disregarding the unique traits of each augmentation and struggling with large data volumes. To address these challenges, we propose a Multi-encoder Augmentation-Aware Learning (MEAL) framework that leverages four distinct augmentation variants processed through dedicated encoders. Three fusion strategies such as concatenation (CC), fusion layer (FL), and adaptive controller block (BD) are integrated to build multi-encoder models that combine augmentation-specific features before decoding. MEAL-BD uniquely preserves augmentation-aware representations, enabling robust, protocol-invariant feature learning. As demonstrated in a Computed Tomography (CT)-to-T1-weighted Magnetic Resonance Imaging (MRI) translation study, MEAL-BD consistently achieved the best performance on both unseen- and predefined-test data. On both geometric transformations (like rotations and flips) and non-augmented inputs, MEAL-BD outperformed other competing methods, achieving higher mean peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) scores. These results establish MEAL as a reliable framework for preserving structural fidelity and generalizing across clinically relevant variability. By reframing augmentation as a source of diverse, generalizable features, MEAL supports robust, protocol-invariant learning, advancing clinically reliable medical imaging solutions.

Large Language Models (LLMs) have recently achieved remarkable progress in mathematical reasoning. To enable such capabilities, many existing works distill strong reasoning models into long chains of thought or design algorithms to construct high-quality math QA data for training. However, these efforts primarily focus on generating correct reasoning paths and answers, while largely overlooking the validity of the questions themselves. In this work, we propose Math Question Verification (MathQ-Verify), a novel five-stage pipeline designed to rigorously filter ill-posed or under-specified math problems. MathQ-Verify first performs format-level validation to remove redundant instructions and ensure that each question is syntactically well-formed. It then formalizes each question, decomposes it into atomic conditions, and verifies them against mathematical definitions. Next, it detects logical contradictions among these conditions, followed by a goal-oriented completeness check to ensure the question provides sufficient information for solving. To evaluate this task, we use existing benchmarks along with an additional dataset we construct, containing 2,147 math questions with diverse error types, each manually double-validated. Experiments show that MathQ-Verify achieves state-of-the-art performance across multiple benchmarks, improving the F1 score by up to 25 percentage points over the direct verification baseline. It further attains approximately 90% precision and 63% recall through a lightweight model voting scheme. MathQ-Verify offers a scalable and accurate solution for curating reliable mathematical datasets, reducing label noise and avoiding unnecessary computation on invalid questions. Our code and data are available at https://github.com/scuuy/MathQ-Verify.

The advancement in generative AI could be boosted with more accessible mathematics. Beyond human-AI chat, large language models (LLMs) are emerging in programming, algorithm discovery, and theorem proving, yet their genomics application is limited. This project introduces Math Agents and mathematical embedding as fresh entries to the "Moore's Law of Mathematics", using a GPT-based workflow to convert equations from literature into LaTeX and Python formats. While many digital equation representations exist, there's a lack of automated large-scale evaluation tools. LLMs are pivotal as linguistic user interfaces, providing natural language access for human-AI chat and formal languages for large-scale AI-assisted computational infrastructure. Given the infinite formal possibility spaces, Math Agents, which interact with math, could potentially shift us from "big data" to "big math". Math, unlike the more flexible natural language, has properties subject to proof, enabling its use beyond traditional applications like high-validation math-certified icons for AI alignment aims. This project aims to use Math Agents and mathematical embeddings to address the ageing issue in information systems biology by applying multiscalar physics mathematics to disease models and genomic data. Generative AI with episodic memory could help analyse causal relations in longitudinal health records, using SIR Precision Health models. Genomic data is suggested for addressing the unsolved Alzheimer's disease problem.

Leveraging Stable Diffusion for the generation of personalized portraits has emerged as a powerful and noteworthy tool, enabling users to create high-fidelity, custom character avatars based on their specific prompts. However, existing personalization methods face challenges, including test-time fine-tuning, the requirement of multiple input images, low preservation of identity, and limited diversity in generated outcomes. To overcome these challenges, we introduce IDAdapter, a tuning-free approach that enhances the diversity and identity preservation in personalized image generation from a single face image. IDAdapter integrates a personalized concept into the generation process through a combination of textual and visual injections and a face identity loss. During the training phase, we incorporate mixed features from multiple reference images of a specific identity to enrich identity-related content details, guiding the model to generate images with more diverse styles, expressions, and angles compared to previous works. Extensive evaluations demonstrate the effectiveness of our method, achieving both diversity and identity fidelity in generated images.

Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet demand for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core "skills" from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an "out of distribution" task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH^2 - a dataset of higher-quality math questions, as evidenced by: (a) Lower performance of all models on MATH^2 than on MATH (b) Higher performance on MATH when using MATH^2 questions as in-context examples. Although focused on mathematics, our methodology seems applicable to other domains requiring structured reasoning, and potentially as a component of scalable oversight. Also of interest is a striking relationship observed between models' performance on the new dataset: the success rate on MATH^2 is the square on MATH, suggesting that successfully solving the question in MATH^2 requires a nontrivial combination of two distinct math skills.

Large Language Models (LLMs) have shown impressive progress in mathematical reasoning. While data augmentation is promising to enhance mathematical problem-solving ability, current approaches are predominantly limited to instance-level modifications-such as rephrasing or generating syntactic variations-which fail to capture and leverage the intrinsic relational structures inherent in mathematical knowledge. Inspired by human learning processes, where mathematical proficiency develops through systematic exposure to interconnected concepts, we introduce MathFusion, a novel framework that enhances mathematical reasoning through cross-problem instruction synthesis. MathFusion implements this through three fusion strategies: (1) sequential fusion, which chains related problems to model solution dependencies; (2) parallel fusion, which combines analogous problems to reinforce conceptual understanding; and (3) conditional fusion, which creates context-aware selective problems to enhance reasoning flexibility. By applying these strategies, we generate a new dataset, MathFusionQA, followed by fine-tuning models (DeepSeekMath-7B, Mistral-7B, Llama3-8B) on it. Experimental results demonstrate that MathFusion achieves substantial improvements in mathematical reasoning while maintaining high data efficiency, boosting performance by 18.0 points in accuracy across diverse benchmarks while requiring only 45K additional synthetic instructions, representing a substantial improvement over traditional single-instruction approaches. Our datasets, models, and code are publicly available at https://github.com/QizhiPei/mathfusion.

Recent advancements in video generation have significantly impacted various downstream applications, particularly in identity-preserving video generation (IPT2V). However, existing methods struggle with "copy-paste" artifacts and low similarity issues, primarily due to their reliance on low-level facial image information. This dependence can result in rigid facial appearances and artifacts reflecting irrelevant details. To address these challenges, we propose EchoVideo, which employs two key strategies: (1) an Identity Image-Text Fusion Module (IITF) that integrates high-level semantic features from text, capturing clean facial identity representations while discarding occlusions, poses, and lighting variations to avoid the introduction of artifacts; (2) a two-stage training strategy, incorporating a stochastic method in the second phase to randomly utilize shallow facial information. The objective is to balance the enhancements in fidelity provided by shallow features while mitigating excessive reliance on them. This strategy encourages the model to utilize high-level features during training, ultimately fostering a more robust representation of facial identities. EchoVideo effectively preserves facial identities and maintains full-body integrity. Extensive experiments demonstrate that it achieves excellent results in generating high-quality, controllability and fidelity videos.

Identity-consistent generation has become an important focus in text-to-image research, with recent models achieving notable success in producing images aligned with a reference identity. Yet, the scarcity of large-scale paired datasets containing multiple images of the same individual forces most approaches to adopt reconstruction-based training. This reliance often leads to a failure mode we term copy-paste, where the model directly replicates the reference face rather than preserving identity across natural variations in pose, expression, or lighting. Such over-similarity undermines controllability and limits the expressive power of generation. To address these limitations, we (1) construct a large-scale paired dataset MultiID-2M, tailored for multi-person scenarios, providing diverse references for each identity; (2) introduce a benchmark that quantifies both copy-paste artifacts and the trade-off between identity fidelity and variation; and (3) propose a novel training paradigm with a contrastive identity loss that leverages paired data to balance fidelity with diversity. These contributions culminate in WithAnyone, a diffusion-based model that effectively mitigates copy-paste while preserving high identity similarity. Extensive qualitative and quantitative experiments demonstrate that WithAnyone significantly reduces copy-paste artifacts, improves controllability over pose and expression, and maintains strong perceptual quality. User studies further validate that our method achieves high identity fidelity while enabling expressive controllable generation.

Person re-identification (re-id), the process of matching pedestrian images across different camera views, is an important task in visual surveillance. Substantial development of re-id has recently been observed, and the majority of existing models are largely dependent on color appearance and assume that pedestrians do not change their clothes across camera views. This limitation, however, can be an issue for re-id when tracking a person at different places and at different time if that person (e.g., a criminal suspect) changes his/her clothes, causing most existing methods to fail, since they are heavily relying on color appearance and thus they are inclined to match a person to another person wearing similar clothes. In this work, we call the person re-id under clothing change the "cross-clothes person re-id". In particular, we consider the case when a person only changes his clothes moderately as a first attempt at solving this problem based on visible light images; that is we assume that a person wears clothes of a similar thickness, and thus the shape of a person would not change significantly when the weather does not change substantially within a short period of time. We perform cross-clothes person re-id based on a contour sketch of person image to take advantage of the shape of the human body instead of color information for extracting features that are robust to moderate clothing change. Due to the lack of a large-scale dataset for cross-clothes person re-id, we contribute a new dataset that consists of 33698 images from 221 identities. Our experiments illustrate the challenges of cross-clothes person re-id and demonstrate the effectiveness of our proposed method.

We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most major branches of modern mathematics -- from computationally intensive problems in number theory and real analysis to abstract questions in algebraic geometry and category theory. Solving a typical problem requires multiple hours of effort from a researcher in the relevant branch of mathematics, and for the upper end questions, multiple days. FrontierMath uses new, unpublished problems and automated verification to reliably evaluate models while minimizing risk of data contamination. Current state-of-the-art AI models solve under 2% of problems, revealing a vast gap between AI capabilities and the prowess of the mathematical community. As AI systems advance toward expert-level mathematical abilities, FrontierMath offers a rigorous testbed that quantifies their progress.

Generating high-fidelity human videos that match user-specified identities is important yet challenging in the field of generative AI. Existing methods often rely on an excessive number of training parameters and lack compatibility with other AIGC tools. In this paper, we propose Stand-In, a lightweight and plug-and-play framework for identity preservation in video generation. Specifically, we introduce a conditional image branch into the pre-trained video generation model. Identity control is achieved through restricted self-attentions with conditional position mapping, and can be learned quickly with only 2000 pairs. Despite incorporating and training just sim1\% additional parameters, our framework achieves excellent results in video quality and identity preservation, outperforming other full-parameter training methods. Moreover, our framework can be seamlessly integrated for other tasks, such as subject-driven video generation, pose-referenced video generation, stylization, and face swapping.

Linear transformation of the inputs alters the training performance of feed-forward networks that are otherwise equivalent. However, most linear transforms are viewed as a pre-processing operation separate from the actual training. Starting from equivalent networks, it is shown that pre-processing inputs using linear transformation are equivalent to multiplying the negative gradient matrix with an autocorrelation matrix per training iteration. Second order method is proposed to find the autocorrelation matrix that maximizes learning in a given iteration. When the autocorrelation matrix is diagonal, the method optimizes input gains. This optimal input gain (OIG) approach is used to improve two first-order two-stage training algorithms, namely back-propagation (BP) and hidden weight optimization (HWO), which alternately update the input weights and solve linear equations for output weights. Results show that the proposed OIG approach greatly enhances the performance of the first-order algorithms, often allowing them to rival the popular Levenberg-Marquardt approach with far less computation. It is shown that HWO is equivalent to BP with Whitening transformation applied to the inputs. HWO effectively combines Whitening transformation with learning. Thus, OIG improved HWO could be a significant building block to more complex deep learning architectures.

Recent advancements in personalized Text-to-Video (T2V) generation highlight the importance of integrating character-specific identities and actions. However, previous T2V models struggle with identity consistency and controllable motion dynamics, mainly due to limited fine-grained facial and action-based textual prompts, and datasets that overlook key human attributes and actions. To address these challenges, we propose MotionCharacter, an efficient and high-fidelity human video generation framework designed for identity preservation and fine-grained motion control. We introduce an ID-preserving module to maintain identity fidelity while allowing flexible attribute modifications, and further integrate ID-consistency and region-aware loss mechanisms, significantly enhancing identity consistency and detail fidelity. Additionally, our approach incorporates a motion control module that prioritizes action-related text while maintaining subject consistency, along with a dataset, Human-Motion, which utilizes large language models to generate detailed motion descriptions. For simplify user control during inference, we parameterize motion intensity through a single coefficient, allowing for easy adjustments. Extensive experiments highlight the effectiveness of MotionCharacter, demonstrating significant improvements in ID-preserving, high-quality video generation.

Accurate mathematical reasoning with Large Language Models (LLMs) is crucial in revolutionizing domains that heavily rely on such reasoning. However, LLMs often encounter difficulties in certain aspects of mathematical reasoning, leading to flawed reasoning and erroneous results. To mitigate these issues, we introduce a novel mechanism, the Chain of Self-Correction (CoSC), specifically designed to embed self-correction as an inherent ability in LLMs, enabling them to validate and rectify their own results. The CoSC mechanism operates through a sequence of self-correction stages. In each stage, the LLMs generate a program to address a given problem, execute this program using program-based tools to obtain an output, subsequently verify this output. Based on the verification, the LLMs either proceed to the next correction stage or finalize the answer. This iterative self-correction process allows the LLMs to refine their reasoning steps and improve the accuracy of their mathematical reasoning. To enable the CoSC mechanism at a low cost, we employ a two-phase finetuning approach. In the first phase, the LLMs are trained with a relatively small volume of seeding data generated from GPT-4, establishing an initial CoSC capability. In the second phase, the CoSC capability is further enhanced by training with a larger volume of self-generated data using the trained model in the first phase, without relying on the paid GPT-4. Our comprehensive experiments demonstrate that CoSC significantly improves performance on traditional mathematical datasets among existing open-source LLMs. Notably, our CoSC-Code-34B model achieved a 53.5% score on MATH, the most challenging mathematical reasoning dataset in the public domain, surpassing the performance of well-established models such as ChatGPT, GPT-4, and even multi-modal LLMs like GPT-4V, Gemini-1.0 Pro, and Gemini-1.0 Ultra.

AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines algorithmic solutions to challenging scientific and practical problems. In this paper we showcase AlphaEvolve as a tool for autonomously discovering novel mathematical constructions and advancing our understanding of long-standing open problems. To demonstrate its breadth, we considered a list of 67 problems spanning mathematical analysis, combinatorics, geometry, and number theory. The system rediscovered the best known solutions in most of the cases and discovered improved solutions in several. In some instances, AlphaEvolve is also able to generalize results for a finite number of input values into a formula valid for all input values. Furthermore, we are able to combine this methodology with Deep Think and AlphaProof in a broader framework where the additional proof-assistants and reasoning systems provide automated proof generation and further mathematical insights. These results demonstrate that large language model-guided evolutionary search can autonomously discover mathematical constructions that complement human intuition, at times matching or even improving the best known results, highlighting the potential for significant new ways of interaction between mathematicians and AI systems. We present AlphaEvolve as a powerful new tool for mathematical discovery, capable of exploring vast search spaces to solve complex optimization problems at scale, often with significantly reduced requirements on preparation and computation time.

The Euler Characteristic Transform (ECT) has proven to be a powerful representation, combining geometrical and topological characteristics of shapes and graphs. However, the ECT was hitherto unable to learn task-specific representations. We overcome this issue and develop a novel computational layer that enables learning the ECT in an end-to-end fashion. Our method, the Differentiable Euler Characteristic Transform (DECT), is fast and computationally efficient, while exhibiting performance on a par with more complex models in both graph and point cloud classification tasks. Moreover, we show that this seemingly simple statistic provides the same topological expressivity as more complex topological deep learning layers.

Digital identity is unsolved: after many years of research there is still no trusted communication over the Internet. To provide identity within the context of mutual distrust, this paper presents a blockchain-based digital identity solution. Without depending upon a single trusted third party, the proposed solution achieves passport-level legally valid identity. This solution for making identities Self-Sovereign, builds on a generic provable claim model for which attestations of truth from third parties need to be collected. The claim model is then shown to be both blockchain structure and proof method agnostic. Four different implementations in support of these two claim model properties are shown to offer sub-second performance for claim creation and claim verification. Through the properties of Self-Sovereign Identity, legally valid status and acceptable performance, our solution is considered to be fit for adoption by the general public.

We introduce a parametric nonlinear transformation that is well-suited for Gaussianizing data from natural images. The data are linearly transformed, and each component is then normalized by a pooled activity measure, computed by exponentiating a weighted sum of rectified and exponentiated components and a constant. We optimize the parameters of the full transformation (linear transform, exponents, weights, constant) over a database of natural images, directly minimizing the negentropy of the responses. The optimized transformation substantially Gaussianizes the data, achieving a significantly smaller mutual information between transformed components than alternative methods including ICA and radial Gaussianization. The transformation is differentiable and can be efficiently inverted, and thus induces a density model on images. We show that samples of this model are visually similar to samples of natural image patches. We demonstrate the use of the model as a prior probability density that can be used to remove additive noise. Finally, we show that the transformation can be cascaded, with each layer optimized using the same Gaussianization objective, thus offering an unsupervised method of optimizing a deep network architecture.

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test splits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.

Signature synthesis is a computation technique that generates artificial specimens which can support decision making in automatic signature verification. A lot of work has been dedicated to this subject, which centres on synthesizing dynamic and static two-dimensional handwriting on canvas. This paper proposes a framework to generate synthetic 3D on-air signatures exploiting the lognormality principle, which mimics the complex neuromotor control processes at play as the fingertip moves. Addressing the usual cases involving the development of artificial individuals and duplicated samples, this paper contributes to the synthesis of: (1) the trajectory and velocity of entirely 3D new signatures; (2) kinematic information when only the 3D trajectory of the signature is known, and (3) duplicate samples of 3D real signatures. Validation was conducted by generating synthetic 3D signature databases mimicking real ones and showing that automatic signature verifications of genuine and skilled forgeries report performances similar to those of real and synthetic databases. We also observed that training 3D automatic signature verifiers with duplicates can reduce errors. We further demonstrated that our proposal is also valid for synthesizing 3D air writing and gestures. Finally, a perception test confirmed the human likeness of the generated specimens. The databases generated are publicly available, only for research purposes, at .

Privacy concerns around ever increasing number of cameras are increasing in today's digital age. Although existing anonymization methods are able to obscure identity information, they often struggle to preserve the utility of the images. In this work, we introduce a training-free method for face anonymization that preserves key non-identity-related attributes. Our approach utilizes a pre-trained text-to-image diffusion model without requiring optimization or training. It begins by inverting the input image to recover its initial noise. The noise is then denoised through an identity-conditioned diffusion process, where modified identity embeddings ensure the anonymized face is distinct from the original identity. Our approach also supports localized anonymization, giving users control over which facial regions are anonymized or kept intact. Comprehensive evaluations against state-of-the-art methods show our approach excels in anonymization, attribute preservation, and image quality. Its flexibility, robustness, and practicality make it well-suited for real-world applications. Code and data can be found at https://github.com/hanweikung/nullface .

We introduce Score identity Distillation (SiD), an innovative data-free method that distills the generative capabilities of pretrained diffusion models into a single-step generator. SiD not only facilitates an exponentially fast reduction in Fr\'echet inception distance (FID) during distillation but also approaches or even exceeds the FID performance of the original teacher diffusion models. By reformulating forward diffusion processes as semi-implicit distributions, we leverage three score-related identities to create an innovative loss mechanism. This mechanism achieves rapid FID reduction by training the generator using its own synthesized images, eliminating the need for real data or reverse-diffusion-based generation, all accomplished within significantly shortened generation time. Upon evaluation across four benchmark datasets, the SiD algorithm demonstrates high iteration efficiency during distillation and surpasses competing distillation approaches, whether they are one-step or few-step, data-free, or dependent on training data, in terms of generation quality. This achievement not only redefines the benchmarks for efficiency and effectiveness in diffusion distillation but also in the broader field of diffusion-based generation. The PyTorch implementation is available at https://github.com/mingyuanzhou/SiD

Code has been shown to be effective in enhancing the mathematical reasoning abilities of large language models due to its precision and accuracy. Previous works involving continued mathematical pretraining often include code that utilizes math-related packages, which are primarily designed for fields such as engineering, machine learning, signal processing, or module testing, rather than being directly focused on mathematical reasoning. In this paper, we introduce a novel method for generating mathematical code accompanied with corresponding reasoning steps for continued pretraining. Our approach begins with the construction of a high-quality mathematical continued pretraining dataset by incorporating math-related web data, code using mathematical packages, math textbooks, and synthetic data. Next, we construct reasoning steps by extracting LaTeX expressions, the conditions needed for the expressions, and the results of the expressions from the previously collected dataset. Based on this extracted information, we generate corresponding code to accurately capture the mathematical reasoning process. Appending the generated code to each reasoning step results in data consisting of paired natural language reasoning steps and their corresponding code. Combining this data with the original dataset results in a 19.2B-token high-performing mathematical pretraining corpus, which we name MathCode-Pile. Training several popular base models with this corpus significantly improves their mathematical abilities, leading to the creation of the MathCoder2 family of models. All of our data processing and training code is open-sourced, ensuring full transparency and easy reproducibility of the entire data collection and training pipeline. The code is released at https://github.com/mathllm/MathCoder2 .

We propose MegaPortrait. It's an innovative system for creating personalized portrait images in computer vision. It has three modules: Identity Net, Shading Net, and Harmonization Net. Identity Net generates learned identity using a customized model fine-tuned with source images. Shading Net re-renders portraits using extracted representations. Harmonization Net fuses pasted faces and the reference image's body for coherent results. Our approach with off-the-shelf Controlnets is better than state-of-the-art AI portrait products in identity preservation and image fidelity. MegaPortrait has a simple but effective design and we compare it with other methods and products to show its superiority.

Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. This reliance limits their deeper understanding of mathematical theorems and related concepts. Inspired by the pedagogical method of "proof by counterexamples" commonly used in human mathematics education, our work aims to enhance LLMs' ability to conduct mathematical reasoning and proof through counterexamples. Specifically, we manually create a high-quality, university-level mathematical benchmark, CounterMATH, which requires LLMs to prove mathematical statements by providing counterexamples, thereby assessing their grasp of mathematical concepts. Additionally, we develop a data engineering framework to automatically obtain training data for further model improvement. Extensive experiments and detailed analyses demonstrate that CounterMATH is challenging, indicating that LLMs, such as OpenAI o1, have insufficient counterexample-driven proof capabilities. Moreover, our exploration into model training reveals that strengthening LLMs' counterexample-driven conceptual reasoning abilities is crucial for improving their overall mathematical capabilities. We believe that our work offers new perspectives on the community of mathematical LLMs.

In recent decades, a growing number of discoveries in fields of mathematics have been assisted by computer algorithms, primarily for exploring large parameter spaces that humans would take too long to investigate. As computers and algorithms become more powerful, an intriguing possibility arises - the interplay between human intuition and computer algorithms can lead to discoveries of novel mathematical concepts that would otherwise remain elusive. To realize this perspective, we have developed a massively parallel computer algorithm that discovers an unprecedented number of continued fraction formulas for fundamental mathematical constants. The sheer number of formulas discovered by the algorithm unveils a novel mathematical structure that we call the conservative matrix field. Such matrix fields (1) unify thousands of existing formulas, (2) generate infinitely many new formulas, and most importantly, (3) lead to unexpected relations between different mathematical constants, including multiple integer values of the Riemann zeta function. Conservative matrix fields also enable new mathematical proofs of irrationality. In particular, we can use them to generalize the celebrated proof by Ap\'ery for the irrationality of zeta(3). Utilizing thousands of personal computers worldwide, our computer-supported research strategy demonstrates the power of experimental mathematics, highlighting the prospects of large-scale computational approaches to tackle longstanding open problems and discover unexpected connections across diverse fields of science.

Creating content for a specific identity (ID) has shown significant interest in the field of generative models. In the field of text-to-image generation (T2I), subject-driven content generation has achieved great progress with the ID in the images controllable. However, extending it to video generation is not well explored. In this work, we propose a simple yet effective subject identity controllable video generation framework, termed Video Custom Diffusion (VCD). With a specified subject ID defined by a few images, VCD reinforces the identity information extraction and injects frame-wise correlation at the initialization stage for stable video outputs with identity preserved to a large extent. To achieve this, we propose three novel components that are essential for high-quality ID preservation: 1) an ID module trained with the cropped identity by prompt-to-segmentation to disentangle the ID information and the background noise for more accurate ID token learning; 2) a text-to-video (T2V) VCD module with 3D Gaussian Noise Prior for better inter-frame consistency and 3) video-to-video (V2V) Face VCD and Tiled VCD modules to deblur the face and upscale the video for higher resolution. Despite its simplicity, we conducted extensive experiments to verify that VCD is able to generate stable and high-quality videos with better ID over the selected strong baselines. Besides, due to the transferability of the ID module, VCD is also working well with finetuned text-to-image models available publically, further improving its usability. The codes are available at https://github.com/Zhen-Dong/Magic-Me.