Daily Papers

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we present a novel method based on the expectation-maximization algorithm for training diffusion models from incomplete and noisy observations only. Unlike previous works, our method leads to proper diffusion models, which is crucial for downstream tasks. As part of our method, we propose and motivate an improved posterior sampling scheme for unconditional diffusion models. We present empirical evidence supporting the effectiveness of our method.

This paper presents a video inversion approach for zero-shot video editing, which aims to model the input video with low-rank representation during the inversion process. The existing video editing methods usually apply the typical 2D DDIM inversion or na\"ive spatial-temporal DDIM inversion before editing, which leverages time-varying representation for each frame to derive noisy latent. Unlike most existing approaches, we propose a Spatial-Temporal Expectation-Maximization (STEM) inversion, which formulates the dense video feature under an expectation-maximization manner and iteratively estimates a more compact basis set to represent the whole video. Each frame applies the fixed and global representation for inversion, which is more friendly for temporal consistency during reconstruction and editing. Extensive qualitative and quantitative experiments demonstrate that our STEM inversion can achieve consistent improvement on two state-of-the-art video editing methods.

Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural images are highly non-Gaussian so that GMM cannot be applied to perform clustering task on pixel space. To overcome such limitation, we propose a GAN based EM learning framework that can maximize the likelihood of images and estimate the latent variables with only the constraint of L-Lipschitz continuity. We call this model GAN-EM, which is a framework for image clustering, semi-supervised classification and dimensionality reduction. In M-step, we design a novel loss function for discriminator of GAN to perform maximum likelihood estimation (MLE) on data with soft class label assignments. Specifically, a conditional generator captures data distribution for K classes, and a discriminator tells whether a sample is real or fake for each class. Since our model is unsupervised, the class label of real data is regarded as latent variable, which is estimated by an additional network (E-net) in E-step. The proposed GAN-EM achieves state-of-the-art clustering and semi-supervised classification results on MNIST, SVHN and CelebA, as well as comparable quality of generated images to other recently developed generative models.

Large language models (LLMs) exhibit hallucinations in long-form question-answering tasks across various domains and wide applications. Current hallucination detection and mitigation datasets are limited in domains and sizes, which struggle to scale due to prohibitive labor costs and insufficient reliability of existing hallucination annotators. To facilitate the scalable oversight of LLM hallucinations, this paper introduces an iterative self-training framework that simultaneously and progressively scales up the hallucination annotation dataset and improves the accuracy of the hallucination annotator. Based on the Expectation Maximization (EM) algorithm, in each iteration, the framework first applies a hallucination annotation pipeline to annotate a scaled dataset and then trains a more accurate hallucination annotator on the dataset. This new hallucination annotator is adopted in the hallucination annotation pipeline used for the next iteration. Extensive experimental results demonstrate that the finally obtained hallucination annotator with only 7B parameters surpasses the performance of GPT-4 and obtains new state-of-the-art hallucination detection results on HaluEval and HalluQA by zero-shot inference. Such an annotator can not only evaluate the hallucination levels of various LLMs on the large-scale dataset but also help to mitigate the hallucination of LLMs generations, with the Natural Language Inference (NLI) metric increasing from 25% to 37% on HaluEval.

Standard human preference-based alignment methods, such as Reinforcement Learning from Human Feedback (RLHF), are a cornerstone technology for aligning Large Language Models (LLMs) with human values. However, these methods are all underpinned by a critical, yet flawed assumption: human preferences are homogeneous (representing a single, unified preference) and the collected data is noiseless (free from error). In reality, neither is true since human preference is pluralistic and annotators can make mistakes. This creates a discrepancy between the recorded data and the ground-truth preferences, which can misguide the model and degrade its performance. To address this challenge, we introduce Latent Collective Preference Optimization (LCPO). LCPO leverages an Expectation-Maximization (EM) algorithm to learn the latent collective consensus from noisy data. It operates by inferring the correctness of each preference label and using this probability as an adaptive weight to re-calibrate each data point's contribution to the training loss, thereby mitigating noise. We generalize this approach by establishing a theoretical link between arbitrary preference losses and their corresponding probabilistic models, elevating LCPO from a specific algorithm to a general framework for robust preference alignment. Theoretically, we prove that under the condition of a perfectly calibrated model, LCPO is guaranteed to converge to the true noise level of the dataset. Our experiments demonstrate LCPO's effectiveness as a general framework, consistently enhancing four state-of-the-art alignment algorithms (DPO, IPO, SimPO, and CPO). When applied to Mistral and Llama 3 models, the LCPO-enhanced methods achieve substantial win rate gains on AlpacaEval 2 and Arena-Hard, with improvements of up to 7.0% on both benchmarks.

Latent variable models (LVMs) with discrete compositional latents are an important but challenging setting due to a combinatorially large number of possible configurations of the latents. A key tradeoff in modeling the posteriors over latents is between expressivity and tractable optimization. For algorithms based on expectation-maximization (EM), the E-step is often intractable without restrictive approximations to the posterior. We propose the use of GFlowNets, algorithms for sampling from an unnormalized density by learning a stochastic policy for sequential construction of samples, for this intractable E-step. By training GFlowNets to sample from the posterior over latents, we take advantage of their strengths as amortized variational inference algorithms for complex distributions over discrete structures. Our approach, GFlowNet-EM, enables the training of expressive LVMs with discrete compositional latents, as shown by experiments on non-context-free grammar induction and on images using discrete variational autoencoders (VAEs) without conditional independence enforced in the encoder.

Automatic Music Transcription (AMT) converts audio recordings into symbolic musical representations. Training deep neural networks (DNNs) for AMT typically requires strongly aligned training pairs with precise frame-level annotations. Since creating such datasets is costly and impractical for many musical contexts, weakly aligned approaches using segment-level annotations have gained traction. However, existing methods often rely on Dynamic Time Warping (DTW) or soft alignment loss functions, both of which still require local semantic correspondences, making them error-prone and computationally expensive. In this article, we introduce CountEM, a novel AMT framework that eliminates the need for explicit local alignment by leveraging note event histograms as supervision, enabling lighter computations and greater flexibility. Using an Expectation-Maximization (EM) approach, CountEM iteratively refines predictions based solely on note occurrence counts, significantly reducing annotation efforts while maintaining high transcription accuracy. Experiments on piano, guitar, and multi-instrument datasets demonstrate that CountEM matches or surpasses existing weakly supervised methods, improving AMT's robustness, scalability, and efficiency. Our project page is available at https://yoni-yaffe.github.io/count-the-notes.

During the preference optimization of large language models (LLMs), distribution shifts may arise between newly generated model samples and the data used to train the reward model (RM). This shift reduces the efficacy of the RM, which in turn negatively impacts the performance of the policy model (PM). To address this challenge, we propose Mutual-Taught, a self-training method that iteratively improves both the PM and RM without requiring additional human annotation. Our approach mirrors the expectation-maximization (EM) algorithm. In the E-step, the PM is updated using feedback from the current RM, guiding the PM toward a better approximation of the latent optimal preference distribution. In the M-step, we update the RM by constructing training data from the outputs of the PM before and after the E-step update. This process ensures that the RM adapts to the evolving policy distribution. Experimental results demonstrate that this iterative approach leads to consistent improvements in both models. Specifically, our 8B policy model, LLaMA-3-8B-Instruct-MT, achieves a length-controlled win rate of 54.1\% on AlpacaEval-2, while our 8B reward model, FsfairX-LLaMA3-RM-MT, performs on par with GPT-4o-2024-08-06 on RewardBench.

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxima even in the special case of the standard Gaussian mixture model with common isotropic covariance matrices. On the other hand, recent studies reveal that the unique global solution of a semidefinite programming (SDP) relaxed K-means achieves the information-theoretically sharp threshold for perfectly recovering the cluster labels under the standard Gaussian mixture model. In this paper, we extend the SDP approach to a general setting by integrating cluster labels as model parameters and propose an iterative likelihood adjusted SDP (iLA-SDP) method that directly maximizes the exact observed likelihood in the presence of data heterogeneity. By lifting the cluster assignment to group-specific membership matrices, iLA-SDP avoids centroids estimation -- a key feature that allows exact recovery under well-separateness of centroids without being trapped by their adversarial configurations. Thus iLA-SDP is less sensitive than EM to initialization and more stable on high-dimensional data. Our numeric experiments demonstrate that iLA-SDP can achieve lower mis-clustering errors over several widely used clustering methods including K-means, SDP and EM algorithms.

We propose the neural string edit distance model for string-pair matching and string transduction based on learnable string edit distance. We modify the original expectation-maximization learned edit distance algorithm into a differentiable loss function, allowing us to integrate it into a neural network providing a contextual representation of the input. We evaluate on cognate detection, transliteration, and grapheme-to-phoneme conversion, and show that we can trade off between performance and interpretability in a single framework. Using contextual representations, which are difficult to interpret, we match the performance of state-of-the-art string-pair matching models. Using static embeddings and a slightly different loss function, we force interpretability, at the expense of an accuracy drop.

Fine-tuning language models~(LMs) on human-generated data remains a prevalent practice. However, the performance of such models is often limited by the quantity and diversity of high-quality human data. In this paper, we explore whether we can go beyond human data on tasks where we have access to scalar feedback, for example, on math problems where one can verify correctness. To do so, we investigate a simple self-training method based on expectation-maximization, which we call ReST^{EM}, where we (1) generate samples from the model and filter them using binary feedback, (2) fine-tune the model on these samples, and (3) repeat this process a few times. Testing on advanced MATH reasoning and APPS coding benchmarks using PaLM-2 models, we find that ReST^{EM} scales favorably with model size and significantly surpasses fine-tuning only on human data. Overall, our findings suggest self-training with feedback can substantially reduce dependence on human-generated data.

Unsupervised object-centric learning methods allow the partitioning of scenes into entities without additional localization information and are excellent candidates for reducing the annotation burden of multiple-object tracking (MOT) pipelines. Unfortunately, they lack two key properties: objects are often split into parts and are not consistently tracked over time. In fact, state-of-the-art models achieve pixel-level accuracy and temporal consistency by relying on supervised object detection with additional ID labels for the association through time. This paper proposes a video object-centric model for MOT. It consists of an index-merge module that adapts the object-centric slots into detection outputs and an object memory module that builds complete object prototypes to handle occlusions. Benefited from object-centric learning, we only require sparse detection labels (0%-6.25%) for object localization and feature binding. Relying on our self-supervised Expectation-Maximization-inspired loss for object association, our approach requires no ID labels. Our experiments significantly narrow the gap between the existing object-centric model and the fully supervised state-of-the-art and outperform several unsupervised trackers.

We provide a probabilistic interpretation of attention and show that the standard dot-product attention in transformers is a special case of Maximum A Posteriori (MAP) inference. The proposed approach suggests the use of Expectation Maximization algorithms for online adaptation of key and value model parameters. This approach is useful for cases in which external agents, e.g., annotators, provide inference-time information about the correct values of some tokens, e.g, the semantic category of some pixels, and we need for this new information to propagate to other tokens in a principled manner. We illustrate the approach on an interactive semantic segmentation task in which annotators and models collaborate online to improve annotation efficiency. Using standard benchmarks, we observe that key adaptation boosts model performance (sim10% mIoU) in the low feedback regime and value propagation improves model responsiveness in the high feedback regime. A PyTorch layer implementation of our probabilistic attention model will be made publicly available here: https://github.com/apple/ml-probabilistic-attention.

While diffusion models can learn complex distributions, sampling requires a computationally expensive iterative process. Existing distillation methods enable efficient sampling, but have notable limitations, such as performance degradation with very few sampling steps, reliance on training data access, or mode-seeking optimization that may fail to capture the full distribution. We propose EM Distillation (EMD), a maximum likelihood-based approach that distills a diffusion model to a one-step generator model with minimal loss of perceptual quality. Our approach is derived through the lens of Expectation-Maximization (EM), where the generator parameters are updated using samples from the joint distribution of the diffusion teacher prior and inferred generator latents. We develop a reparametrized sampling scheme and a noise cancellation technique that together stabilizes the distillation process. We further reveal an interesting connection of our method with existing methods that minimize mode-seeking KL. EMD outperforms existing one-step generative methods in terms of FID scores on ImageNet-64 and ImageNet-128, and compares favorably with prior work on distilling text-to-image diffusion models.

The recent trend towards Personalized Federated Learning (PFL) has garnered significant attention as it allows for the training of models that are tailored to each client while maintaining data privacy. However, current PFL techniques primarily focus on modeling the conditional distribution heterogeneity (i.e. concept shift), which can result in suboptimal performance when the distribution of input data across clients diverges (i.e. covariate shift). Additionally, these techniques often lack the ability to adapt to unseen data, further limiting their effectiveness in real-world scenarios. To address these limitations, we propose a novel approach, FedGMM, which utilizes Gaussian mixture models (GMM) to effectively fit the input data distributions across diverse clients. The model parameters are estimated by maximum likelihood estimation utilizing a federated Expectation-Maximization algorithm, which is solved in closed form and does not assume gradient similarity. Furthermore, FedGMM possesses an additional advantage of adapting to new clients with minimal overhead, and it also enables uncertainty quantification. Empirical evaluations on synthetic and benchmark datasets demonstrate the superior performance of our method in both PFL classification and novel sample detection.

Retrieval-augmented generation (RAG) has become a widely recognized paradigm to combine parametric memory with non-parametric memories. An RAG model consists of two serial connecting components (retriever and generator). A major challenge in end-to-end optimization of the RAG model is that marginalization over relevant passages (modeled as discrete latent variables) from a knowledge base is required. Traditional top-K marginalization and variational RAG (VRAG) suffer from biased or high-variance gradient estimates. In this paper, we propose and develop joint stochastic approximation (JSA) based end-to-end training of RAG, which is referred to as JSA-RAG. The JSA algorithm is a stochastic extension of the EM (expectation-maximization) algorithm and is particularly powerful in estimating discrete latent variable models. Extensive experiments are conducted on five datasets for two tasks (open-domain question answering, knowledge-grounded dialogs) and show that JSA-RAG significantly outperforms both vanilla RAG and VRAG. Further analysis shows the efficacy of JSA-RAG from the perspectives of generation, retrieval, and low-variance gradient estimate.

Transductive few-shot learning has recently triggered wide attention in computer vision. Yet, current methods introduce key hyper-parameters, which control the prediction statistics of the test batches, such as the level of class balance, affecting performances significantly. Such hyper-parameters are empirically grid-searched over validation data, and their configurations may vary substantially with the target dataset and pre-training model, making such empirical searches both sub-optimal and computationally intractable. In this work, we advocate and introduce the unrolling paradigm, also referred to as "learning to optimize", in the context of few-shot learning, thereby learning efficiently and effectively a set of optimized hyper-parameters. Specifically, we unroll a generalization of the ubiquitous Expectation-Maximization (EM) optimizer into a neural network architecture, mapping each of its iterates to a layer and learning a set of key hyper-parameters over validation data. Our unrolling approach covers various statistical feature distributions and pre-training paradigms, including recent foundational vision-language models and standard vision-only classifiers. We report comprehensive experiments, which cover a breadth of fine-grained downstream image classification tasks, showing significant gains brought by the proposed unrolled EM algorithm over iterative variants. The achieved improvements reach up to 10% and 7.5% on vision-only and vision-language benchmarks, respectively.

Weakly-Supervised Semantic Segmentation (WSSS) aims to train segmentation models by weak labels, which is receiving significant attention due to its low annotation cost. Existing approaches focus on generating pseudo labels for supervision while largely ignoring to leverage the inherent semantic correlation among different pseudo labels. We observe that pseudo-labeled pixels that are close to each other in the feature space are more likely to share the same class, and those closer to the distribution centers tend to have higher confidence. Motivated by this, we propose to model the underlying label distributions and employ cross-label constraints to generate more accurate pseudo labels. In this paper, we develop a unified WSSS framework named Adaptive Gaussian Mixtures Model, which leverages a GMM to model the label distributions. Specifically, we calculate the feature distribution centers of pseudo-labeled pixels and build the GMM by measuring the distance between the centers and each pseudo-labeled pixel. Then, we introduce an Online Expectation-Maximization (OEM) algorithm and a novel maximization loss to optimize the GMM adaptively, aiming to learn more discriminative decision boundaries between different class-wise Gaussian mixtures. Based on the label distributions, we leverage the GMM to generate high-quality pseudo labels for more reliable supervision. Our framework is capable of solving different forms of weak labels: image-level labels, points, scribbles, blocks, and bounding-boxes. Extensive experiments on PASCAL, COCO, Cityscapes, and ADE20K datasets demonstrate that our framework can effectively provide more reliable supervision and outperform the state-of-the-art methods under all settings. Code will be available at https://github.com/Luffy03/AGMM-SASS.

The cross-lingual language models are typically pretrained with masked language modeling on multilingual text or parallel sentences. In this paper, we introduce denoising word alignment as a new cross-lingual pre-training task. Specifically, the model first self-labels word alignments for parallel sentences. Then we randomly mask tokens in a bitext pair. Given a masked token, the model uses a pointer network to predict the aligned token in the other language. We alternately perform the above two steps in an expectation-maximization manner. Experimental results show that our method improves cross-lingual transferability on various datasets, especially on the token-level tasks, such as question answering, and structured prediction. Moreover, the model can serve as a pretrained word aligner, which achieves reasonably low error rates on the alignment benchmarks. The code and pretrained parameters are available at https://github.com/CZWin32768/XLM-Align.

In this paper, we present a cross-entropy optimization method for hyperparameter optimization in stochastic gradient-based approaches to train deep neural networks. The value of a hyperparameter of a learning algorithm often has great impact on the performance of a model such as the convergence speed, the generalization performance metrics, etc. While in some cases the hyperparameters of a learning algorithm can be part of learning parameters, in other scenarios the hyperparameters of a stochastic optimization algorithm such as Adam [5] and its variants are either fixed as a constant or are kept changing in a monotonic way over time. We give an in-depth analysis of the presented method in the framework of expectation maximization (EM). The presented algorithm of cross-entropy optimization for hyperparameter optimization of a learning algorithm (CEHPO) can be equally applicable to other areas of optimization problems in deep learning. We hope that the presented methods can provide different perspectives and offer some insights for optimization problems in different areas of machine learning and beyond.

Identifying cell types and understanding their functional properties is crucial for unraveling the mechanisms underlying perception and cognition. In the retina, functional types can be identified by carefully selected stimuli, but this requires expert domain knowledge and biases the procedure towards previously known cell types. In the visual cortex, it is still unknown what functional types exist and how to identify them. Thus, for unbiased identification of the functional cell types in retina and visual cortex, new approaches are needed. Here we propose an optimization-based clustering approach using deep predictive models to obtain functional clusters of neurons using Most Discriminative Stimuli (MDS). Our approach alternates between stimulus optimization with cluster reassignment akin to an expectation-maximization algorithm. The algorithm recovers functional clusters in mouse retina, marmoset retina and macaque visual area V4. This demonstrates that our approach can successfully find discriminative stimuli across species, stages of the visual system and recording techniques. The resulting most discriminative stimuli can be used to assign functional cell types fast and on the fly, without the need to train complex predictive models or show a large natural scene dataset, paving the way for experiments that were previously limited by experimental time. Crucially, MDS are interpretable: they visualize the distinctive stimulus patterns that most unambiguously identify a specific type of neuron.

We study the sparse recovery problem with an underdetermined linear system characterized by a Kronecker-structured dictionary and a Kronecker-supported sparse vector. We cast this problem into the sparse Bayesian learning (SBL) framework and rely on the expectation-maximization method for a solution. To this end, we model the Kronecker-structured support with a hierarchical Gaussian prior distribution parameterized by a Kronecker-structured hyperparameter, leading to a non-convex optimization problem. The optimization problem is solved using the alternating minimization (AM) method and a singular value decomposition (SVD)-based method, resulting in two algorithms. Further, we analytically guarantee that the AM-based method converges to the stationary point of the SBL cost function. The SVD-based method, though it adopts approximations, is empirically shown to be more efficient and accurate. We then apply our algorithm to estimate the uplink wireless channel in an intelligent reflecting surface-aided MIMO system and extend the AM-based algorithm to address block sparsity in the channel. We also study the SBL cost to show that the minima of the cost function are achieved at sparse solutions and that incorporating the Kronecker structure reduces the number of local minima of the SBL cost function. Our numerical results demonstrate the effectiveness of our algorithms compared to the state-of-the-art.

Point cloud rigid registration is a fundamental problem in 3D computer vision. In the multiview case, we aim to find a set of 6D poses to align a set of objects. Methods based on pairwise registration rely on a subsequent synchronization algorithm, which makes them poorly scalable with the number of views. Generative approaches overcome this limitation, but are based on Gaussian Mixture Models and use an Expectation-Maximization algorithm. Hence, they are not well suited to handle large transformations. Moreover, most existing methods cannot handle high levels of degradations. In this paper, we introduce POLAR (POint cloud LAtent Registration), a multiview registration method able to efficiently deal with a large number of views, while being robust to a high level of degradations and large initial angles. To achieve this, we transpose the registration problem into the latent space of a pretrained autoencoder, design a loss taking degradations into account, and develop an efficient multistart optimization strategy. Our proposed method significantly outperforms state-of-the-art approaches on synthetic and real data. POLAR is available at github.com/pypolar/polar or as a standalone package which can be installed with pip install polaregistration.

[This paper was initially published in PHME conference in 2016, selected for further publication in International Journal of Prognostics and Health Management.] This paper describes an Autoregressive Partially-hidden Markov model (ARPHMM) for fault detection and prognostics of equipments based on sensors' data. It is a particular dynamic Bayesian network that allows to represent the dynamics of a system by means of a Hidden Markov Model (HMM) and an autoregressive (AR) process. The Markov chain assumes that the system is switching back and forth between internal states while the AR process ensures a temporal coherence on sensor measurements. A sound learning procedure of standard ARHMM based on maximum likelihood allows to iteratively estimate all parameters simultaneously. This paper suggests a modification of the learning procedure considering that one may have prior knowledge about the structure which becomes partially hidden. The integration of the prior is based on the Theory of Weighted Distributions which is compatible with the Expectation-Maximization algorithm in the sense that the convergence properties are still satisfied. We show how to apply this model to estimate the remaining useful life based on health indicators. The autoregressive parameters can indeed be used for prediction while the latent structure can be used to get information about the degradation level. The interest of the proposed method for prognostics and health assessment is demonstrated on CMAPSS datasets.

Audio Descriptions (ADs) aim to provide a narration of a movie in text form, describing non-dialogue-related narratives, such as characters, actions, or scene establishment. Automatic generation of ADs remains challenging due to: i) the domain gap between movie-AD data and existing data used to train vision-language models, and ii) the issue of contextual redundancy arising from highly similar neighboring visual clips in a long movie. In this work, we propose DistinctAD, a novel two-stage framework for generating ADs that emphasize distinctiveness to produce better narratives. To address the domain gap, we introduce a CLIP-AD adaptation strategy that does not require additional AD corpora, enabling more effective alignment between movie and AD modalities at both global and fine-grained levels. In Stage-II, DistinctAD incorporates two key innovations: (i) a Contextual Expectation-Maximization Attention (EMA) module that reduces redundancy by extracting common bases from consecutive video clips, and (ii) an explicit distinctive word prediction loss that filters out repeated words in the context, ensuring the prediction of unique terms specific to the current AD. Comprehensive evaluations on MAD-Eval, CMD-AD, and TV-AD benchmarks demonstrate the superiority of DistinctAD, with the model consistently outperforming baselines, particularly in Recall@k/N, highlighting its effectiveness in producing high-quality, distinctive ADs.

Open-world 3D part segmentation is pivotal in diverse applications such as robotics and AR/VR. Traditional supervised methods often grapple with limited 3D data availability and struggle to generalize to unseen object categories. PartSLIP, a recent advancement, has made significant strides in zero- and few-shot 3D part segmentation. This is achieved by harnessing the capabilities of the 2D open-vocabulary detection module, GLIP, and introducing a heuristic method for converting and lifting multi-view 2D bounding box predictions into 3D segmentation masks. In this paper, we introduce PartSLIP++, an enhanced version designed to overcome the limitations of its predecessor. Our approach incorporates two major improvements. First, we utilize a pre-trained 2D segmentation model, SAM, to produce pixel-wise 2D segmentations, yielding more precise and accurate annotations than the 2D bounding boxes used in PartSLIP. Second, PartSLIP++ replaces the heuristic 3D conversion process with an innovative modified Expectation-Maximization algorithm. This algorithm conceptualizes 3D instance segmentation as unobserved latent variables, and then iteratively refines them through an alternating process of 2D-3D matching and optimization with gradient descent. Through extensive evaluations, we show that PartSLIP++ demonstrates better performance over PartSLIP in both low-shot 3D semantic and instance-based object part segmentation tasks. Code released at https://github.com/zyc00/PartSLIP2.

Multi-modality image fusion aims to combine different modalities to produce fused images that retain the complementary features of each modality, such as functional highlights and texture details. To leverage strong generative priors and address challenges such as unstable training and lack of interpretability for GAN-based generative methods, we propose a novel fusion algorithm based on the denoising diffusion probabilistic model (DDPM). The fusion task is formulated as a conditional generation problem under the DDPM sampling framework, which is further divided into an unconditional generation subproblem and a maximum likelihood subproblem. The latter is modeled in a hierarchical Bayesian manner with latent variables and inferred by the expectation-maximization (EM) algorithm. By integrating the inference solution into the diffusion sampling iteration, our method can generate high-quality fused images with natural image generative priors and cross-modality information from source images. Note that all we required is an unconditional pre-trained generative model, and no fine-tuning is needed. Our extensive experiments indicate that our approach yields promising fusion results in infrared-visible image fusion and medical image fusion. The code is available at https://github.com/Zhaozixiang1228/MMIF-DDFM.

Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not robust, as they are sensitive to outliers. To alleviate this problem, this paper introduces the Self-Paced Learning mechanism into PPCA, and proposes a novel method called Self-Paced Probabilistic Principal Component Analysis (SP-PPCA). Furthermore, we design the corresponding optimization algorithm based on the alternative search strategy and the expectation-maximization algorithm. SP-PPCA looks for optimal projection vectors and filters out outliers iteratively. Experiments on both synthetic problems and real-world datasets clearly demonstrate that SP-PPCA is able to reduce or eliminate the impact of outliers.

In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into Expectation-Maximization (EM)-based sparse Bayesian learning (SBL). In particular, GGAMP is used to implement the E-step in SBL in place of matrix inversion, leveraging the fact that GGAMP is guaranteed to converge with appropriate damping. The resulting GGAMP-SBL algorithm is much more robust to arbitrary measurement matrix A than the standard damped GAMP algorithm while being much lower complexity than the standard SBL algorithm. We then extend the approach from the single measurement vector (SMV) case to the temporally correlated multiple measurement vector (MMV) case, leading to the GGAMP-TSBL algorithm. We verify the robustness and computational advantages of the proposed algorithms through numerical experiments.

We propose MESA and DMESA as novel feature matching methods, which utilize Segment Anything Model (SAM) to effectively mitigate matching redundancy. The key insight of our methods is to establish implicit-semantic area matching prior to point matching, based on advanced image understanding of SAM. Then, informative area matches with consistent internal semantic are able to undergo dense feature comparison, facilitating precise inside-area point matching. Specifically, MESA adopts a sparse matching framework and first obtains candidate areas from SAM results through a novel Area Graph (AG). Then, area matching among the candidates is formulated as graph energy minimization and solved by graphical models derived from AG. To address the efficiency issue of MESA, we further propose DMESA as its dense counterpart, applying a dense matching framework. After candidate areas are identified by AG, DMESA establishes area matches through generating dense matching distributions. The distributions are produced from off-the-shelf patch matching utilizing the Gaussian Mixture Model and refined via the Expectation Maximization. With less repetitive computation, DMESA showcases a speed improvement of nearly five times compared to MESA, while maintaining competitive accuracy. Our methods are extensively evaluated on five datasets encompassing indoor and outdoor scenes. The results illustrate consistent performance improvements from our methods for five distinct point matching baselines across all datasets. Furthermore, our methods exhibit promise generalization and improved robustness against image resolution variations. The code is publicly available at https://github.com/Easonyesheng/A2PM-MESA.

Large language models (LLMs) are evolving from conversational systems into strong reasoners for tasks such as Olympiad mathematics and competitive programming. While scaling parameters and test-time computation has driven progress, a key bottleneck is the lack of high-quality training problems: human-curated datasets are costly and limited, while existing synthetic corpora are often too easy or narrow. PromptCoT 1.0 showed that injecting rationales into prompt synthesis increases problem difficulty. Building on this, we present PromptCoT 2.0, a scalable framework that replaces hand-crafted heuristics with an expectation-maximization (EM) loop, where rationales are iteratively refined to guide prompt construction. This produces problems that are both harder and more diverse than prior corpora. The synthetic prompts support two post-training regimes: (1) Self-Play, where strong models improve autonomously via verifiable feedback without stronger teachers; and (2) Supervised Fine-Tuning (SFT), where weaker models learn from teacher-distilled traces. Extensive experiments demonstrate the effectiveness of this approach. In self-play, applying PromptCoT 2.0 to Qwen3-30B-A3B-Thinking-2507 sets new state-of-the-art results at the 30B scale, with +4.4, +4.8, and +5.3 on AIME 24/25 and HMMT 25, +6.1 and +5.0 on LiveCodeBench v5/v6, and +35 Elo on Codeforces. In SFT, training Qwen2.5-7B-Instruct solely on synthetic prompts boosts accuracy to 73.1 (AIME 24), 65.6 (AIME 25), and 53.4 (LiveCodeBench v5), surpassing models trained on human or hybrid data. Analyses further confirm that PromptCoT 2.0 yields fundamentally harder and distributionally distinct problems. These results establish prompt synthesis as a new axis for scaling reasoning and position PromptCoT 2.0 as a scalable foundation for future open-source models. The implementation is available at https://github.com/inclusionAI/PromptCoT.

Large language models (LLMs) solve problems more accurately and interpretably when instructed to work out the answer step by step using a ``chain-of-thought'' (CoT) prompt. One can also improve LLMs' performance on a specific task by supervised fine-tuning, i.e., by using gradient ascent on some tunable parameters to maximize the average log-likelihood of correct answers from a labeled training set. Naively combining CoT with supervised tuning requires supervision not just of the correct answers, but also of detailed rationales that lead to those answers; these rationales are expensive to produce by hand. Instead, we propose a fine-tuning strategy that tries to maximize the marginal log-likelihood of generating a correct answer using CoT prompting, approximately averaging over all possible rationales. The core challenge is sampling from the posterior over rationales conditioned on the correct answer; we address it using a simple Markov-chain Monte Carlo (MCMC) expectation-maximization (EM) algorithm inspired by the self-taught reasoner (STaR), memoized wake-sleep, Markovian score climbing, and persistent contrastive divergence. This algorithm also admits a novel control-variate technique that drives the variance of our gradient estimates to zero as the model improves. Applying our technique to GSM8K and the tasks in BIG-Bench Hard, we find that this MCMC-EM fine-tuning technique typically improves the model's accuracy on held-out examples more than STaR or prompt-tuning with or without CoT.

Large Language Models (LLMs) are increasingly used in applications requiring long context lengths, but the key-value (KV) cache often becomes a memory bottleneck on GPUs as context grows. To address this, we propose Commutative Vector Quantization (CommVQ) to significantly reduce memory usage for long-context LLM inference. We first introduce additive quantization with a lightweight encoder and codebook to compress the KV cache, which can be decoded via simple matrix multiplication. To further reduce computational costs during decoding, we design the codebook to be commutative with Rotary Position Embedding (RoPE) and train it using an Expectation-Maximization (EM) algorithm. This enables efficient integration of decoding into the self-attention mechanism. Our approach achieves high accuracy with additive quantization and low overhead via the RoPE-commutative codebook. Experiments on long-context benchmarks and GSM8K show that our method reduces FP16 KV cache size by 87.5% with 2-bit quantization, while outperforming state-of-the-art KV cache quantization methods. Notably, it enables 1-bit KV cache quantization with minimal accuracy loss, allowing a LLaMA-3.1 8B model to run with a 128K context length on a single RTX 4090 GPU. The source code is available at: https://github.com/UMass-Embodied-AGI/CommVQ.

Continuous latent variables (LVs) are a key ingredient of many generative models, as they allow modelling expressive mixtures with an uncountable number of components. In contrast, probabilistic circuits (PCs) are hierarchical discrete mixtures represented as computational graphs composed of input, sum and product units. Unlike continuous LV models, PCs provide tractable inference but are limited to discrete LVs with categorical (i.e. unordered) states. We bridge these model classes by introducing probabilistic integral circuits (PICs), a new language of computational graphs that extends PCs with integral units representing continuous LVs. In the first place, PICs are symbolic computational graphs and are fully tractable in simple cases where analytical integration is possible. In practice, we parameterise PICs with light-weight neural nets delivering an intractable hierarchical continuous mixture that can be approximated arbitrarily well with large PCs using numerical quadrature. On several distribution estimation benchmarks, we show that such PIC-approximating PCs systematically outperform PCs commonly learned via expectation-maximization or SGD.

Reinforcement Learning from Human Feedback (RLHF) aligns language models to human preferences by employing a singular reward model derived from preference data. However, such an approach overlooks the rich diversity of human preferences inherent in data collected from multiple users. In this work, we first derive an impossibility result of alignment with single reward RLHF, thereby highlighting its insufficiency in representing diverse human preferences. To provide an equitable solution to the problem, we learn a mixture of preference distributions via an expectation-maximization algorithm and propose a MaxMin alignment objective for policy learning inspired by the Egalitarian principle in social choice theory to better represent diverse human preferences. We elucidate the connection of our proposed approach to distributionally robust optimization and general utility RL, thereby highlighting the generality and robustness of our proposed solution. We present comprehensive experimental results on small-scale (GPT-2) and large-scale language models (with Tulu2-7B) and show the efficacy of the proposed approach in the presence of diversity among human preferences. Our algorithm achieves an average improvement of more than 16% in win-rates over conventional RLHF algorithms and improves the win-rate (accuracy) for minority groups by over 33% without compromising the performance of majority groups, showcasing the robustness and fairness of our approach. We remark that our findings in this work are not only limited to language models but also extend to reinforcement learning in general.

Existing preference optimization methods are mainly designed for directly learning from human feedback with the assumption that paired examples (preferred vs. dis-preferred) are available. In contrast, we propose a method that can leverage unpaired preferred or dis-preferred examples, and works even when only one type of feedback (positive or negative) is available. This flexibility allows us to apply it in scenarios with varying forms of feedback and models, including training generative language models based on human feedback as well as training policies for sequential decision-making problems, where learned (value) functions are available. Our approach builds upon the probabilistic framework introduced in (Dayan and Hinton, 1997), which proposes to use expectation-maximization (EM) to directly optimize the probability of preferred outcomes (as opposed to classic expected reward maximization). To obtain a practical algorithm, we identify and address a key limitation in current EM-based methods: when applied to preference optimization, they solely maximize the likelihood of preferred examples, while neglecting dis-preferred samples. We show how one can extend EM algorithms to explicitly incorporate dis-preferred outcomes, leading to a novel, theoretically grounded, preference optimization algorithm that offers an intuitive and versatile way to learn from both positive and negative feedback.

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via either Monte Carlo or expectation-maximization methods. In this work we introduce an alternative, variational inference algorithm for Markov jump processes which relies on neural ordinary differential equations, and is trainable via back-propagation. Our methodology learns neural, continuous-time representations of the observed data, that are used to approximate the initial distribution and time-dependent transition probability rates of the posterior Markov jump process. The time-independent rates of the prior process are in contrast trained akin to generative adversarial networks. We test our approach on synthetic data sampled from ground-truth Markov jump processes, experimental switching ion channel data and molecular dynamics simulations. Source code to reproduce our experiments is available online.

This paper studies learning on text-attributed graphs (TAGs), where each node is associated with a text description. An ideal solution for such a problem would be integrating both the text and graph structure information with large language models and graph neural networks (GNNs). However, the problem becomes very challenging when graphs are large due to the high computational complexity brought by training large language models and GNNs together. In this paper, we propose an efficient and effective solution to learning on large text-attributed graphs by fusing graph structure and language learning with a variational Expectation-Maximization (EM) framework, called GLEM. Instead of simultaneously training large language models and GNNs on big graphs, GLEM proposes to alternatively update the two modules in the E-step and M-step. Such a procedure allows training the two modules separately while simultaneously allowing the two modules to interact and mutually enhance each other. Extensive experiments on multiple data sets demonstrate the efficiency and effectiveness of the proposed approach.

The class activation mapping, or CAM, has been the cornerstone of feature attribution methods for multiple vision tasks. Its simplicity and effectiveness have led to wide applications in the explanation of visual predictions and weakly-supervised localization tasks. However, CAM has its own shortcomings. The computation of attribution maps relies on ad-hoc calibration steps that are not part of the training computational graph, making it difficult for us to understand the real meaning of the attribution values. In this paper, we improve CAM by explicitly incorporating a latent variable encoding the location of the cue for recognition in the formulation, thereby subsuming the attribution map into the training computational graph. The resulting model, class activation latent mapping, or CALM, is trained with the expectation-maximization algorithm. Our experiments show that CALM identifies discriminative attributes for image classifiers more accurately than CAM and other visual attribution baselines. CALM also shows performance improvements over prior arts on the weakly-supervised object localization benchmarks. Our code is available at https://github.com/naver-ai/calm.

Functional linear discriminant analysis (FLDA) is a powerful tool that extends LDA-mediated multiclass classification and dimension reduction to univariate time-series functions. However, in the age of large multivariate and incomplete data, statistical dependencies between features must be estimated in a computationally tractable way, while also dealing with missing data. There is a need for a computationally tractable approach that considers the statistical dependencies between features and can handle missing values. We here develop a multivariate version of FLDA (MUDRA) to tackle this issue and describe an efficient expectation/conditional-maximization (ECM) algorithm to infer its parameters. We assess its predictive power on the "Articulary Word Recognition" data set and show its improvement over the state-of-the-art, especially in the case of missing data. MUDRA allows interpretable classification of data sets with large proportions of missing data, which will be particularly useful for medical or psychological data sets.

Recently, conditional score-based diffusion models have gained significant attention in the field of supervised speech enhancement, yielding state-of-the-art performance. However, these methods may face challenges when generalising to unseen conditions. To address this issue, we introduce an alternative approach that operates in an unsupervised manner, leveraging the generative power of diffusion models. Specifically, in a training phase, a clean speech prior distribution is learnt in the short-time Fourier transform (STFT) domain using score-based diffusion models, allowing it to unconditionally generate clean speech from Gaussian noise. Then, we develop a posterior sampling methodology for speech enhancement by combining the learnt clean speech prior with a noise model for speech signal inference. The noise parameters are simultaneously learnt along with clean speech estimation through an iterative expectationmaximisation (EM) approach. To the best of our knowledge, this is the first work exploring diffusion-based generative models for unsupervised speech enhancement, demonstrating promising results compared to a recent variational auto-encoder (VAE)-based unsupervised approach and a state-of-the-art diffusion-based supervised method. It thus opens a new direction for future research in unsupervised speech enhancement.