Probabilistic Circuits (PCs) are a class of generative models that allow exact and tractable inference for a wide range of queries. While recent developments have enabled the learning of deep and expressive PCs, this increased capacity can often lead to overfitting, especially when data is limited. We analyze PC overfitting from a log-likelihood-landscape perspective and show that it is often caused by convergence to sharp optima that generalize poorly. Inspired by sharpness aware minimization in neural networks, we propose a Hessian-based regularizer for training PCs. As a key contribution, we show that the trace of the Hessian of the log-likelihood--a sharpness proxy that is typically intractable in deep neural networks--can be computed efficiently for PCs. Minimizing this Hessian trace induces a gradient-norm-based regularizer that yields simple closed-form parameter updates for EM, and integrates seamlessly with gradient based learning methods. Experiments on synthetic and real-world datasets demonstrate that our method consistently guides PCs toward flatter minima, improving generalization performance.
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Single-channel audio separation aims to separate individual sources from a single-channel mixture. Most existing methods rely on supervised learning with synthetically generated paired data. However, obtaining high-quality paired data in real-world scenarios is often difficult. This data scarcity can degrade model performance under unseen conditions and limit generalization ability. To this end, in this work, we approach this problem from an unsupervised perspective, framing it as a probabilistic inverse problem. Our method requires only diffusion priors trained on individual sources. Separation is then achieved by iteratively guiding an initial state toward the solution through reconstruction guidance. Importantly, we introduce an advanced inverse problem solver specifically designed for separation, which mitigates gradient conflicts caused by interference between the diffusion prior and reconstruction guidance during inverse denoising. This design ensures high-quality and balanced separation performance across individual sources. Additionally, we find that initializing the denoising process with an augmented mixture instead of pure Gaussian noise provides an informative starting point that significantly improves the final performance. To further enhance audio prior modeling, we design a novel time–frequency attention-based network architecture that demonstrates strong audio modeling capability. Collectively, these improvements lead to significant performance gains, as validated across speech–sound event, sound event, and speech separation tasks.
We introduce the Probabilistic Coin Change Problem (PCCP), a novel variant of the classical Combination Coin Change Problem (CCCP), motivated by a real-world scientific inverse task. The goal of CCCP is to enumerate all unordered combinations of coin denominations that sum to a given target. In PCCP, each coin type’s value follows a discrete probability distribution, and the aggregate value of a combination of coins is thus stochastic. Given a set of such coin types and noisy observations of total sums, the task is to infer the most likely latent coin combination. To address the combinatorial and probabilistic complexity of PCCP, we propose DeepProReasoner (Deep Combinatorial Probabilistic Reasoning with Embedded Representations), an unsupervised, end-to-end, deep-learning framework that integrates combinatorial reasoning, latent-space modeling, and differentiable probabilistic reasoning. The model is trained using a reconstruction loss between the observed empirical distribution and a decoded probability mass function (PMF), enabling efficient gradient-based search over a continuous relaxation of the combinatorial space. We evaluate DeepProReasoner on two instances of PCCP: (1) a synthetic Candy Mix problem for ablation studies, and (2) a real-world task of molecular formula inference from ultrahigh resolution mass spectrometry (MS) data. Besides the two given instances, PCCP captures a wide range of inverse settings in biology, chemistry, environmental sciences, and medicine, where latent combinatorial structures give rise to noisy aggregate observations through stochastic processes. Our results show that DeepProReasoner achieves high accuracy and robustness, outperforming state-of-the-art methods.
Learning on multi-view data is a fundamental task, which integrates the information from different views to improve the final performance. It is also a basic task for learning on the long-tailed data in real applications, followed by the downstream tasks, i.e., classification. The existing works for trusted classification on multi-view data or long-tailed data usually aim to improve the final performance and dynamically consider the confidence of prediction for the data which is crucial in cost-sensitive domains. However, these methods pay few attentions to the pairwise trusted problem which considers the trusted pairs instead of trusted annotated data points. Besides, the problem of classification on long-tailed multi-view data has never been studied so far. In this work, we focus on the pairwise trusted problem on long-tailed multi-view classification and give a general framework, which considers the trusted pairs instead of trusted annotated data points. We then construct a specific example under the general framework and introduce a novel Enhanced Normal-Inverse Gamma distribution (ENIG). ENIG is a joint probabilistic distribution built on Dirichlet distribution and NIG. A novel combination rule based on ENIG for long-tailed multi-view data is also given, which adaptively integrates the long-tailed data from different views to achieve a consensus one at the level of evidence and effectively produces a trusted long-tailed multi-view classification result. Our method is robust and able to be dynamically aware of the uncertainty for the long-tailed data from each view. The accurate uncertainty can be induced by the proposed learning framework, leading to both robustness and reliability for classification on long-tailed multi-view data. Experimental results on different long-tailed multi-view datasets demonstrate the effectiveness of our method in terms of accuracy, robustness and reliability.
Preference learning has gained significant attention in tasks involving subjective human judgments, such as speech emotion recognition (SER) and image aesthetic assessment. While pairwise frameworks such as RankNet offer robust modeling of relative preferences, they are inherently limited to local comparisons and struggle to capture global ranking consistency. To address these limitations, we propose RankList, a novel listwise preference learning framework that generalizes RankNet to structured list-level supervision. Our formulation explicitly models local and non-local ranking constraints within a probabilistic framework. The paper introduces a log-sum-exp approximation to improve training efficiency. We further extend RankList with skip-wise comparisons, enabling progressive exposure to complex list structures and enhancing global ranking fidelity. Extensive experiments demonstrate the superiority of our method across diverse modalities. On benchmark SER datasets (MSP-Podcast, IEMOCAP, BIIC Podcast), RankList achieves consistent improvements in Kendall's Tau and ranking accuracy compared to standard listwise baselines. We also validate our approach on aesthetic image ranking using the Artistic Image Aesthetics dataset, highlighting its broad applicability. Through ablation and cross-domain studies, we show that RankList not only improves in-domain ranking but also generalizes better across datasets. Our framework offers a unified, extensible approach for modeling ordered preferences in subjective learning scenarios.
Shapley values are widely recognized as a principled method for attributing importance to input features in machine learning. However, the exact computation of Shapley values scales exponentially with the number of features, severely limiting the practical application of this powerful approach. The challenge is further compounded when the predictive model is probabilistic---as in Gaussian processes (GPs)---where the outputs are random variables rather than point estimates, necessitating additional computational effort in modeling higher-order moments. In this work, we demonstrate that for an important class of GPs known as FANOVA GP, which explicitly models all main effects and interactions, exact Shapley attributions for both local and global explanations can be computed in *quadratic* time. For *local, instance-wise explanations*, we define a stochastic cooperative game over function components and compute the *exact stochastic Shapley value* in quadratic time only, capturing both the expected contribution and uncertainty. For *global explanations*, we introduce a deterministic, variance-based value function and compute exact Shapley values that quantify each feature’s contribution to the model’s overall sensitivity. Our methods leverage a closed-form (stochastic) Möbiusrepresentation of the FANOVA decomposition and introduce recursive algorithms, inspired by Newton's identities, to efficiently compute the mean and variance of Shapley values. Our work enhances the utility of explainable AI, as demonstrated by empirical studies, by providing more scalable, axiomatically sound, and uncertainty-aware explanations for predictions generated by structured probabilistic models.
Uncovering Hidden Degeneration: A Physics-Guided Bidirectional Inference Framework for Industrial Time Series Prediction
PDF ↗Hidden degenerations in industrial time series often precede observable failures, they remain undetected by standard monitoring systems until anomalies become apparent. This gap between microscopic degradation and macroscopic observation renders conventional predictors inherently reactive, as they rely on correlations in sensor data rather than uncovering the underlying, physics‑consistent degradation states. Crucially, the microscopic mechanisms governing system evolution depend on macroscopic state variables—whose measurements are expectations over microscopic probability distributions—so purely data‑driven “top‑down” or purely physics‑guided “bottom‑up” approaches cannot forecast degeneration‑entangled industrial faults. To address these challenges, we propose a Physics-Guided Bidirectional Inference Framework that represents hidden microscopic states from macroscopic measurements. Our approach uniquely combines: (1) bottom-up physics-based simulation using Continuum Damage Mechanics to model micro-scale damage evolution under environmental stressors, and (2) top-down probabilistic inference via maximum entropy formalism to estimate latent microstate distributions from sparse sensor data. This bidirectional mechanism enables early failure prediction by bridging observable measurements with unobservable degeneration. Validation on real-world railway infrastruc datasets demonstrates significant improvements in early fault prediction compared to state-of-the-art baselines. Our method establishes a new paradigm for safety-critical industrial applications requiring reliable prediction of hidden degeneration processes.
We study streaming data with categorical features where the vocabulary of categorical feature values is changing and can even grow unboundedly over time. Feature hashing is commonly used as a pre-processing step to map these categorical values into a feature space of fixed size before learning their embeddings. While these methods have been developed and evaluated for offline or batch settings, in this paper we consider online settings. We show that deterministic embeddings are sensitive to the arrival order of categories and suffer from forgetting in online learning, leading to performance deterioration. To mitigate this issue, we propose a probabilistic hash embedding (PHE) model that treats hash embeddings as stochastic and applies Bayesian online learning to learn incrementally from data. Based on the structure of PHE, we derive a scalable inference algorithm to learn model parameters and infer/update the posteriors of hash embeddings and other latent variables. Our algorithm (i) can handle an evolving vocabulary of categorical items, (ii) is adaptive to new items without forgetting old items, (iii) is implementable with a bounded set of parameters that does not grow with the number of distinct observed values on the stream, and (iv) is invariant to the item arrival order. Experiments in classification, sequence modeling, and recommendation systems in online learning setups demonstrate the superior performance of PHE while maintaining high memory efficiency (consumes as low as 2→4% memory of a one-hot embedding table).
Conformal prediction constructs a set of labels instead of a single point prediction, while providing a probabilistic coverage guarantee. Beyond the coverage guarantee, adaptiveness to example difficulty is an important property. It means that the method should produce larger prediction sets for more difficult examples, and smaller ones for easier examples. Existing evaluation methods for adaptiveness typically analyze coverage rate violation or average set size across bins of examples grouped by difficulty. However, these approaches often suffer from imbalanced binning, which can lead to inaccurate estimates of coverage or set size. To address this issue, we propose a binning method that leverages input transformations to sort examples by difficulty, followed by uniform-mass binning. Building on this binning, we introduce two metrics to better evaluate adaptiveness. These metrics provide more reliable estimates of coverage rate violation and average set size due to balanced binning, leading to more accurate adaptivity assessment. Through experiments, we demonstrate that our proposed metric correlates more strongly with the desired adaptiveness property compared to existing ones. Furthermore, motivated by our findings, we propose a new adaptive prediction set algorithm that groups examples by estimated difficulty and applies group-conditional conformal prediction. This allows us to determine appropriate thresholds for each group. Experimental results on both (a) an Image Classification (ImageNet) (b) a medical task (visual acuity prediction) show that our method outperforms existing approaches according to the new metrics.
BayesAgent: Bayesian Agentic Reasoning Under Uncertainty via Verbalized Probabilistic Graphical Modeling
PDF ↗Human cognition excels at transcending sensory input and forming latent representations that structure our understanding of the world. While Large Language Model (LLM) agents demonstrate emergent reasoning and decision-making abilities, they lack a principled framework for capturing latent structures and modeling uncertainty. In this work, we explore for the first time how to bridge LLM agents with probabilistic graphical models (PGMs) to address agentic reasoning under uncertainty. To this end, we introduce Verbalized Probabilistic Graphical Modeling (vPGM), a Bayesian agentic framework that (i) guides LLM agents in following key principles of PGMs through natural language and (ii) refines the resulting posterior distributions via numerical Bayesian inference. Unlike many traditional probabilistic methods requiring substantial domain expertise, vPGM bypasses expert‐driven model design, making it well‐suited for scenarios with limited assumptions. We evaluated our model on several agentic reasoning tasks, both close-ended and open-ended. Our results indicate that the model effectively enhances confidence calibration and text generation quality.
Diffusion models have recently shown promise in time series forecasting, particularly for probabilistic predictions. However, they often fail to achieve state-of-the-art point estimation performance compared to regression-based methods. This limitation stems from difficulties in providing sufficient contextual bias to track distribution shifts and in balancing output diversity with the stability and precision required for point forecasts. Existing diffusion-based approaches mainly focus on full-distribution modeling under probabilistic frameworks, often with likelihood maximization objectives, while paying little attention to dedicated strategies for high-accuracy point estimation. Moreover, other existing point prediction diffusion methods frequently rely on pre-trained or jointly trained mature models for contextual bias, sacrificing the generative flexibility of diffusion models. To address these challenges, we propose SimDiff, a single-stage, end-to-end framework. SimDiff employs a single unified Transformer network carefully tailored to serve as both denoiser and predictor, eliminating the need for external pre-trained or jointly trained regressors. It achieves state-of-the-art point estimation performance by leveraging intrinsic output diversity and improving mean squared error accuracy through multiple inference ensembling. Key innovations, including normalization independence and the median-of-means estimator, further enhance adaptability and stability. Extensive experiments demonstrate that SimDiff significantly outperforms existing methods in time series point forecasting.
Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these methods effectively model the relationships between latent factors and the low-rank tensor using Dirac delta distributions. However, tensor low-rank decomposition is inherently non-unique, leading to a multimodal distribution over possible solutions. Critically, such prior knowledge is rarely available in practical scenarios, particularly regarding the optimal rank structure and contraction rules. To address this issue, we propose a score-based model that eliminates the need for predefined structural or distributional assumptions, enabling the learning of compatibility between tensors and latent factors. Specifically, a neural network is designed to learn the energy function, which is optimized via score matching to capture the gradient of the joint log-probability of tensor entries and latent factors. Our method allows for modeling structures and distributions beyond the Dirac delta assumption. Moreover, integrating the block coordinate descent (BCD) algorithm with the proposed smooth regularization enables the model to perform both tensor completion and denoising. Experimental results demonstrate significant performance improvements across various tensor types, including sparse and continuous-time tensors, as well as visual data.
Operationalizing definitions of fairness is difficult in practice, as multiple definitions can be incompatible while each being arguably desirable. Instead, it may be easier to directly describe algorithmic bias through ad-hoc assumptions specific to a particular real-world task, e.g., based on background information on systemic biases in its context. Such assumptions can, in turn, be used to mitigate this bias during training. Yet, a framework for incorporating such assumptions that is simultaneously principled, flexible, and interpretable is currently lacking. Our approach is to formalize bias assumptions as programs in ProbLog, a probabilistic logic programming language that allows for the description of probabilistic causal relationships through logic. Neurosymbolic extensions of ProbLog then allow for easy integration of these assumptions in a neural network's training process. We propose a set of templates to express different types of bias and show the versatility of our approach on synthetic tabular datasets with known biases. Using estimates of the bias distortions present, we also succeed in mitigating algorithmic bias in real-world tabular and image data. We conclude that ProbLog4Fairness outperforms baselines due to its ability to flexibly model the relevant bias assumptions, where other methods typically uphold a fixed bias type or notion of fairness.
Ensuring alignment with human values is essential for modern large language models (LLMs), especially amid growing concerns around AI safety and social impact. Yet achieving such alignment remains challenging due to the limited, noisy, and often conflicting nature of human feedback from diverse annotators. Most existing approaches, such as Direct Preference Optimization (DPO), assume consistent and conflict-free supervision, overlooking the ambiguity, inconsistency, and value trade-offs inherent in real-world preferences—often leading to reduced robustness and exclusion of minority views. To address this, we propose FGD-Align, a novel pluralistic alignment framework grounded in Fuzzy Group Decision-Making theory. Our approach rigorously models and aggregates human preferences while retaining the complexity of real-world value trade-offs. Unlike traditional methods that rely on coarse-grained preference pairs, FGD-Align introduces fuzzy preference modeling via triangular fuzzy numbers to capture nuanced, multi-criteria human judgments. We further develop a new training objective, Probabilistic Fuzzy DPO, which incorporates fuzzy preference strength as adaptive loss weights and gradient filters, enhancing robustness to ambiguity and inconsistency in feedback. Comprehensive experiments demonstrate that FGD-Align consistently outperforms both DPO variants and advanced preference aggregation methods in terms of preference accuracy and robustness to ambiguity. It achieves superior alignment stability and better preserves minority preferences, all with minimal computational overhead. Our work bridges the gap between algorithmic tractability and the nuanced landscape of human values, enabling more scalable, inclusive, and socially-aware AI alignment.
Precipitation nowcasting, a critical task for weather-sensitive applications, is highly challenging owing to the chaotic nature of atmospheric dynamics. Despite recent progress in deep learning, existing methods are limited in their capacity to model turbulent motions, one of the key drivers of precipitation evolution. Thus, we propose MoCast, the first work that incorporates turbulence knowledge to decompose turbulent motions into solvable components for precipitation nowcasting. Specifically, inspired by the continuity equation, MoCast introduces two core innovations: (1) a physics-guided motion module that learns turbulent motions from physically interpretable mean and fluctuating components based on Reynolds, Helmholtz, and Wavelet decomposition techniques, and (2) a motion-guided source-sink module that learns source-sink features considering the multi-scale impact from motions based on a mixture-of-experts architecture. Extensive experiments on three real-world datasets demonstrate that MoCast achieves the state-of-the-art performance. MoCast and its diffusion-based variant MoCast+ reduce CSI error by an average of 4.9% and 4.5% compared to the best deterministic and probabilistic baselines, respectively.
CoordAR: One-Reference 6D Pose Estimation of Novel Objects via Autoregressive Coordinate Map Generation
PDF ↗Object 6D pose estimation, a crucial task for robotics and augmented reality applications, becomes particularly challenging when dealing with novel objects whose 3D models are not readily available. To reduce dependency on 3D models, recent studies have explored one-reference-based pose estimation, which requires only a single reference view instead of a complete 3D model. However, existing methods that rely on real-valued coordinate regression suffer from limited global consistency due to the local nature of convolutional architectures and face challenges in symmetric or occluded scenarios owing to a lack of uncertainty modeling. We present CoordAR, a novel autoregressive framework for one-reference 6D pose estimation of unseen objects. CoordAR formulates 3D-3D correspondences between the reference and query views as a map of discrete tokens, which is obtained in an autoregressive and probabilistic manner. To enable accurate correspondence regression, CoordAR introduces 1) a novel coordinate map tokenization that enables probabilistic prediction over discretized 3D space; 2) a modality-decoupled encoding strategy that separately encodes RGB appearance and coordinate cues; and 3) an autoregressive transformer decoder conditioned on both position-aligned query features and the partially generated token sequence. With these novel mechanisms, CoordAR significantly outperforms existing methods on multiple benchmarks and demonstrates strong robustness to symmetry, occlusion, and other challenges in real-world tests.
Diffusion probabilistic models have set a new standard for generative fidelity but are hindered by a slow iterative sampling process. A powerful training-free strategy to accelerate this process is Schedule Optimization, which aims to find an optimal distribution of timesteps for a fixed and small Number of Function Evaluations (NFE) to maximize sample quality. To this end, a successful schedule optimization method must adhere to four core principles: effectiveness, adaptivity, practical robustness, and computational efficiency. However, existing paradigms struggle to satisfy these principles simultaneously, motivating the need for a more advanced solution. To overcome these limitations, we propose the Hierarchical-Schedule-Optimizer (HSO), a novel and efficient bi-level optimization framework. HSO reframes the search for a globally optimal schedule into a more tractable problem by iteratively alternating between two synergistic levels: an upper-level global search for an optimal initialization strategy and a lower-level local optimization for schedule refinement. This process is guided by two key innovations: the Midpoint Error Proxy (MEP), a solver-agnostic and numerically stable objective for effective local optimization, and the Spacing-Penalized Fitness (SPF) function, which ensures practical robustness by penalizing pathologically close timesteps. Extensive experiments show that HSO sets a new state-of-the-art for training-free sampling in the extremely low-NFE regime. For instance, with an NFE of just 5, HSO achieves a remarkable FID of 11.94 on LAION-Aesthetics with Stable Diffusion v2.1. Crucially, this level of performance is attained not through costly retraining, but with a one-time optimization cost of less than 8 seconds, presenting a highly practical and efficient paradigm for diffusion model acceleration.
OW-DAR: Dual-Granularity Adaptive Reconstruction-Error Modeling for Open-World Object Detection
PDF ↗Open-world object detection (OWOD) aims to detect known and unknown objects in dynamic environments. However, only known classes are labeled during training, making it challenging for detectors to recognize unknown objects during inference. Existing methods typically rely on supervision from known categories, leading models to overconfidently misclassify visually similar unknowns as known, and dissimilar ones as background. This known-class prior bias limits the model’s ability to detect unknown objects. In this paper, we propose a novel method, OW-DAR, which enhances foreground-background separability through collaborative fine-grained and coarse-grained modeling. At the fine-grained level, we propose Fine-grained Masked Reconstruction (FMR), which randomly masks regions of the feature map to guide the reconstruction toward semantic structures, rather than memorizing low-level patterns. At the coarse-grained level, we propose Adaptive Region-based Error Aggregation (AREA), which operates on object proposals to aggregate reconstruction errors. This enables the model to attend to semantically ambiguous foreground-background boundaries while suppressing the influence of local outliers during optimization. Finally, we leverage robust reconstruction errors to perform unsupervised foreground-background modeling, enabling probabilistic estimation for potential unknown objects. We validate the effectiveness of OW-DAR on standard OWOD benchmark. Experimental results demonstrate that OW-DAR consistently outperforms existing state-of-the-art methods, achieving a +18.8 improvement in unknown object recall (U-Recall).
TSPE-GS: Probabilistic Depth Extraction for Semi-Transparent Surface Reconstruction via 3D Gaussian Splatting
PDF ↗3D Gaussian Splatting-based geometry reconstruction is regarded as an excellent paradigm due to its favorable trade-off between speed and reconstruction quality. However, such 3D Gaussian-based reconstruction pipelines often face challenges when reconstructing semi-transparent surfaces, hindering their broader application in real-world scenes. The primary reason is the assumption in mainstream methods that each pixel corresponds to one specific depth—an assumption that fails under semi-transparent conditions where multiple surfaces are visible, leading to depth ambiguity and ineffective recovery of geometric structures. To address these challenges, we propose TSPE-GS (Transparent Surface Probabilistic Extraction for Gaussian Splatting), a novel probabilistic depth extraction approach that uniformly samples transmittance to model the multi-modal distribution of opacity and depth per pixel, replacing the previous single-peak distribution that caused depth confusion across surfaces. By progressively fusing truncated signed distance functions, TSPE-GS separately reconstructs distinct external and internal surfaces in a unified framework. Our method can be easily generalized to other Gaussian-based reconstruction pipelines, effectively extracting semi-transparent surfaces without requiring additional training overhead. Extensive experiments on both public and self-collected semi-transparent datasets, as well as opaque object datasets, demonstrate that TSPE-GS significantly enhances reconstruction accuracy for semi-transparent surfaces while maintaining reconstruction quality in opaque scenes.
In this paper, we propose a novel unsupervised shape matching framework based on probabilistic deformation consistency in the spectral domain, termed as PDCMatch. Axiomatic optimization methods suffer from expensive geodesic distance calculations and vulnerability to local optima, and learning-based methods typically lack geometric consistency in pointwise correspondences. To overcome both limitations, we develop a non-Euclidean probabilistic deformation model that jointly estimates the underlying deformation and the correspondence probability via a linear Expectation-Maximization procedure. Building on this formulation, we further design a task-specific deformation loss that explicitly encourages geometric smoothness and structural consistency in an unsupervised manner. This tailored loss function plays a central role in improving the matching performance across challenging scenarios. Extensive experiments on public benchmarks involving near-isometric shapes, anisotropic meshing, cross-dataset generalization, topological noise, and non-isometric shapes demonstrate that our method consistently outperforms state-of-the-art methods, highlighting both its effectiveness and generalizability.