Mutual Information (MI) is a fundamental measure of statistical dependence widely used in representation learning. While direct optimization of MI via its definition as a Kullback-Leibler divergence (KLD) is often intractable, many recent methods have instead maximized alternative dependence measures, most notably, the JensenShannon divergence (JSD) between joint and product of marginal distributions via discriminative losses. However, the connection between these surrogate objectives and MI remains poorly understood.

Mutual Information (MI) is a fundamental measure of statistical dependence widely used in representation learning. While direct optimization of MI via its definition as a Kullback-Leibler divergence (KLD) is often intractable, many recent methods have instead maximized alternative dependence measures, most notably, the Jensen-Shannon divergence (JSD) between joint and product of marginal distributions via discriminative losses. However, the connection between these surrogate objectives and MI remains poorly understood.

Neural Information Processing Systems http://nips.cc/

Learning a probability model from data samples is a fundamental task in unsupervised learning.

Current evaluations of LLMs for code generation emphasize functional correctness, overlooking the fact that functionally correct solutions can differ significantly in algorithmic complexity. For instance, an $(O(n^2))$ versus $(O(n \log n))$ sorting algorithm may yield similar output but incur vastly different performance costs in production. This discrepancy reveals a critical limitation in current evaluation methods: they fail to capture the behavioral and performance diversity among correct solutions. To address this, we introduce a principled framework for evaluating the dynamic stability of generated code. We propose two metrics derived from opcode distributions: Static Canonical Trace Divergence (SCTD), which captures algorithmic structure diversity across generated solutions, and Dynamic Canonical Trace Divergence (DCTD), which quantifies runtime behavioral variance. Their ratio, the Behavioral Expression Factor (BEF), serves as a diagnostic signal: it indicates critical runtime instability when BEF $\ll$ 1 and functional redundancy when BEF $\gg$ 1. Empirical results on BigOBench and CodeContests show that state-of-the-art LLMs exhibit significant algorithmic variance even among functionally correct outputs. Notably, increasing sampling temperature improves pass@1 rates but degrades stability, revealing an unrecognized trade-off: searching for correct solutions in diverse output spaces introduces a "penalty of instability" between correctness and behavioral consistency. Our findings call for stability-aware objectives in code generation and new benchmarks with asymptotic test cases for robust, real-world LLM evaluation.

Human trajectory data is crucial in urban planning, traffic engineering, and public health. However, directly using real-world trajectory data often faces challenges such as privacy concerns, data acquisition costs, and data quality. A practical solution to these challenges is trajectory generation, a method developed to simulate human mobility behaviors. Existing trajectory generation methods mainly focus on capturing individual movement patterns but often overlook the influence of population distribution on trajectory generation. In reality, dynamic population distribution reflects changes in population density across different regions, significantly impacting individual mobility behavior. Thus, we propose a novel trajectory generation framework based on a diffusion model, which integrates the dynamic population distribution constraints to guide high-fidelity generation outcomes. Specifically, we construct a spatial graph to enhance the spatial correlation of trajectories. Then, we design a dynamic population distribution aware denoising network to capture the spatiotemporal dependencies of human mobility behavior as well as the impact of population distribution in the denoising process. Extensive experiments show that the trajectories generated by our model can resemble real-world trajectories in terms of some critical statistical metrics, outperforming state-of-the-art algorithms by over 54%.

Developing trustworthy Machine Learning (ML) models requires their predicted probabilities to be well-calibrated, meaning they should reflect true-class frequencies. Among calibration notions in multiclass classification, strong calibration is the most stringent, as it requires all predicted probabilities to be simultaneously calibrated across all classes. However, existing approaches to multiclass calibration lack a notion of distance among inputs, which makes them vulnerable to proximity bias: predictions in sparse regions of the feature space are systematically miscalibrated. This is especially relevant in high-stakes settings, such as healthcare, where the sparse instances are exactly those most at risk of biased treatment. In this work, we address this main shortcoming by introducing a local perspective on multiclass calibration. First, we formally define multiclass local calibration and establish its relationship with strong calibration. Second, we theoretically analyze the pitfalls of existing evaluation metrics when applied to multiclass local calibration. Third, we propose a practical method for enhancing local calibration in Neural Networks, which enforces alignment between predicted probabilities and local estimates of class frequencies using the Jensen-Shannon distance. Finally, we empirically validate our approach against existing multiclass calibration techniques.

Recent work reports that Large Reasoning Models (LRMs) undergo a collapse in performance on solving puzzles beyond certain perplexity thresholds. In subsequent discourse, questions have arisen as to whether the nature of the task muddles an evaluation of true reasoning. One potential confound is the requirement that the model keep track of the state space on its own. We provide a large language model (LLM) with an environment interface for Tower of Hanoi problems, allowing it to make a move with a tool call, provide written justification, observe the resulting state space, and reprompt itself for the next move. We observe that access to an environment interface does not delay or eradicate performance collapse. Furthermore, LLM-parameterized policy analysis reveals increasing divergence from both optimal policies and uniformly random policies, suggesting that the model exhibits mode-like collapse at each level of complexity, and that performance is dependent upon whether the mode reflects the correct solution for the problem. We suggest that a similar phenomena might take place in LRMs.

Unsupervised neural grammar induction aims to learn interpretable hierarchical structures from language data. However, existing models face an expressiveness bottleneck, often resulting in unnecessarily large yet underperforming grammars. We identify a core issue, $\textit{probability distribution collapse}$, as the underlying cause of this limitation. We analyze when and how the collapse emerges across key components of neural parameterization and introduce a targeted solution, $\textit{collapse-relaxing neural parameterization}$, to mitigate it. Our approach substantially improves parsing performance while enabling the use of significantly more compact grammars across a wide range of languages, as demonstrated through extensive empirical analysis.

Large Video Models (LVMs) build on the semantic capabilities of Large Language Models (LLMs) and vision modules by integrating temporal information to better understand dynamic video content. Despite their progress, LVMs are prone to hallucinations-producing inaccurate or irrelevant descriptions. Current benchmarks for video hallucination depend heavily on manual categorization of video content, neglecting the perception-based processes through which humans naturally interpret videos. We introduce MESH, a benchmark designed to evaluate hallucinations in LVMs systematically. MESH uses a Question-Answering framework with binary and multi-choice formats incorporating target and trap instances. It follows a bottom-up approach, evaluating basic objects, coarse-to-fine subject features, and subject-action pairs, aligning with human video understanding. We demonstrate that MESH offers an effective and comprehensive approach for identifying hallucinations in videos. Our evaluations show that while LVMs excel at recognizing basic objects and features, their susceptibility to hallucinations increases markedly when handling fine details or aligning multiple actions involving various subjects in longer videos.