When and why representations learned by different deep neural networks are similar is an active research topic. We choose to address these questions from the perspective of identifiability theory, which suggests that a measure of representational similarity should be invariant to transformations that leave the model distribution unchanged. Focusing on a model family which includes several popular pre-training approaches, e.g., autoregressive language models, we explore when models which generate distributions that are close have similar representations. We prove that a small Kullback--Leibler divergence between the model distributions does not guarantee that the corresponding representations are similar. This has the important corollary that models with near-maximum data likelihood can still learn dissimilar representations---a phenomenon mirrored in our experiments with models trained on CIFAR-10. We then define a distributional distance for which closeness implies representational similarity, and in synthetic experiments, we find that wider networks learn distributions which are closer with respect to our distance and have more similar representations. Our results thus clarify the link between closeness in distribution and representational similarity.

SAM aims to find a perturbed model within the vicinity of a current model that maximizes the loss over a training set.

The past few years have witnessed great success in the use of diffusion models (DMs) to generate high-fidelity images with the help of stochastic differential equations (SDEs). However, discretization error is an inevitable limitation when utilizing numerical solvers to solve SDEs. To address this limitation, we provide a theoretical analysis demonstrating that an appropriate combination of the contrastive loss and score matching serves as an upper bound of the KL divergence between the true data distribution and the model distribution. To obtain this bound, we utilize a contrastive loss to construct a contrastive sampling chain to fine-tuning the pre-trained DM. In this manner, our method reduces the discretization error and thus yields a smaller gap between the true data distribution and our model distribution. Moreover, the presented method can be applied to fine-tuning various pre-trained DMs, both with or without fast sampling algorithms, contributing to better sample quality or slightly faster sampling speeds. To validate the efficacy of our method, we conduct comprehensive experiments. For example, on CIFAR10, when applied to a pre-trained EDM, our method improves the FID from 2.04 to 1.88 with 35 neural function evaluations (NFEs), and reduces NFEs from 35 to 25 to achieve the same 2.04 FID.

Energy-based models (EBMs) are generative models inspired by statistical physics with a wide range of applications in unsupervised learning. Their performance is well measured by the cross-entropy (CE) of the model distribution relative to the data distribution. Using the CE as the objective for training is however challenging because the computation of its gradient with respect to the model parameters requires sampling the model distribution. Here we show how results for nonequilibrium thermodynamics based on Jarzynski equality together with tools from sequential Monte-Carlo sampling can be used to perform this computation efficiently and avoid the uncontrolled approximations made using the standard contrastive divergence algorithm. Specifically, we introduce a modification of the unadjusted Langevin algorithm (ULA) in which each walker acquires a weight that enables the estimation of the gradient of the cross-entropy at any step during GD, thereby bypassing sampling biases induced by slow mixing of ULA. We illustrate these results with numerical experiments on Gaussian mixture distributions as well as the MNIST and CIFAR-10 datasets. We show that the proposed approach outperforms methods based on the contrastive divergence algorithm in all the considered situations.

Distributional robustness is a promising framework for training deep learning models that are less vulnerable to adversarial examples and data distribution shifts. Previous works have mainly focused on exploiting distributional robustness in the data space. In this work, we explore an optimal transport-based distributional robustness framework in model spaces. Specifically, we examine a model distribution within a Wasserstein ball centered on a given model distribution that maximizes the loss. We have developed theories that enable us to learn the optimal robust center model distribution. Interestingly, our developed theories allow us to flexibly incorporate the concept of sharpness awareness into training, whether it's a single model, ensemble models, or Bayesian Neural Networks, by considering specific forms of the center model distribution. These forms include a Dirac delta distribution over a single model, a uniform distribution over several models, and a general Bayesian Neural Network. Furthermore, we demonstrate that Sharpness-Aware Minimization (SAM) is a specific case of our framework when using a Dirac delta distribution over a single model, while our framework can be seen as a probabilistic extension of SAM. To validate the effectiveness of our framework in the aforementioned settings, we conducted extensive experiments, and the results reveal remarkable improvements compared to the baselines.

In what follows, we will take Eq.

SAM aims to find a perturbed model within the vicinity of a current model that maximizes the loss over a training set.

Abstract--Large-scale low-Earth-orbit (LEO) satellite systems are increasingly valued for their ability to enable rapid and wide-area data exchange, thereby facilitating the collaborative training of artificial intelligence (AI) models across geographically distributed regions. Due to privacy concerns and regulatory constraints, raw data collected at remote clients cannot be centrally aggregated, posing a major obstacle to traditional AI training methods. Federated learning offers a privacy-preserving alternative by training local models on distributed devices and exchanging only model parameters. However, the dynamic topology and limited bandwidth of satellite systems will hinder timely parameter aggregation and distribution, resulting in prolonged training times. To address this challenge, we investigate the problem of scheduling federated learning over satellite networks and identify key bottlenecks that impact the overall duration of each training round. We propose a discrete temporal graph-based on-demand scheduling framework that dynamically allocates communication resources to accelerate federated learning. Simulation results demonstrate that the proposed approach achieves significant performance gains over traditional statistical multiplexing-based model exchange strategies, reducing overall round times by 14.20% to 41.48%. Moreover, the acceleration effect becomes more pronounced for larger models and higher numbers of clients, highlighting the scalability of the proposed approach.

Large Language Models (LLMs) often produce hallucinations in retrieval-augmented or long-context generation, even when relevant evidence is present. This stems from two issues: head importance is treated as input-agnostic, and raw attention weights poorly reflect each token's true contribution. We present HAVE (Head-Adaptive Gating and ValuE Calibration), a parameter-free decoding framework that directly addresses both challenges. HAVE introduces head-adaptive gating, which performs instance-level soft reweighing of attention heads, and value calibration, which augments attention with the magnitude of value vectors to approximate write-back contribution. Together, these modules construct token-level evidence aligned with model updates and fuse it with the LM distribution through a lightweight uncertainty-scaled policy. HAVE requires no finetuning and operates in a single forward pass, making it efficient and broadly applicable. Experiments across multiple QA benchmarks and LLM families demonstrate that HAVE consistently reduces hallucinations and outperforms strong baselines, including DAGCD, with modest overhead. The framework is transparent, reproducible, and readily integrates with off-the-shelf LLMs, advancing trustworthy generation in real-world settings.

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