Stochastic Interpolants (SI) are a powerful framework for generative modeling, capable of flexibly transforming between two probability distributions. However, their use in jointly optimized latent variable models remains unexplored as they require direct access to the samples from the two distributions. This work presents Latent Stochastic Interpolants (LSI) enabling joint learning in a latent space with end-to-end optimized encoder, decoder and latent SI models. We achieve this by developing a principled Evidence Lower Bound (ELBO) objective derived directly in continuous time. The joint optimization allows LSI to learn effective latent representations along with a generative process that transforms an arbitrary prior distribution into the encoder-defined aggregated posterior. LSI sidesteps the simple priors of the normal diffusion models and mitigates the computational demands of applying SI directly in high-dimensional observation spaces, while preserving the generative flexibility of the SI framework. We demonstrate the efficacy of LSI through comprehensive experiments on the standard large scale ImageNet generation benchmark.

Understanding the complex interactions within dynamic multilayer networks is critical for advancements in various scientific domains. Existing models often fail to capture such networks' temporal and cross-layer dynamics. This paper introduces a novel Tensor State Space Model for Dynamic Multilayer Networks (TSSDMN), utilizing a latent space model framework. TSSDMN employs a symmetric Tucker decomposition to represent latent node features, their interaction patterns, and layer transitions. Then by fixing the latent features and allowing the interaction patterns to evolve over time, TSSDMN uniquely captures both the temporal dynamics within layers and across different layers. The model identifiability conditions are discussed. By treating latent features as variables whose posterior distributions are approximated using a mean-field variational inference approach, a variational Expectation Maximization algorithm is developed for efficient model inference. Numerical simulations and case studies demonstrate the efficacy of TSSDMN for understanding dynamic multilayer networks.

What are the essential components of world models? How far do we get with world models that are not employing RNNs, transformers, discrete representations, and image reconstructions? This paper introduces SGF, a Simple, Good, and Fast world model that uses self-supervised representation learning, captures short-time dependencies through frame and action stacking, and enhances robustness against model errors through data augmentation. We extensively discuss SGF's connections to established world models, evaluate the building blocks in ablation studies, and demonstrate good performance through quantitative comparisons on the Atari 100k benchmark.

In recent years, federated learning (FL) has made significant advance in privacy-sensitive applications. However, it can be hard to ensure that FL participants provide well-annotated data for training. The corresponding annotations from different clients often contain complex label noise at varying levels. This label noise issue has a substantial impact on the performance of the trained models, and clients with greater noise levels can be largely attributed for this degradation. To this end, it is necessary to develop an effective optimization strategy to alleviate the adverse effects of these noisy clients.In this study, we present a two-stage optimization framework, MaskedOptim, to address this intricate label noise problem. The first stage is designed to facilitate the detection of noisy clients with higher label noise rates. The second stage focuses on rectifying the labels of the noisy clients' data through an end-to-end label correction mechanism, aiming to mitigate the negative impacts caused by misinformation within datasets. This is achieved by learning the potential ground-truth labels of the noisy clients' datasets via backpropagation. To further enhance the training robustness, we apply the geometric median based model aggregation instead of the commonly-used vanilla averaged model aggregation. We implement sixteen related methods and conduct evaluations on three image datasets and one text dataset with diverse label noise patterns for a comprehensive comparison. Extensive experimental results indicate that our proposed framework shows its robustness in different scenarios. Additionally, our label correction framework effectively enhances the data quality of the detected noisy clients' local datasets. % Our codes will be open-sourced to facilitate related research communities. Our codes are available via https://github.com/Sprinter1999/MaskedOptim .

We study the recovery of multiple high-dimensional signals from two noisy, correlated modalities: a spiked matrix and a spiked tensor sharing a common low-rank structure. This setting generalizes classical spiked matrix and tensor models, unveiling intricate interactions between inference channels and surprising algorithmic behaviors. Notably, while the spiked tensor model is typically intractable at low signal-to-noise ratios, its correlation with the matrix enables efficient recovery via Bayesian Approximate Message Passing, inducing staircase-like phase transitions reminiscent of neural network phenomena. In contrast, empirical risk minimization for joint learning fails: the tensor component obstructs effective matrix recovery, and joint optimization significantly degrades performance, highlighting the limitations of naive multi-modal learning. We show that a simple Sequential Curriculum Learning strategy-first recovering the matrix, then leveraging it to guide tensor recovery-resolves this bottleneck and achieves optimal weak recovery thresholds. This strategy, implementable with spectral methods, emphasizes the critical role of structural correlation and learning order in multi-modal high-dimensional inference.

We introduce the attention-indexed model (AIM), a theoretical framework for analyzing learning in deep attention layers. Inspired by multi-index models, AIM captures how token-level outputs emerge from layered bilinear interactions over high-dimensional embeddings. Unlike prior tractable attention models, AIM allows full-width key and query matrices, aligning more closely with practical transformers. Using tools from statistical mechanics and random matrix theory, we derive closed-form predictions for Bayes-optimal generalization error and identify sharp phase transitions as a function of sample complexity, model width, and sequence length. We propose a matching approximate message passing algorithm and show that gradient descent can reach optimal performance. AIM offers a solvable playground for understanding learning in modern attention architectures.

Differential privacy (DP) has become an essential framework for privacy-preserving machine learning. Existing DP learning methods, however, often have disparate impacts on model predictions, e.g., for minority groups. Gradient clipping, which is often used in DP learning, can suppress larger gradients from challenging samples. We show that this problem is amplified by adaptive clipping, which will often shrink the clipping bound to tiny values to match a well-fitting majority, while significantly reducing the accuracy for others. We propose bounded adaptive clipping, which introduces a tunable lower bound to prevent excessive gradient suppression. Our method improves the accuracy of the worst-performing class on average over 10 percentage points on skewed MNIST and Fashion MNIST compared to the unbounded adaptive clipping, and over 5 percentage points over constant clipping.

Mixture of Experts (MoE), an ensemble of specialized models equipped with a router that dynamically distributes each input to appropriate experts, has achieved successful results in the field of machine learning. However, theoretical understanding of this architecture is falling behind due to its inherent complexity. In this paper, we theoretically study the sample and runtime complexity of MoE following the stochastic gradient descent (SGD) when learning a regression task with an underlying cluster structure of single index models. On the one hand, we prove that a vanilla neural network fails in detecting such a latent organization as it can only process the problem as a whole. This is intrinsically related to the concept of information exponent which is low for each cluster, but increases when we consider the entire task. On the other hand, we show that a MoE succeeds in dividing this problem into easier subproblems by leveraging the ability of each expert to weakly recover the simpler function corresponding to an individual cluster. To the best of our knowledge, this work is among the first to explore the benefits of the MoE framework by examining its SGD dynamics in the context of nonlinear regression.

Mutual information (MI) is a measure of statistical dependencies between two variables, widely used in data analysis. Thus, accurate methods for estimating MI from empirical data are crucial. Such estimation is a hard problem, and there are provably no estimators that are universally good for finite datasets. Common estimators struggle with high-dimensional data, which is a staple of modern experiments. Recently, promising machine learning-based MI estimation methods have emerged. Yet it remains unclear if and when they produce accurate results, depending on dataset sizes, statistical structure of the data, and hyperparameters of the estimators, such as the embedding dimensionality or the duration of training. There are also no accepted tests to signal when the estimators are inaccurate. Here, we systematically explore these gaps. We propose and validate a protocol for MI estimation that includes explicit checks ensuring reliability and statistical consistency. Contrary to accepted wisdom, we demonstrate that reliable MI estimation is achievable even with severely undersampled, high-dimensional datasets, provided these data admit accurate low-dimensional representations. These findings broaden the potential use of machine learning-based MI estimation methods in real-world data analysis and provide new insights into when and why modern high-dimensional, self-supervised algorithms perform effectively.

Large language models (LLMs) have become pervasive in our everyday life. Yet, a fundamental obstacle prevents their use in many critical applications: their propensity to generate fluent, human-quality content that is not grounded in reality. The detection of such hallucinations is thus of the highest importance. In this work, we propose a new method to flag hallucinated content, MMD-Flagger. It relies on Maximum Mean Discrepancy (MMD), a non-parametric distance between distributions. On a high-level perspective, MMD-Flagger tracks the MMD between the generated documents and documents generated with various temperature parameters. We show empirically that inspecting the shape of this trajectory is sufficient to detect most hallucinations. This novel method is benchmarked on two machine translation datasets, on which it outperforms natural competitors.