In this paper, we explore the properties of loss curvature with respect to input data in deep neural networks. Curvature of loss with respect to input (termed input loss curvature) is the trace of the Hessian of the loss with respect to the input. We investigate how input loss curvature varies between train and test sets, and its implications for train-test distinguishability. We develop a theoretical framework that derives an upper bound on the train-test distinguishability based on privacy and the size of the training set.

Scaling deep learning models has been at the heart of recent revolutions in language modelling and image generation. Practitioners have observed a strong relationship between model size, dataset size, and performance. However, structure-based architectures such as Graph Neural Networks (GNNs) are yet to show the benefits of scale mainly due to lower efficiency of sparse operations, large data requirements, and lack of clarity about the effectiveness of various architectures. We address this drawback of GNNs by studying their scaling behavior. Specifically, we analyze message-passing networks, graph Transformers, and hybrid architectures on the largest public collection of 2D molecular graphs for supervised pretraining.

The lack of transparency in the decision-making processes of deep learning systems presents a significant challenge in modern artificial intelligence (AI), as it impairs users' ability to rely on and verify these systems. To address this challenge, Concept Bottleneck Models (CBMs) have made significant progress by incorporating human-interpretable concepts into deep learning architectures. This approach allows predictions to be traced back to specific concept patterns that users can understand and potentially intervene on. However, existing CBMs' task predictors are not fully interpretable, preventing a thorough analysis and any form of formal verification of their decision-making process prior to deployment, thereby raising significant reliability concerns. To bridge this gap, we introduce Concept-based Memory Reasoner (CMR), a novel CBM designed to provide a human-understandable and provably-verifiable task prediction process. Our approach is to model each task prediction as a neural selection mechanism over a memory of learnable logic rules, followed by a symbolic evaluation of the selected rule. The presence of an explicit memory and the symbolic evaluation allow domain experts to inspect and formally verify the validity of certain global properties of interest for the task prediction process. Experimental results demonstrate that CMR achieves better accuracy-interpretability trade-offs to state-of-the-art CBMs, discovers logic rules consistent with ground truths, allows for rule interventions, and allows pre-deployment verification.

Recent advances in generative AI have led to increasingly realistic synthetic data, yet evaluation criteria remain focused on marginal distribution matching. While these diagnostics assess local realism, they provide limited insight into whether a generative model preserves the multivariate dependence structures governing downstream inference. We introduce covariance-level dependence fidelity as a practical criterion for evaluating whether a generative distribution preserves joint structure beyond univariate marginals. We establish three core results. First, distributions can match all univariate marginals exactly while exhibiting substantially different dependence structures, demonstrating marginal fidelity alone is insufficient. Second, dependence divergence induces quantitative instability in downstream inference, including sign reversals in regression coefficients despite identical marginal behavior. Third, explicit control of covariance-level dependence divergence ensures stable behavior for dependence-sensitive tasks such as principal component analysis. Synthetic constructions illustrate how dependence preservation failures lead to incorrect conclusions despite identical marginal distributions. These results highlight dependence fidelity as a useful diagnostic for evaluating generative models in dependence-sensitive downstream tasks, with implications for diffusion models and variational autoencoders. These guarantees apply specifically to procedures governed by covariance structure; tasks requiring higher-order dependence such as tail-event estimation require richer criteria.

Understanding the distance between human languages is central to linguistics, anthropology, and tracing human evolutionary history. Yet, while linguistics has long provided rich qualitative accounts of cross-linguistic variation, a unified and scalable quantitative approach to measuring language distance remains lacking. In this paper, we introduce a method that leverages pretrained multilingual language models as systematic instruments for linguistic measurement. Specifically, we show that the spontaneously emerged attention mechanisms of these models provide a robust, tokenization-agnostic measure of cross-linguistic distance, termed Attention Transport Distance (ATD). By treating attention matrices as probability distributions and measuring their geometric divergence via optimal transport, we quantify the representational distance between languages during translation. Applying ATD to a large and diverse set of languages, we demonstrate that the resulting distances recover established linguistic groupings with high fidelity and reveal patterns aligned with geographic and contact-induced relationships. Furthermore, incorporating ATD as a regularizer improves transfer performance in low-resource machine translation. Our results establish a principled foundation for testing linguistic hypotheses using artificial neural networks. This framework transforms multilingual models into powerful tools for quantitative linguistic discovery, facilitating more equitable multilingual AI.

Neural networks are central to modern artificial intelligence, yet their training remains highly sensitive to data contamination. Standard neural classifiers are trained by minimizing the categorical cross-entropy loss, corresponding to maximum likelihood estimation under a multinomial model. While statistically efficient under ideal conditions, this approach is highly vulnerable to contaminated observations including label noises corrupting supervision in the output space, and adversarial perturbations inducing worst-case deviations in the input space. In this paper, we propose a unified and statistically grounded framework for robust neural classification that addresses both forms of contamination within a single learning objective. We formulate neural network training as a minimum-divergence estimation problem and introduce rSDNet, a robust learning algorithm based on the general class of $S$-divergences. The resulting training objective inherits robustness properties from classical statistical estimation, automatically down-weighting aberrant observations through model probabilities. We establish essential population-level properties of rSDNet, including Fisher consistency, classification calibration implying Bayes optimality, and robustness guarantees under uniform label noise and infinitesimal feature contamination. Experiments on three benchmark image classification datasets show that rSDNet improves robustness to label corruption and adversarial attacks while maintaining competitive accuracy on clean data, Our results highlight minimum-divergence learning as a principled and effective framework for robust neural classification under heterogeneous data contamination.

In the field of computational advertising, the integration of ads into the outputs of large language models (LLMs) presents an opportunity to support these services without compromising content integrity. This paper introduces novel auction mechanisms for ad allocation and pricing within the textual outputs of LLMs, leveraging retrieval-augmented generation (RAG). We propose a \emph{segment auction} where an ad is probabilistically retrieved for each discourse segment (paragraph, section, or entire output) according to its bid and relevance, following the RAG framework, and priced according to competing bids. We show that our auction maximizes logarithmic social welfare, a new notion of welfare that balances allocation efficiency and fairness, and we characterize the associated incentive-compatible pricing rule. These results are extended to multi-ad allocation per segment. An empirical evaluation validates the feasibility and effectiveness of our approach over several ad auction scenarios, and exhibits inherent tradeoffs in metrics as we allow the LLM more flexibility to allocate ads.

We propose ESPACE, an LLM compression technique based on dimensionality reduction of activations. Unlike prior works on weight-centric tensor decomposition, ESPACE projects activations onto a pre-calibrated set of principal components. The activation-centrality of the approach enables retraining LLMs with no loss of expressivity; while at inference, weight decomposition is obtained as a byproduct of matrix multiplication associativity. Theoretical results on the construction of projection matrices with optimal computational accuracy are provided. Experimentally, we find ESPACE enables 50% compression of GPT3, Llama2, and Nemotron4 models with small accuracy degradation, as low as a 0.18 perplexity increase on GPT3-22B. At lower compression rates of 20% to 40%, ESPACE drives GPT3 models to outperforming their baseline, by up to a 0.38 decrease in perplexity for GPT3-8B. ESPACE also reduces GEMM execution time and prefill inference latency on existing hardware. Comparison with related works on compressing Llama2-7B via matrix factorization shows that ESPACE is a first step in advancing the state-of-the-art in tensor decomposition compression of LLMs.

Vision-language models (VLMs) have made significant progress in recent visual-question-answering (VQA) benchmarks that evaluate complex visio-linguistic reasoning. However, are these models truly effective? In this work, we show that VLMs still struggle with natural images and questions that humans can easily answer, which we term $\textbf{natural adversarial samples}$. We also find it surprisingly easy to generate these VQA samples from natural image-text corpora using off-the-shelf models like CLIP and ChatGPT. We propose a semi-automated approach to collect a new benchmark, ${\bf NaturalBench}$, for reliably evaluating VLMs with 10,000 human-verified VQA samples.

Recurrent Neural Networks (RNNs) are used to learn representations in partially observable environments. For agents that learn online and continually interact with the environment, it is desirable to train RNNs with real-time recurrent learning (RTRL); unfortunately, RTRL is prohibitively expensive for standard RNNs. A promising direction is to use linear recurrent architectures (LRUs), where dense recurrent weights are replaced with a complex-valued diagonal, making RTRL efficient. In this work, we build on these insights to provide a lightweight but effective approach for training RNNs in online RL. We introduce Recurrent Trace Units (RTUs), a small modification on LRUs that we nonetheless find to have significant performance benefits over LRUs when trained with RTRL. We find RTUs significantly outperform GRUs and Transformers across several partially observable environments while using significantly less computation.