Many training methods, such as Adam(W) and Shampoo, learn a positive-definite curvature matrix and apply an inverse root before preconditioning. Recently, non-diagonal training methods, such as Shampoo, have gained significant attention; however, they remain computationally inefficient and are limited to specific types of curvature information due to the costly matrix root computation via matrix decomposition. To address this, we propose a Riemannian optimization approach that dynamically adapts spectral-factorized positive-definite curvature estimates, enabling the efficient application of arbitrary matrix roots and generic curvature learning. We demonstrate the efficacy and versatility of our approach in positive-definite matrix optimization and covariance adaptation for gradient-free optimization, as well as its efficiency in curvature learning for neural net training.

We examine the representation of African American English (AAE) in large language models (LLMs), exploring (a) the perceptions Black Americans have of how effective these technologies are at producing authentic AAE, and (b) in what contexts Black Americans find this desirable. Through both a survey of Black Americans ($n=$ 104) and annotation of LLM-produced AAE by Black Americans ($n=$ 228), we find that Black Americans favor choice and autonomy in determining when AAE is appropriate in LLM output. They tend to prefer that LLMs default to communicating in Mainstream U.S. English in formal settings, with greater interest in AAE production in less formal settings. When LLMs were appropriately prompted and provided in context examples, our participants found their outputs to have a level of AAE authenticity on par with transcripts of Black American speech. Select code and data for our project can be found here: https://github.com/smelliecat/AAEMime.git

Previously, methods for learning marginally stable linear dynamical systems either required the transition matrix to be symmetric or incurred regret bounds that scale polynomially with the system's hidden dimension. In this work, we introduce a novel method that overcomes this trade-off, achieving dimension-free regret despite the presence of asymmetric matrices and marginal stability. Our method combines spectral filtering with linear predictors and employs Chebyshev polynomials in the complex plane to construct a novel spectral filtering basis. This construction guarantees sublinear regret in an online learning framework, without relying on any statistical or generative assumptions. Specifically, we prove that as long as the transition matrix has eigenvalues with complex component bounded by $1/\mathrm{poly} \log T$, then our method achieves regret $\tilde{O}(T^{9/10})$ when compared to the best linear dynamical predictor in hindsight.

Recent advances in machine learning have transformed our ability to develop high quality predictive and generative models for complex data. This work introduces a framework for developing decisionmaking algorithms, specifically for contextual bandit problems, that can take advantage of these machine learning advances. By design, we assume the algorithm developer is able to effectively apply these machine learning techniques (e.g., minimize a loss via gradient descent) and employ these methods as subroutines in our decision-making algorithm. Moreover, our theory formally connects the quality of effective (self-)supervised learning via loss minimization to the quality of decision-making. Classically, contextual Thompson sampling algorithms form a parametric model of the environment and consider the decision-maker's uncertainty as arising from unknown latent parameters of that model [51]. In this classical perspective, the primitive operations that are assumed to be feasible (at least approximately) include i) the ability to specify an informative prior for the latent parameter using domain knowledge, ii) the ability to sample from the posterior distribution of the latent parameter, and iii) the ability to update the posterior distribution as more data is collected. Unfortunately, it is well known that all three of these primitive operations are non-trivial to perform with neural networks [20, 61]. Building on our previous work [8] which focuses on multi-armed bandits without contexts, we view missing, but potentially observable, future outcomes as the source of the decision-maker's uncertainty. This perspective allows us to replace the primitive operations required in the classical view with new primitives that are more compatible with neural networks: i) the ability to effectively minimize an offline sequence prediction loss, ii) the ability to autoregressively generate from the optimized sequence model, and iii) the ability to fit a desired policy given access to a complete dataset (outcomes from all actions and decision-times).

In this work, we argue that large language models (LLMs), though trained to predict only the next token, exhibit emergent planning behaviors: $\textbf{their hidden representations encode future outputs beyond the next token}$. Through simple probing, we demonstrate that LLM prompt representations encode global attributes of their entire responses, including $\textit{structural attributes}$ (response length, reasoning steps), $\textit{content attributes}$ (character choices in storywriting, multiple-choice answers at the end of response), and $\textit{behavioral attributes}$ (answer confidence, factual consistency). In addition to identifying response planning, we explore how it scales with model size across tasks and how it evolves during generation. The findings that LLMs plan ahead for the future in their hidden representations suggests potential applications for improving transparency and generation control.

In modern large-scale deep learning, a prevalent and effective workflow for solving low-data problems is adapting powerful pre-trained foundation models (FMs) to new tasks via parameter-efficient fine-tuning (PEFT). However, while empirically effective, the resulting solutions lack generalisation guarantees to certify their accuracy - which may be required for ethical or legal reasons prior to deployment in high-importance applications. In this paper we develop a novel transfer learning approach that is designed to facilitate non-vacuous learning theoretic generalisation guarantees for downstream tasks, even in the low-shot regime. Specifically, we first use upstream tasks to train a distribution over PEFT parameters. We then learn the downstream task by a sample-and-evaluate procedure -- sampling plausible PEFTs from the trained diffusion model and selecting the one with the highest likelihood on the downstream data. Crucially, this confines our model hypothesis to a finite set of PEFT samples. In contrast to learning in the typical continuous hypothesis spaces of neural network weights, this facilitates tighter risk certificates. We instantiate our bound and show non-trivial generalization guarantees compared to existing learning approaches which lead to vacuous bounds in the low-shot regime.

In traditional machine learning, models are defined by a set of parameters, which are optimized to perform specific tasks. In neural networks, these parameters correspond to the synaptic weights. However, in reality, it is often infeasible to control or update all weights. This challenge is not limited to artificial networks but extends to biological networks, such as the brain, where the extent of distributed synaptic weight modification during learning remains unclear. Motivated by these insights, we theoretically investigate how different allocations of a fixed number of learnable weights influence the capacity of neural networks. Using a teacher-student setup, we introduce a benchmark to quantify the expressivity associated with each allocation. We establish conditions under which allocations have maximal or minimal expressive power in linear recurrent neural networks and linear multi-layer feedforward networks. For suboptimal allocations, we propose heuristic principles to estimate their expressivity. These principles extend to shallow ReLU networks as well. Finally, we validate our theoretical findings with empirical experiments. Our results emphasize the critical role of strategically distributing learnable weights across the network, showing that a more widespread allocation generally enhances the network's expressive power.

We study the fundamental problem of offline assortment optimization under the Multinomial Logit (MNL) model, where sellers must determine the optimal subset of the products to offer based solely on historical customer choice data. While most existing approaches to learning-based assortment optimization focus on the online learning of the optimal assortment through repeated interactions with customers, such exploration can be costly or even impractical in many real-world settings. In this paper, we consider the offline learning paradigm and investigate the minimal data requirements for efficient offline assortment optimization. To this end, we introduce Pessimistic Rank-Breaking (PRB), an algorithm that combines rank-breaking with pessimistic estimation. We prove that PRB is nearly minimax optimal by establishing the tight suboptimality upper bound and a nearly matching lower bound. This further shows that "optimal item coverage" - where each item in the optimal assortment appears sufficiently often in the historical data - is both sufficient and necessary for efficient offline learning. This significantly relaxes the previous requirement of observing the complete optimal assortment in the data. Our results provide fundamental insights into the data requirements for offline assortment optimization under the MNL model.

This paper introduces Text2Net, an innovative text-based network simulation engine that leverages natural language processing (NLP) and large language models (LLMs) to transform plain-text descriptions of network topologies into dynamic, interactive simulations. Text2Net simplifies the process of configuring network simulations, eliminating the need for users to master vendor-specific syntaxes or navigate complex graphical interfaces. Through qualitative and quantitative evaluations, we demonstrate Text2Net's ability to significantly reduce the time and effort required to deploy network scenarios compared to traditional simulators like EVE-NG. By automating repetitive tasks and enabling intuitive interaction, Text2Net enhances accessibility for students, educators, and professionals. The system facilitates hands-on learning experiences for students that bridge the gap between theoretical knowledge and practical application. The results showcase its scalability across various network complexities, marking a significant step toward revolutionizing network education and professional use cases, such as proof-of-concept testing.

AI advancements have been significantly driven by a combination of foundation models and curiosity-driven learning aimed at increasing capability and adaptability. A growing area of interest within this field is Open-Endedness - the ability of AI systems to continuously and autonomously generate novel and diverse artifacts or solutions. This has become relevant for accelerating scientific discovery and enabling continual adaptation in AI agents. This position paper argues that the inherently dynamic and self-propagating nature of Open-Ended AI introduces significant, underexplored risks, including challenges in maintaining alignment, predictability, and control. This paper systematically examines these challenges, proposes mitigation strategies, and calls for action for different stakeholders to support the safe, responsible and successful development of Open-Ended AI.