Related papers: Iterate to Accelerate: A Unified Framework for Ite…
Self-improvement is a critical capability for large language models and other intelligent systems, enabling them to refine their behavior and internal consistency without external supervision. Despite its importance, prior approaches…
Measuring how quickly iterative methods converge is essential in computational mathematics, but current approaches have significant limitations. Q-order analysis requires strict smoothness conditions, while R-order analysis lacks precision…
Large pre-trained models exhibit distinct and complementary capabilities dependent on the data they are trained on. Language models such as GPT-3 are capable of textual reasoning but cannot understand visual information, while vision models…
Recent Iterated Response (IR) models of pragmatics conceptualize language use as a recursive process in which agents reason about each other to increase communicative efficiency. These models are generally defined over complete utterances.…
Recently, there has been significant progress in the development of distributed first order methods. (At least) two different types of methods, designed from very different perspectives, have been proposed that achieve both exact and linear…
Training large language models with reinforcement learning (RL) against verifiable rewards significantly enhances their reasoning abilities, yet remains computationally expensive due to inefficient uniform prompt sampling. We introduce…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
Scaling test-time compute via long Chain-of-Thought unlocks remarkable gains in reasoning capabilities, yet it faces practical limits due to the linear growth of KV cache and quadratic attention complexity. In this paper, we introduce…
Evaluating the alignment between textual prompts and generated images is critical for ensuring the reliability and usability of text-to-image (T2I) models. However, most existing evaluation methods rely on coarse-grained metrics or static…
Retrieval-Augmented Generation (RAG) systems enhance text generation by incorporating external knowledge but often struggle when retrieving context across different text modalities due to semantic gaps. We introduce a generalized…
While multi-modal learning has advanced significantly, current approaches often create inconsistencies in representation and reasoning of different modalities. We propose UMaT, a theoretically-grounded framework that unifies visual and…
We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent…
It is well known that mirror descent may diverge or cycle on merely monotone variational inequalities. In this paper, we propose \emph{Target Mirror Descent} (TMD), a unified framework that stabilizes monotone flows via a target point…
Large Language Models (LLMs) have made remarkable breakthroughs in reasoning, yet continue to struggle with hallucinations, logical errors, and inability to self-correct during complex multi-step tasks. Current approaches like…
Existing prompt-optimization techniques rely on local signals to update behavior, often neglecting broader and recurring patterns across tasks, leading to poor generalization; they further rely on full-prompt rewrites or unstructured…
Recent advances in large language models (LLMs) have made reasoning a central benchmark for evaluating intelligence. While prior surveys focus on efficiency by examining how to shorten reasoning chains or reduce computation, this view…
Iterative algorithms based on thresholding, feedback and null space tuning (NST+HT+FB) for sparse signal recovery are exceedingly effective and fast, particularly for large scale problems. The core algorithm is shown to converge in finitely…
Large language models (LLMs) have been routinely used to solve various tasks using step-by-step reasoning. However, the structure of intermediate reasoning steps, or thoughts, is rigid and unidirectional, such as chains, trees, or…
Classical mathematical models of information sharing and updating in multi-agent networks use linear operators. In the paradigmatic DeGroot model, agents update their states with linear combinations of their neighbors' current states. In…
We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…