Related papers: Tight Typings and Split Bounds

We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…

In this study, we propose a structured methodology that utilizes large language models (LLMs) in a cost-efficient and parsimonious manner, integrating the strengths of scholars and machines while offsetting their respective weaknesses. Our…

Harnessing the power of dependently typed languages can be difficult. Programmers must manually construct proofs to produce well-typed programs, which is not an easy task. In particular, migrating code to these languages is challenging.…

We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…

This paper addresses the challenge of solving Constrained Markov Decision Processes (CMDPs) with $d > 1$ constraints when the transition dynamics are unknown, but samples can be drawn from a generative model. We propose a model-based…

Large language models (LLMs) demonstrate outstanding performance in various tasks in machine learning and have thus become one of the most important workloads in today's computing landscape. However, deploying LLM inference poses challenges…

While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…

Policy evaluation in reinforcement learning is often conducted using two-timescale stochastic approximation, which results in various gradient temporal difference methods such as GTD(0), GTD2, and TDC. Here, we provide convergence rate…

Large language model (LLM) has marked a pivotal moment in the field of machine learning and deep learning. Recently its capability for query planning has been investigated, including both single-modal and multi-modal queries. However, there…

Large Language Models (LLMs) are increasingly applied to complex tasks that require extended reasoning. In such settings, models often benefit from diverse chains-of-thought to arrive at multiple candidate solutions. This requires two…

We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…

The viability of chain-of-thought (CoT) monitoring hinges on models being unable to reason effectively in their latent representations. Yet little is known about the limits of such latent reasoning in LLMs. We test these limits by studying…

Penalty methods are a well known class of algorithms for constrained optimization. They transform a constrained problem into a sequence of unconstrained \emph{penalized} problems in the hope that approximate solutions of the latter converge…

Large Language Models (LLMs) have exhibited remarkable capabilities in many complex tasks including mathematical reasoning. However, traditional approaches heavily rely on ensuring self-consistency within single prompting method, which…

Natural generation allows Large Language Models (LLMs) to produce free-form responses with rich reasoning, yet the lack of structure makes outputs difficult to verify. Conversely, constrained decoding ensures standardized formats but can…

A fundamental component of neural network verification is the computation of bounds on the values their outputs can take. Previous methods have either used off-the-shelf solvers, discarding the problem structure, or relaxed the problem even…

A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…

Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle…

We present a new algorithm for computing upper bounds on the number of executions of each program instruction during any single program run. The upper bounds are expressed as functions of program input values. The algorithm is primarily…

This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…