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Retrieval-Augmented Generation (RAG) has become a standard approach for knowledge-intensive question answering, but existing systems remain brittle on multi-hop questions, where solving the task requires chaining multiple retrieval and…

The inherent capabilities of a language model (LM) and the reasoning strategies it employs jointly determine its performance in reasoning tasks. While test-time scaling is regarded as an effective approach to tackling complex reasoning…

We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…

Sequence prediction models can be learned from example sequences with a variety of training algorithms. Maximum likelihood learning is simple and efficient, yet can suffer from compounding error at test time. Reinforcement learning such as…

Constraint Handling Rules (CHR) is a rule-based programming language that rewrites collections of constraints. It is typically embedded into a general-purpose language. There exists a plethora of implementation for numerous host languages.…

In his article "Powerlist: A Structure for Parallel Recursion" Jayadev Misra wrote: "Many data parallel algorithms Fast Fourier Transform, Batcher's sorting schemes and prefix sum -exhibit recursive structure. We propose a data structure,…

Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…

Large language models (LLMs) are increasingly used for complex tasks that require multiple generation calls, advanced prompting techniques, control flow, and structured inputs/outputs. However, efficient systems are lacking for programming…

A range of methodologies and techniques are available to guide the design and implementation of language extensions and domain-specific languages. A simple yet powerful technique is based on source-to-source transformations interleaved…

The problem of learning logical rules from examples arises in diverse fields, including program synthesis, logic programming, and machine learning. Existing approaches either involve solving computationally difficult combinatorial problems,…

Narrowing is a procedure that was first studied in the context of equational E-unification and that has been used in a wide range of applications. The classic completeness result due to Hullot states that any term rewriting derivation…

We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…

Practical guidance on training Large Language Models (LLMs) to leverage Code Interpreter across diverse tasks remains lacking. We present R1-Code-Interpreter, an extension of a text-only LLM trained via multi-turn supervised fine-tuning…

The use of Reinforcement Learning in real-world scenarios is strongly limited by issues of scale. Most RL learning algorithms are unable to deal with problems composed of hundreds or sometimes even dozens of possible actions, and therefore…

Program synthesis with Genetic Programming searches for a correct program that satisfies the input specification, which is usually provided as input-output examples. One particular challenge is how to effectively handle loops and recursion…

Group relative policy optimization (GRPO) has demonstrated significant potential in improving the reasoning capabilities of large language models (LLMs) via reinforcement learning. However, its practical deployment is impeded by an…

As test-time scaling becomes a pivotal research frontier in Large Language Models (LLMs) development, contemporary and advanced post-training methodologies increasingly focus on extending the generation length of long Chain-of-Thought (CoT)…

Drawdown (resp. drawup) of a stochastic process, also referred as the reflected process at its supremum (resp. infimum), has wide applications in many areas including financial risk management, actuarial mathematics and statistics. In this…

For many applications involving a sequence of linear systems with slowly changing system matrices, subspace recycling, which exploits relationships among systems and reuses search space information, can achieve huge gains in iterations…

Automatic differentiation is a technique which allows a programmer to define a numerical computation via compositions of a broad range of numeric and computational primitives and have the underlying system support the computation of partial…