Related papers: Goedel Machines: Self-Referential Universal Proble…
Query Reformulation (QR) is a set of techniques used to transform a user's original search query to a text that better aligns with the user's intent and improves their search experience. Recently, zero-shot QR has been a promising approach…
The recently introduced Gradient Methods with Memory use a subset of the past oracle information to create an accurate model of the objective function that enables them to surpass the Gradient Method in practical performance. The model…
Iteration methods based on barycentric rational interpolation are derived that exhibit accelerating orders of convergence. For univariate root search, the derivative-free methods approach quadratic convergence and the first-derivative…
Reinforcement learning with verifiable rewards (RLVR) has shown promise in enhancing the reasoning performance of large language models (LLMs) by increasing test-time compute. However, even after extensive RLVR training, such models still…
Large language models have achieved remarkable success on final-answer mathematical problems, largely due to the ease of applying reinforcement learning with verifiable rewards. However, the reasoning underlying these solutions is often…
<Q>_e is the effective list of all finite predicate logic programs. <T_e> is the list of recursive trees. We modify constructions of Marek, Nerode, and Remmel [25] to construct recursive functions f and g such that for all indices e, (i)…
Context: Recent research indicates that Web queries written by software developers are not very successful in retrieving relevant results, performing measurably worse compared to general purpose Web queries. Most approaches up to this point…
We identify a structural property of term-rewriting proof systems called operational inexpressibility: no derivation depends on a specified input dimension and also constrains the target question. The canonical instance is direct…
Information retrieval models have witnessed a paradigm shift from unsupervised statistical approaches to feature-based supervised approaches to completely data-driven ones that make use of the pre-training of large language models. While…
Goedel Incompleteness Theorem leaves open a way around it, vaguely perceived for a long time but not clearly identified. (Thus, Goedel believed informal arguments can answer any math question.) Closing this loophole does not seem obvious…
Large Language Models (LLMs) often fail to utilize their latent reasoning capabilities due to a distributional mismatch between ambiguous human inquiries and the structured logic required for machine activation. Existing alignment methods…
Retrieval-Augmented Generation (RAG) systems for Large Language Models (LLMs) hold promise in knowledge-intensive tasks but face limitations in complex multi-step reasoning. While recent methods have integrated RAG with chain-of-thought…
Recently, slow-thinking systems like GPT-o1 and DeepSeek-R1 have demonstrated great potential in solving challenging problems through explicit reflection. They significantly outperform the best fast-thinking models, such as GPT-4o, on…
An algorithm $M$ is described that solves any well-defined problem $p$ as quickly as the fastest algorithm computing a solution to $p$, save for a factor of 5 and low-order additive terms. $M$ optimally distributes resources between the…
A fundamental challenge in neurosymbolic systems is applying continuous gradient-based optimization to discrete logical domains. While fuzzy relaxations provide differentiability, they often lack a formal structural alignment with classical…
We introduce Refinement Reflection, a new framework for building SMT-based deductive verifiers. The key idea is to reflect the code implementing a user-defined function into the function's (output) refinement type. As a consequence, at uses…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Refinement Reflection turns your favorite programming language into a proof assistant by reflecting the code implementing a user-defined function into the function's (output) refinement type. As a consequence, at uses of the function, the…
Most functional languages rely on some garbage collection for automatic memory management. They usually eschew reference counting in favor of a tracing garbage collector, which has less bookkeeping overhead at runtime. On the other hand,…
Query rewrite is essential for optimizing SQL queries to improve their execution efficiency without changing their results. Traditionally, this task has been tackled through heuristic and learning-based methods, each with its limitations in…