Related papers: Goedel Machines: Self-Referential Universal Proble…

Knowledge-intensive language tasks require NLP systems to both provide the correct answer and retrieve supporting evidence for it in a given corpus. Autoregressive language models are emerging as the de-facto standard for generating…

Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…

Code refactoring is a fundamental software engineering practice aimed at improving code quality and maintainability. Despite its importance, developers often neglect refactoring due to the significant time, effort, and resources it…

We present two algorithms for constructing orthonormal bases of rational function vectors with respect to a discrete inner product, and discuss how to use them for a rational approximation problem. Building on the pencil-based formulation…

Recent reasoning-focused language models such as DeepSeek R1 and OpenAI o1 have demonstrated strong performance on structured reasoning benchmarks including GSM8K, MATH, and multi-hop question answering tasks. However, their performance…

This article discusses completeness of Boolean Algebra as First Order Theory in Goedel's meaning. If Theory is complete then any possible transformation is equivalent to some transformation using axioms, predicates etc. defined for this…

One of the challenges in optimization of high dimensional problems is finding appropriate solutions in a way that are as close as possible to the global optima. In this regard, one of the most common phenomena that occurs is the curse of…

Code super-optimization is the task of transforming any given program to a more efficient version while preserving its input-output behaviour. In some sense, it is similar to the paraphrase problem from natural language processing where the…

Sequential learning systems are used in a wide variety of problems from decision making to optimization, where they provide a 'belief' (opinion) to nature, and then update this belief based on the feedback (result) to minimize (or maximize)…

The success of DeepSeek-R1 demonstrates the immense potential of using reinforcement learning (RL) to enhance LLMs' reasoning capabilities. This paper introduces Retrv-R1, the first R1-style MLLM specifically designed for multimodal…

Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not…

The search of information in large text repositories has been plagued by the so-called document-query vocabulary gap, i.e. the semantic discordance between the contents in the stored document entities on the one hand and the human query on…

Large language models are increasingly solving tasks that are commonly believed to require human-level reasoning ability. However, these models still perform very poorly on benchmarks of general intelligence such as the Abstraction and…

Improved local numerical solution for the ADER-DG numerical method with a local DG predictor for solving the initial value problem for a first-order ODE system is proposed. The improved local numerical solution demonstrates convergence…

Large Language Models (LLMs) have achieved remarkable capabilities, yet their improvement methods remain fundamentally constrained by human design. We present Self-Developing, a framework that enables LLMs to autonomously discover,…

The Retrieval-Augmented Language Model (RALM) has shown remarkable performance on knowledge-intensive tasks by incorporating external knowledge during inference, which mitigates the factual hallucinations inherited in large language models…

We present a new algorithm to solve polynomial equations, and publish its code, which is 1.6-3 times faster than the ZROOTS subroutine that is commercially available from Numerical Recipes, depending on application. The largest improvement,…

Resolution and superposition are common techniques which have seen widespread use with propositional and first-order logic in modern theorem provers. In these cases, resolution proof production is a key feature of such tools; however, the…

We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler…

It is common to encounter situations where one must solve a sequence of similar computational problems. Running a standard algorithm with worst-case runtime guarantees on each instance will fail to take advantage of valuable structure…