Related papers: Limits of CDCL Learning via Merge Resolution

Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs…

This paper presents a general framework to integrate prior knowledge in the form of logic constraints among a set of task functions into kernel machines. The logic propositions provide a partial representation of the environment, in which…

Many of the machine learning (ML) tasks are focused on centralized learning (CL), which requires the transmission of local datasets from the clients to a parameter server (PS) leading to a huge communication overhead. Federated learning…

Current evaluations of Continual Learning (CL) methods typically assume that there is no constraint on training time and computation. This is an unrealistic assumption for any real-world setting, which motivates us to propose: a practical…

We propose a new parameter called proofdoor in an attempt to explain the efficiency of CDCL SAT solvers over formulas derived from circuit (esp., arithmetic) verification applications. Informally, given an unsatisfiable CNF formula F over n…

Large Language Models (LLMs) have achieved remarkable performance across various reasoning tasks, yet post-training is constrained by inefficient sample utilization and inflexible difficulty samples processing. To address these limitations,…

Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems for polynomial systems over the reals. It has long been studied by the Symbolic Computation…

Over the past few decades, combinatorial solvers have seen remarkable performance improvements, enabling their practical use in real-world applications. In some of these applications, ensuring the correctness of the solver's output is…

The success of Conflict Driven Clause Learning (CDCL) for Boolean satisfiability has inspired adoption in other domains. We present a novel lifting of CDCL to program analysis called Abstract Conflict Driven Learning for Programs (ACDLP).…

The emergence of in-context learning (ICL) enables large pre-trained language models (PLMs) to make predictions for unseen inputs without updating parameters. Despite its potential, ICL's effectiveness heavily relies on the quality,…

Multimodal LLMs can accurately perceive numerical content across modalities yet fail to perform exact multi-digit multiplication when the identical underlying arithmetic problem is presented as numerals, number words, images, or in audio…

Complementary-Label Learning (CLL) is a weakly-supervised learning problem that aims to learn a multi-class classifier from only complementary labels, which indicate a class to which an instance does not belong. Existing approaches mainly…

Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…

Self-evolving scientific agents capable of conquering the hard tail of formal mathematics require Compositional Learning Behaviours (CLBs) -- the capacity to ground and recombine novel symbolic structures in context, beyond mere…

We study the problem of obtaining lower bounds for polynomial calculus (PC) and polynomial calculus resolution (PCR) on proof degree, and hence by [Impagliazzo et al. '99] also on proof size. [Alekhnovich and Razborov '03] established that…

Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has…

Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…

Continual Learning (CL) aims to enable models to continuously acquire new knowledge from a sequence of tasks with avoiding the forgetting of learned information. However, existing CL methods only rely on the parameters of the most recent…

We propose and study a realistic Continual Learning (CL) setting where learning algorithms are granted a restricted computational budget per time step while training. We apply this setting to large-scale semi-supervised Continual Learning…

Complementary Labels Learning (CLL) arises in many real-world tasks such as private questions classification and online learning, which aims to alleviate the annotation cost compared with standard supervised learning. Unfortunately, most…