相关论文: Subsumption Demodulation in First-Order Theorem Pr…

Optimization problems often involve vector norms, which has led to extensive research on developing algorithms that can handle objectives beyond the $\ell_p$ norms. Our work introduces the concept of submodular norms, which are a versatile…

\emph{Approximation Theory} uses nicely-behaved subcategories to understand entire categories, just as projective modules are used to approximate arbitrary modules in classical homological algebra. We use set-theoretic \emph{elementary…

We are motivated by large scale submodular optimization problems, where standard algorithms that treat the submodular functions in the \emph{value oracle model} do not scale. In this paper, we present a model called the…

Reverse-mode differentiation is used for optimization, but it introduces references, which break the purity of the underlying programs, making them notoriously harder to optimize. We present a reverse-mode differentiation on a purely…

Subword-level models have been the dominant paradigm in NLP. However, character-level models have the benefit of seeing each character individually, providing the model with more detailed information that ultimately could lead to better…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…

In view of training increasingly complex learning architectures, we establish a nonsmooth implicit function theorem with an operational calculus. Our result applies to most practical problems (i.e., definable problems) provided that a…

Table-based reasoning has shown remarkable progress in combining deep models with discrete reasoning, which requires reasoning over both free-form natural language (NL) questions and structured tabular data. However, previous table-based…

Fast algorithms for submodular maximization problems have a vast potential use in applicative settings, such as machine learning, social networks, and economics. Though fast algorithms were known for some special cases, only recently…

Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search. Deep reinforcement learning has been proposed as a way to obviate the need for such heuristics, however, its deployment…

A fundamental task underlying many important optimization problems, from influence maximization to sensor placement to content recommendation, is to select the optimal group of $k$ items from a larger set. Submodularity has been very…

Despite demonstrating emergent reasoning abilities, Large Language Models (LLMS) often lose track of complex, multi-step reasoning. Existing studies show that providing guidance via decomposing the original question into multiple…

We study abduction in First Order Horn logic theories where all atoms can be abduced and we are looking for preferred solutions with respect to three objective functions: cardinality minimality, coherence, and weighted abduction. We…

Open rule refer to the implication from premise atoms to hypothesis atoms, which captures various relations between instances in the real world. Injecting open rule knowledge into the machine helps to improve the performance of downstream…

Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…

Standard gradient descent methods are susceptible to a range of issues that can impede training, such as high correlations and different scaling in parameter space.These difficulties can be addressed by second-order approaches that apply a…

This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…

Dependently-typed proof assistants furnish expressive foundations for mechanised mathematics and verified software. However, automation for these systems has been either modest in scope or complex in implementation. We aim to improve the…