Related papers: Term Orders for Optimistic Lambda-Superposition
We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…
A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal…
The Lasso is a very well known penalized regression model, which adds an $L_{1}$ penalty with parameter $\lambda_{1}$ on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an $L_{1}$…
We consider learning problems of an intuitive and concise preference model, called lexicographic preference lists (LP-lists). Given a set of examples that are pairwise ordinal preferences over a universe of objects built of attributes of…
Existing methods for nonconvex bilevel optimization (NBO) require prior knowledge of first- and second-order problem-specific parameters (e.g., Lipschitz constants and the Polyak-{\L}ojasiewicz (P{\L}) parameters) to set step sizes, a…
This invited paper presents an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations…
Hyperparameter optimization (HPO) is critical for enhancing the performance of machine learning models, yet it often involves a computationally intensive search across a large parameter space. Traditional approaches such as Grid Search and…
The alignment of Large Language Models (LLMs) is crucial for ensuring their safety and reliability in practical applications. Direct Preference Optimization (DPO) has emerged as an efficient method that directly optimizes models using…
Approximate bi-level optimization (ABLO) consists of (outer-level) optimization problems, involving numerical (inner-level) optimization loops. While ABLO has many applications across deep learning, it suffers from time and memory…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
Quadratic Unconstrained Binary Optimization (QUBO) is a standard NP-hard optimization problem. Recently, it has gained renewed interest through quantum computing, as QUBOs directly reduce to the Ising model, on which quantum annealing…
Given the high computational cost of preference alignment training of large language models (LLMs), exploring efficient methods to reduce the training overhead remains an important and compelling research problem. Motivated by the…
We compute the lengths of two particular cases of (possibly non-unital) composition algebras, namely, standard composition algebras and Okubo algebras over an arbitrary field $\mathbb{F}$. These results finish the complete description of…
This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also…
Direct Preference Optimization (DPO) has become a prominent method for aligning Large Language Models (LLMs) with human preferences. While DPO has enabled significant progress in aligning English LLMs, multilingual preference alignment is…
We consider the problem of optimizing expensive black-box functions over high-dimensional combinatorial spaces which arises in many science, engineering, and ML applications. We use Bayesian Optimization (BO) and propose a novel surrogate…
We give an adequate, concrete, categorical-based model for Lambda-S, which is a typed version of a linear-algebraic lambda calculus, extended with measurements. Lambda-S is an extension to first-order lambda calculus unifying two approaches…
The main result from this note provides a constructive characterization of the valuative dimension, which bears a strong analogy to Lombardi's constructive characterization of the Krull dimension. While Lombardi's characterization uses the…
In this paper we derive sufficient conditions for the convergence of two popular alternating minimisation algorithms for dictionary learning - the Method of Optimal Directions (MOD) and Online Dictionary Learning (ODL), which can also be…
We study the problem of aligning large language models (LLMs) with human preference data. Contrastive preference optimization has shown promising results in aligning LLMs with available preference data by optimizing the implicit reward…