Related papers: Linear Additives
While machine-learning models are flourishing and transforming many aspects of everyday life, the inability of humans to understand complex models poses difficulties for these models to be fully trusted and embraced. Thus, interpretability…
We introduce a new framework called linear algebraic number theory (LANT) that reformulates the number-theoretic problem as a regression model and solves it using matrix algebra. This framework restricts all computations to log space,…
We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…
One of the fundamental challenges in reinforcement learning (RL) is to take a complex task and be able to decompose it to subtasks that are simpler for the RL agent to learn. In this paper, we report on our work that would identify subtasks…
A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommutative operations are often not sufficient for modeling even…
Rule learning-based models are widely used in highly interpretable scenarios due to their transparent structures. Inductive logic programming (ILP), a form of machine learning, induces rules from facts while maintaining interpretability.…
MLsub is a minimal language with a type system combining subtyping and parametric polymorphism and a type inference algorithm which infers compact principal types. Simple-sub is an alternative inference algorithm which can be implemented…
Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous…
In several supervised learning scenarios, auxiliary losses are used in order to introduce additional information or constraints into the supervised learning objective. For instance, knowledge distillation aims to mimic outputs of a powerful…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
This work studies the linear convergence of an accelerated scheme of the Alternating Direction Method of Multipliers (ADMM) for strongly convex and Lipschitz-smooth problems. We use the methodology of expressing the accelerated ADMM as a…
Linear/non-linear (LNL) models, as described by Benton, soundly model a LNL term calculus and LNL logic closely related to intuitionistic linear logic. Every such model induces a canonical enrichment that we show soundly models a LNL lambda…
We provide a proof of strong normalisation for lambda+, a recently introduced, explicitly typed, non-deterministic lambda-calculus where isomorphic propositions are identified. Such a proof is a non-trivial adaptation of the reducibility…
Transition Algebra (TA) is a type of infinite logic introduced to discuss rewriting systems. The natural deductive proof systems already introduced in TA satisfy completeness for countable signatures. However, it lacks compactness, making…
Learning to Optimize (L2O) approaches, including algorithm unrolling, plug-and-play methods, and hyperparameter learning, have garnered significant attention and have been successfully applied to the Alternating Direction Method of…
Service composition remains a central challenge in building adaptive and intelligent software systems, often constrained by limited reasoning capabilities or brittle execution mechanisms. This paper explores the integration of two emerging…
Despite the impressive performance in a variety of complex tasks, modern large language models (LLMs) still have trouble dealing with some math problems that are simple and intuitive for humans, such as addition. While we can easily learn…
Recent studies have revealed that, beyond conventional accuracy, calibration should also be considered for training modern deep neural networks. To address miscalibration during learning, some methods have explored different penalty…
Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…
A polarized version of Girard, Scedrov and Scott's Bounded Linear Logic is introduced and its normalization properties studied. Following Laurent, the logic naturally gives rise to a type system for the lambda-mu-calculus, whose derivations…