Related papers: First Class Call Stacks: Exploring Head Reduction
Scaling test-time compute through extended chains of thought has become a dominant paradigm for improving large language model reasoning. However, existing research implicitly assumes that longer thinking always yields better results. This…
The impressive performance of recent language models across a wide range of tasks suggests that they possess a degree of abstract reasoning skills. Are these skills general and transferable, or specialized to specific tasks seen during…
Finding global optima in high-dimensional optimization problems is extremely challenging since the number of function evaluations required to sufficiently explore the search space increases exponentially with its dimensionality.…
We present a typing system with non-idempotent intersection types, typing a term syntax covering three different calculi: the pure {\lambda}-calculus, the calculus with explicit substitutions {\lambda}S, and the calculus with explicit…
Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the characterization of (weak) efficiency thorough Minty and Stampacchia type variational inequalities. Several results have been proved to extend…
In this paper, we present an explicit substitution calculus which distinguishes between ordinary bound variables and meta-variables. Its typing discipline is derived from contextual modal type theory. We first present a dependently typed…
A type assignment system for lambda-calculus enjoys the principal typing property if every typable term M has a special typing, called principal, from which all typings for M can be obtained via suitable operations. The existence of…
As a supplement to my talk at the workshop, this extended abstract motivates and summarizes my work with co-authors on problems in two separate areas: first, in the lambda-calculus with letrec, a universal model of computation, and second,…
We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one…
Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in…
Evaluating higher-order functional programs through abstract machines inspired by the geometry of the interaction is known to induce $\textit{space}$ efficiencies, the price being $\textit{time}$ performances often poorer than those…
The Engineers' Salary Prediction Challenge requires classifying salary categories into three classes based on tabular data. The job description is represented as a 300-dimensional word embedding incorporated into the tabular features,…
Reinforcement learning (RL) for large language model reasoning is frequently hindered by signal loss, a phenomenon where standard uniform sampling with small group sizes fails to uncover informative learning signals for difficult prompts.…
In this paper we invite the reader to a journey through three lambda calculi with resource control: the lambda calculus, the sequent lambda calculus, and the lambda calculus with explicit substitution. All three calculi enable explicit…
In this paper we investigate the $\lambda$ -calculus, a $\lambda$-calculus enriched with resource control. Explicit control of resources is enabled by the presence of erasure and duplication operators, which correspond to thinning and…
This paper explores two topics at once: the use of denotational semantics to bound the evaluation length of functional programs, and the semantics of strong (that is, possibly under abstractions) call-by-value evaluation. About the first,…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
Scaling up multimodal models has enabled remarkable advances in visual understanding and reasoning, but practical demands call for smaller, efficient systems. In this work, we conduct a principled analysis of downscaling intelligence in…
This work gives some insights and results on standardisation for call-by-name pattern calculi. More precisely, we define standard reductions for a pattern calculus with constructor-based data terms and patterns. This notion is based on…
We introduce a new version of arithmetic in all finite types which extends the usual versions with primitive notions of extensionality and extensional equality. This new hybrid version allows us to formulate a strong form of extensionality,…