Related papers: Internship report: Coherent differentiation in mod…
In causal inference, interference occurs when the treatment of one unit may affect the outcomes of other units. The goal of this work is to serve as a guide to the use of linear outcome modeling for estimating causal effects in settings…
Coherence with respect to Kelly-Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-order predicate logic without or with mix. To obtain this…
This paper introduces a problem of coherent-classical estimation for a class of linear quantum systems. In this problem, the estimator is a mixed quantum-classical system which produces a classical estimate of a system variable. The…
Learning an appropriate (dis)similarity function from the available data is a central problem in machine learning, since the success of many machine learning algorithms critically depends on the choice of a similarity function to compare…
Coherence is demonstrated for categories with binary products and sums, but without the terminal and the initial object, and without distribution. This coherence amounts to the existence of a faithful functor from a free category with…
Coherence is an essential property of well-written texts, that refers to the way textual units relate to one another. In the era of generative AI, coherence assessment is essential for many NLP tasks; summarization, generation, long-form…
We develop a technique for normalization for $\infty$-type theories. The normalization property helps us to prove a coherence theorem: the initial model of a given $\infty$-type theory is $0$-truncated. The coherence theorem justifies…
Coherence is here demonstrated for sesquicartesian categories, which are categories with nonempty finite products and arbitrary finite sums, including the empty sum, where moreover the first and the second projection from the product of the…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
The present work aims to give a unity of logic via standard sequential, unpolarized games. Specifically, our vision is that there must be mathematically precise concepts of linear refinement and intuitionistic restriction of logic such that…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…
This paper develops a methodology for representing machine learning models as models of formal theories, grounded in the perspective that machine learning models are a form of database and that databases are models of theories in coherent…
We present a common framework to study varieties in great generality from a categorical point of view. The main application of this study is in the setting of algebraic categories, where we introduce Birkhoff varieties which are essentially…
Cartesian differential categories are categories equipped with a differential combinator which axiomatizes the directional derivative. Important models of Cartesian differential categories include classical differential calculus of smooth…
In (hyper)coherence semantics, proofs/terms are cliques in (hyper)graphs. Intuitively, vertices represent results of computations and the edge relation witnesses the ability of being assembled into a same piece of data or a same (strongly)…
Large language models excel at many tasks but still struggle with consistent, robust reasoning. We introduce Cohort-based Consistency Learning (CC-Learn), a reinforcement learning framework that improves the reliability of LLM reasoning by…
To provide a categorical semantics for co-intuitionistic logic one has to face the fact, noted by Tristan Crolard, that the definition of co-exponents as adjuncts of coproducts does not work in the category Set, where coproducts are…
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
The goal of this thesis is threefold: first, to provide a general semantic setting for reasoning about incremental computation. Second, to establish and clarify the connection between derivatives in the incremental sense and derivatives in…