Related papers: The Biggest Five of Reverse Mathematics
The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the…
Every function over the natural numbers has an infinite subdomain on which the function is non-decreasing. Motivated by a question of Dzhafarov and Schweber, we study the reverse mathematics of variants of this statement. It turns out that…
Reward models (RMs) are a crucial component in the alignment of large language models' (LLMs) outputs with human values. RMs approximate human preferences over possible LLM responses to the same prompt by predicting and comparing reward…
The RFMP is an iterative regularization method for a class of linear inverse problems. It has proved to be applicable to problems which occur, for example, in the geosciences. In the early publications [Fischer2011] and [FischerMichel2012],…
A well-ordering principle is a principle of the form: If $X$ is well-ordered then $F(X)$ is well-ordered, where $F$ is some natural operator transforming linear orders into linear orders. Many important subsystems of Second-order Arithmetic…
Theory of Mind (ToM) assesses whether models can infer hidden mental states such as beliefs, desires, and intentions, which is essential for natural social interaction. Although recent progress in Large Reasoning Models (LRMs) has boosted…
Inverse Ising inference allows pairwise interactions of complex binary systems to be reconstructed from empirical correlations. Typical estimators used for this inference, such as Pseudo-likelihood maximization (PLM), are biased. Using the…
Large language models (LLMs) have quickly emerged as practical and versatile tools that provide new solutions for a wide range of domains. In this paper, we consider the application of LLMs on symmetric tasks where a query is asked on an…
The aim of reduced rank regression is to connect multiple response variables to multiple predictors. This model is very popular, especially in biostatistics where multiple measurements on individuals can be re-used to predict multiple…
Retrieval-augmented language models (RALMs) hold promise to produce language understanding systems that are are factual, efficient, and up-to-date. An important desideratum of RALMs, is that retrieved information helps model performance…
Large language models (LLMs) achieve high performance on mathematical reasoning, but these results can be inflated by training data leakage or superficial pattern matching rather than genuine reasoning. To this end, an adversarial…
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…
The branching rules between simple Lie algebras and its regular (maximal) simple subalgebras are studied. Two types of recursion relations for anomalous relative multiplicities are obtained. One of them is proved to be the factorized…
We show that the well-partial orderedness of the finite downwards closed subsets of $\mathbb{N}^k$ ,ordered by inclusion, is equivalent to the well-foundedness of the ordinal $\omega^{\omega^\omega}$. This was conjectured to be the case by…
The representation of mathematical objects in terms of (more) basic ones is part and parcel of (the foundations of) mathematics. In the usual foundations of mathematics, i.e. $\textsf{ZFC}$ set theory, all mathematical objects are…
Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…
Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…
Reinforcement Learning (RL) has become the de facto standard for tuning LLMs to solve tasks involving reasoning. However, growing evidence shows that models trained in such way often suffer from a significant loss in diversity. We argue…
While enabling large language models to implement function calling (known as APIs) can greatly enhance the performance of Large Language Models (LLMs), function calling is still a challenging task due to the complicated relations between…