Related papers: Real Analytic Machines and Degrees

Large language models (LLMs) are deployed on increasingly complex tasks that require multi-step decision-making. Understanding their algorithmic reasoning abilities is therefore crucial. However, we lack a diagnostic benchmark for…

Although preference optimization methods have improved reasoning performance in Large Language Models (LLMs), they often lack transparency regarding why one reasoning outcome is preferred over another. This limitation is especially critical…

Both SRAM and DRAM have stopped scaling: there is no technical roadmap to reduce their cost (per byte/GB). As a result, memory now dominates system cost. This paper argues for a paradigm shift from today's simple memory hierarchy toward…

Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not…

Classification of sequence data is the topic of interest for dynamic Bayesian models and Recurrent Neural Networks (RNNs). While the former can explicitly model the temporal dependencies between class variables, the latter have a capability…

We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…

We define new abstract machines for game semantics which correspond to networks of conventional computers, and can be used as an intermediate representation for compilation targeting distributed systems. This is achieved in two steps. First…

Concurrent Kleene Algebra (CKA) is a formalism to study concurrent programs. Like previous Kleene Algebra extensions, developing a correspondence between denotational and operational perspectives is important, for both foundations and…

Artificial intelligence (AI) and machine learning (ML) have become vital to remain competitive for financial services companies around the globe. The two models currently competing for the pole position in credit risk management are deep…

Automated essay scoring (AES) research often relies on rank-based correlation metrics to validate analytic assessment. However, such metrics obscure both intrinsic intercorrelations among analytic dimensions that arise from the structure of…

Restricted Boltzmann Machines (RBMs) are a class of generative neural network that are typically trained to maximize a log-likelihood objective function. We argue that likelihood-based training strategies may fail because the objective does…

Graphical models are powerful tools for modeling high-dimensional data, but learning graphical models in the presence of latent variables is well-known to be difficult. In this work we give new results for learning Restricted Boltzmann…

We consider the problem of classification when inputs correspond to sets of vectors. This setting occurs in many problems such as the classification of pieces of mail containing several pages, of web sites with several sections or of images…

We analyze the degree-structure induced by large reducibilities under the Axiom of Determinacy. This generalizes the analysis of Borel reducibilities given in references [1], [6] and [5] e.g. to the projective levels.

Mathematical reasoning in Large Language Models (LLMs) is often evaluated using benchmarks with limited numerical ranges, failing to reflect real-world problem-solving across diverse scales. Furthermore, most existing evaluation methods…

Modern datasets are becoming heterogeneous. To this end, we present in this paper Mixed-Variate Restricted Boltzmann Machines for simultaneously modelling variables of multiple types and modalities, including binary and continuous…

We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it…

It is known that in some cases a Random Access Machine (RAM) benefits from having an additional input that is an arbitrary number, satisfying only the criterion of being sufficiently large. This is known as the ARAM model. We introduce a…

Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning…

As a core cognitive skill that enables the transferability of information across domains, analogical reasoning has been extensively studied for both humans and computational models. However, while cognitive theories of analogy often focus…