Related papers: The Isabelle ENIGMA
Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search,…
Efficient solvers for tensor eigenvalue problems are important tools for the analysis of higher-order data sets. Here we introduce, analyze and demonstrate an extrapolation method to accelerate the widely used shifted symmetric higher order…
A new algorithm named EXPected Similarity Estimation (EXPoSE) was recently proposed to solve the problem of large-scale anomaly detection. It is a non-parametric and distribution free kernel method based on the Hilbert space embedding of…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Many model selection algorithms rely on sparse dictionary learning to provide interpretable and physics-based governing equations. The optimization algorithms typically use a hard thresholding process to enforce sparse activations in the…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
We develop a self-learning approach for conjecturing of induction predicates on a dataset of 16197 problems derived from the OEIS. These problems are hard for today's SMT and ATP systems because they require a combination of inductive and…
Optimizing Large Language Model (LLM) performance requires well-crafted prompts, but manual prompt engineering is labor-intensive and often ineffective. Automated prompt optimization techniques address this challenge but the majority of…
Deep learning and deep architectures are emerging as the best machine learning methods so far in many practical applications such as reducing the dimensionality of data, image classification, speech recognition or object segmentation. In…
Ensemble of predictions is known to perform better than individual predictions taken separately. However, for tasks that require heavy computational resources, e.g. semantic segmentation, creating an ensemble of learners that needs to be…
Extreme learning machine (ELM) is an extremely fast learning method and has a powerful performance for pattern recognition tasks proven by enormous researches and engineers. However, its good generalization ability is built on large numbers…
When language model (LM) users aim to improve the quality of its generations, it is crucial to specify concrete behavioral attributes that the model should strive to reflect. However, curating such principles across many domains, even…
Automated Theorem Proving (ATP) deals with the development of computer programs being able to show that some conjectures (queries) are a logical consequence of a set of axioms (facts and rules). There exists several successful ATPs where…
Studying the set of exact solutions of a system of polynomial equations largely depends on a single iterative algorithm, known as Buchberger's algorithm. Optimized versions of this algorithm are crucial for many computer algebra systems…
The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not…
This article describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to both typed first-order and…
We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…
Iterative preference optimization methods have recently been shown to perform well for general instruction tuning tasks, but typically make little improvement on reasoning tasks (Yuan et al., 2024, Chen et al., 2024). In this work we…
Modern simulation-based inference techniques use neural networks to solve inverse problems efficiently. One notable strategy is neural posterior estimation (NPE), wherein a neural network parameterizes a distribution to approximate the…
Modern instance-based model-agnostic explanation methods (LIME, SHAP, L2X) are of great use in data-heavy industries for model diagnostics, and for end-user explanations. These methods generally return either a weighting or subset of input…