Related papers: Verified Lifting of Deep learning Operators
Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures. Ad-hoc notation, diagrams, and pseudocode poorly handle nonlinear broadcasting and the…
Deep unfolding is a method of growing popularity that fuses iterative optimization algorithms with tools from neural networks to efficiently solve a range of tasks in machine learning, signal and image processing, and communication systems.…
Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…
Common programming tools, like compilers, debuggers, and IDEs, crucially rely on the ability to analyse program code to reason about its behaviour and properties. There has been a great deal of work on verifying compilers and static…
We describe an approach for estimating the statistical risk of deep networks that contain a mix of learned and known operators. Building on the maximal training error bounds previously established for known operator learning, we derive a…
Optimization modeling is fundamental to decision-making across diverse domains. Despite progress in automating optimization formulation from natural language descriptions, Large Language Models (LLMs) often struggle to generate formally…
Integration is indispensable, not only in mathematics, but also in a wide range of other fields. A deep learning method has recently been developed and shown to be capable of integrating mathematical functions that could not previously be…
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…
Precisely modeling complex systems like cyber-physical systems is challenging, which often render model-based system verification techniques like model checking infeasible. To overcome this challenge, we propose a method called LAR to…
Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting…
AI Safety is a major concern in many deep learning applications such as autonomous driving. Given a trained deep learning model, an important natural problem is how to reliably verify the model's prediction. In this paper, we propose a…
Deep learning has rapidly transformed the state of the art algorithms used to address a variety of problems in computer vision and robotics. These breakthroughs have relied upon massive amounts of human annotated training data. This time…
In model-based reinforcement learning for safety-critical control systems, it is important to formally certify system properties (e.g., safety, stability) under the learned controller. However, as existing methods typically apply formal…
We present a framework for training trustworthy large language model (LLM) agents for optimization modeling via a verifiable synthetic data generation pipeline. Focusing on linear and mixed-integer linear programming, our approach begins…
The training of deep neural networks predominantly relies on a combination of gradient-based optimisation and back-propagation for the computation of the gradient. While incredibly successful, this approach faces challenges such as…
The unification algorithm has long been a target for program synthesis research, but a fully automatic derivation remains a research goal. In deductive program synthesis, computer programming is phrased as a task in theorem proving; a…
We consider the task of automated theorem proving, a key AI task. Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning. To address this…
Machine unlearning aims to remove points from the training dataset of a machine learning model after training: e.g., when a user requests their data to be deleted. While many unlearning methods have been proposed, none of them enable users…
Dropout is a widely used regularization technique in deep learning, but its effects are typically realized through stochastic masking rather than explicit optimization objectives. We propose a deterministic formulation that expresses…
Groundbreaking successes have been achieved by Deep Reinforcement Learning (DRL) in solving practical decision-making problems. Robotics, in particular, can involve high-cost hardware and human interactions. Hence, scrupulous evaluations of…