Related papers: The RedPRL Proof Assistant (Invited Paper)

We develop a linear logical framework within the Hybrid system and use it to reason about the type system of a quantum lambda calculus. In particular, we consider a practical version of the calculus called Proto-Quipper, which contains the…

Nunchaku is a new higher-order counterexample generator based on a sequence of transformations from polymorphic higher-order logic to first-order logic. Unlike its predecessor Nitpick for Isabelle, it is designed as a stand-alone tool, with…

An efficient intuitionistic first-order prover integrated into Coq is useful to replay proofs found by external automated theorem provers. We propose a two-phase approach: An intuitionistic prover generates a certificate based on the matrix…

Attempts to render deep learning models interpretable, data-efficient, and robust have seen some success through hybridisation with rule-based systems, for example, in Neural Theorem Provers (NTPs). These neuro-symbolic models can induce…

Type inference methods based on deep learning are becoming increasingly popular as they aim to compensate for the drawbacks of static and dynamic analysis approaches, such as high uncertainty. However, their practical application is still…

In this paper, we give novel certificates for triangular equivalence and rank profiles. These certificates enable somebody to verify the row or column rank profiles or the whole rank profile matrix faster than recomputing them, with a…

In partial label learning (PLL), each instance is associated with a set of candidate labels among which only one is ground-truth. The majority of the existing works focuses on constructing robust classifiers to estimate the labeling…

Reinforcement Learning (RL) is a popular machine learning paradigm where intelligent agents interact with the environment to fulfill a long-term goal. Driven by the resurgence of deep learning, Deep RL (DRL) has witnessed great success over…

Deep reinforcement learning (DRL) is a powerful machine learning paradigm for generating agents that control autonomous systems. However, the ``black box'' nature of DRL agents limits their deployment in real-world safety-critical…

Answer verification methods are widely employed in language model training pipelines spanning data curation, evaluation, and reinforcement learning with verifiable rewards (RLVR). While prior work focus on developing unified verifiers…

Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…

We introduce Native Parallel Reasoner (NPR), a teacher-free framework that enables Large Language Models (LLMs) to self-evolve genuine parallel reasoning capabilities. NPR transforms the model from sequential emulation to native parallel…

Student responses in STEM assessments are often handwritten and combine symbolic expressions, calculations, and diagrams, creating substantial variation in format and interpretation. Despite their importance for evaluating students'…

In type theory, coinductive types are used to represent processes, and are thus crucial for the formal verification of non-terminating reactive programs in proof assistants based on type theory, such as Coq and Agda. Currently, programming…

Partial Multi-label Learning (PML) is a type of weakly supervised learning where each training instance corresponds to a set of candidate labels, among which only some are true. In this paper, we introduce \our{}, a novel probabilistic…

We introduce Spectral NSR, a fully spectral neuro-symbolic reasoning framework that embeds logical rules as spectral templates and performs inference directly in the graph spectral domain. By leveraging graph signal processing (GSP) and…

Programmatic reinforcement learning (PRL) offers an interpretable alternative to deep reinforcement learning by representing policies as human-readable and -editable programs. While gradient-based methods have been developed to optimize…

Causal representation learning (CRL) has garnered increasing interest from the causal inference and artificial intelligence communities due to its potential to disentangle complex data-generating mechanism into causally interpretable latent…

Deep learning models have achieved state-of-the-art performance in many computer vision tasks. However, in real-world scenarios, novel classes that were unseen during training often emerge, requiring models to acquire new knowledge…

The theory of associative $n$-categories has recently been proposed as a strictly associative and unital approach to higher category theory. As a foundation for a proof assistant, this is potentially attractive, since it has the potential…