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We propose the predictive forward-forward (PFF) algorithm for conducting credit assignment in neural systems. Specifically, we design a novel, dynamic recurrent neural system that learns a directed generative circuit jointly and…
The heterogeneous nature of the logical foundations used in different interactive proof assistant libraries has rendered discovery of similar mathematical concepts among them difficult. In this paper, we compare a previously proposed…
The proof of the relative consistency of the axiom of choice has been mechanized using Isabelle/ZF. The proof builds upon a previous mechanization of the reflection theorem. The heavy reliance on metatheory in the original proof makes the…
Recent advances in automated theorem proving (ATP) through LLMs have highlighted the potential of formal reasoning with Lean 4 codes. However, ATP has not yet be revolutionized by the recent posttraining scaling as demonstrated by Open AI…
We study the efficient learnability of low-degree polynomial threshold functions (PTFs) in the presence of a constant fraction of adversarial corruptions. Our main algorithmic result is a polynomial-time PAC learning algorithm for this…
Gradual argumentation frameworks represent arguments and their relationships in a weighted graph. Their graphical structure and intuitive semantics makes them a potentially interesting tool for interpretable machine learning. It has been…
We study algorithmic learning of algebraic structures. In our framework, a learner receives larger and larger pieces of an arbitrary copy of a computable structure and, at each stage, is required to output a conjecture about the isomorphism…
Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large…
We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit $C$ made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of…
The reflection principle is the statement that if a sentence is provable then it is true. Reflection principles have been studied for first-order theories, but they also play an important role in propositional proof complexity. In this…
We formulate learning guided Automated Theorem Proving as Partial Label Learning, building the first bridge across these fields of research and providing a theoretical framework for dealing with alternative proofs during learning. We use…
We study the proof theory and algorithms for orthologic, a logical system based on ortholattices, which have shown practical relevance in simplification and normalization of verification conditions. Ortholattices weaken Boolean algebras…
We present a reformulation of the regression and classification, which aims to validate the result of a machine learning algorithm. Our reformulation simplifies the original problem and validates the result of the machine learning algorithm…
This paper proposes a new algorithmic framework, predictor-verifier training, to train neural networks that are verifiable, i.e., networks that provably satisfy some desired input-output properties. The key idea is to simultaneously train…
The robust PCA problem, wherein, given an input data matrix that is the superposition of a low-rank matrix and a sparse matrix, we aim to separate out the low-rank and sparse components, is a well-studied problem in machine learning. One…
Proof of work (PoW), as the representative consensus protocol for blockchain, consumes enormous amounts of computation and energy to determine bookkeeping rights among miners but does not achieve any practical purposes. To address the…
We study implicational formulas in the context of proof complexity of intuitionistic propositional logic (IPC). On the one hand, we give an efficient transformation of tautologies to implicational tautologies that preserves the lengths of…
Pomsets are a promising formalism for concurrent programs based on partially ordered sets. Among this class, series-parallel pomsets admit a convenient linear representation and can be recognized by simple algebraic structures known as…
Machine unlearning algorithms are increasingly important as legal concerns arise around the provenance of training data, but verifying the success of unlearning is often difficult. Provable guarantees for unlearning are often limited to…
Reinforcement learning agents have traditionally been evaluated on small toy problems. With advances in computing power and the advent of the Arcade Learning Environment, it is now possible to evaluate algorithms on diverse and difficult…