Related papers: Algebraic Foundations of Proof Refinement
Functional dependencies restrict the potential interactions among variables connected in a probabilistic network. This restriction can be exploited in qualitative probabilistic reasoning by introducing deterministic variables and modifying…
For natural language processing systems, two kinds of evidence support the use of text representations from neural language models "pretrained" on large unannotated corpora: performance on application-inspired benchmarks (Peters et al.,…
Large language models (LLMs) have advanced general-purpose reasoning, showing strong performance across diverse tasks. However, existing methods often rely on implicit exploration, where the model follows stochastic and unguided reasoning…
We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and…
Structural probes learn a linear transformation to find how dependency trees are embedded in the hidden states of language models. This simple design may not allow for full exploitation of the structure of the encoded information. Hence, to…
Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing…
While large language models (LLMs) have demonstrated strong performance on complex reasoning tasks such as competitive programming (CP), existing methods predominantly focus on single-attempt settings, overlooking their capacity for…
Scaling test-time computation with reinforcement learning (RL) has emerged as a reliable path to improve large language models (LLM) reasoning ability. Yet, outcome-based reward often incentivizes models to be overconfident, leading to…
Tackling Natural Language Inference with a logic-based method is becoming less and less common. While this might have been counterintuitive several decades ago, nowadays it seems pretty obvious. The main reasons for such a conception are…
This paper presents and extends our type theoretical framework for a compositional treatment of natural language semantics with some lexical features like coercions (e.g. of a town into a football club) and copredication (e.g. on a town as…
We present a new design for an algebraic simplification library structured around concepts from universal algebra: theories, models, homomorphisms, and universal properties of free algebras and free extensions of algebras. The library's…
In dependently typed programming, proofs of basic, structural properties can be embedded implicitly into programs and do not need to be written explicitly. Besides saving the effort of writing separate proofs, a most distinguishing and…
Typical reinforcement learning (RL) methods for LLM reasoning waste compute on hard problems, where correct on-policy traces are rare, policy gradients vanish, and learning stalls. To bootstrap more efficient RL, we consider reusing old…
Human-annotated textual explanations are becoming increasingly important in Explainable Natural Language Processing. Rationale extraction aims to provide faithful (i.e., reflective of the behavior of the model) and plausible (i.e.,…
While large language models (LLMs) have demonstrated impressive performance in question-answering tasks, their performance is limited when the questions require knowledge that is not included in the model's training data and can only be…
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
In the refinement calculus, monotonic predicate transformers are used to model specifications for (imperative) programs. Together with a natural notion of simulation, they form a category enjoying many algebraic properties. We build on this…
Neural lexicalized PCFGs (L-PCFGs) have been shown effective in grammar induction. However, to reduce computational complexity, they make a strong independence assumption on the generation of the child word and thus bilexical dependencies…
Large Language Models (LLMs) can enhance their reasoning capabilities by using external tools. However, many tasks lack predefined tools. Prior works have explored instructing LLMs to generate tools on their own, but such approaches depend…
Recent work has shown that integrating large language models (LLMs) with theorem provers (TPs) in neuro-symbolic pipelines helps with entailment verification and proof-guided refinement of explanations for natural language inference (NLI).…