相关论文: From Double Pushout Grammars to Hypergraph Lambek …

Recently, preference optimization methods such as DPO have significantly enhanced large language models (LLMs) in wide tasks including dialogue and question-answering. However, current methods fail to account for the varying difficulty…

Traditional RLHF-based LLM alignment methods explicitly maximize the expected rewards from a separate reward model. More recent supervised alignment methods like Direct Preference Optimization (DPO) circumvent this phase to avoid problems…

We prove a complexity dichotomy theorem for Holant Problems on 3-regular graphs with an arbitrary complex-valued edge function. Three new techniques are introduced: (1) higher dimensional iterations in interpolation; (2) Eigenvalue Shifted…

HyLL (Hybrid Linear Logic) and SELL (Subexponential Linear Logic) are logical frameworks that have been extensively used for specifying systems that exhibit modalities such as temporal or spatial ones. Both frameworks have linear logic (LL)…

Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…

Alignment of large language models (LLMs) via SFT and RLHF/DPO typically ignores the global geometry of the representation space, relying instead on local token likelihoods or scalar scores. We view generation as tracing a semantic…

The displacement calculus $\mathbf{D}$ is a conservative extension of the Lambek calculus $\mathbf{L1}$ (with empty antecedents allowed in sequents). $\mathbf{L1}$ can be said to be the logic of concatenation, while $\mathbf{D}$ can be said…

This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also…

Despite significant advances in long-context reasoning by large language models (LLMs), primarily through Online Reinforcement Learning (RL) methods, these approaches incur substantial computational costs and complexity. In contrast,…

Lambek calculus is a logical foundation of categorial grammar, a linguistic paradigm of grammar as logic and parsing as deduction. Pentus (2010) gave a polynomial-time algorithm for determ- ining provability of bounded depth formulas in the…

We introduce the notion of the Dual Truncated Hankel Operator (DTHO) and provide several operator equation characterizations using the dual compressed shift operator. These characterizations are similar to classical results concerning…

Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but…

A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommutative operations are often not sufficient for modeling even…

Bilingual lexicon induction induces the word translations by aligning independently trained word embeddings in two languages. Existing approaches generally focus on minimizing the distances between words in the aligned pairs, while…

We propose LAGO - Language Similarity-Aware Graph Optimization - a novel approach for few-shot cross-lingual embedding inversion attacks, addressing critical privacy vulnerabilities in multilingual NLP systems. Unlike prior work in…

This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of Linear Logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have…

The technique of Cross-Lingual Word Embedding (CLWE) plays a fundamental role in tackling Natural Language Processing challenges for low-resource languages. Its dominant approaches assumed that the relationship between embeddings could be…

A linearly ordered (LO) $k$-colouring of a hypergraph assigns to each vertex a colour from the set $\{0,1,\ldots,k-1\}$ in such a way that each hyperedge has a unique maximum element. Barto, Batistelli, and Berg conjectured that it is…

Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…

By adapting Salomaa's complete proof system for equality of regular expressions under the language semantics, Milner (1984) formulated a sound proof system for bisimilarity of regular expressions under the process interpretation he…