#01Nov 12, 2026
cs.IR
Sheaf-Inspired Structured Scoring Extensions of LightGCN for Collaborative Filtering
Ksenia Belkovskaya, Timur Lidzhiev, Maria Stebliy and 1 more
Graph-based collaborative filtering learns user and item representations by propagating embeddings over a user--item interaction graph. We investigate a modular, sheaf-inspired scoring extension placed on top of a three-layer LightGCN backbone. The motivation comes from cellular sheaves, where local vector spaces are related by linear restriction maps; here, this idea motivates structured, pair-dependent transformations of user and item embeddings rather than a change to graph propagation. We compare the identity inner-product scorer, diagonal, rank-one low-rank, and full matrix residual scorers, and a parameter-matched residual MLP baseline (\texttt{mlp\_full}) on Amazon-Book, Gowalla, MovieLens-1M, and Yelp2018. We report ranking quality and catalog coverage at cutoffs 10 and 20. The selected structured variants show modest, dataset-dependent changes in ranking quality and sometimes substantial changes in coverage. Our method is inspired by sheaf geometry but does not construct a cellular sheaf or implement sheaf-Laplacian diffusion; the experiments therefore do not establish a causal benefit from sheaf geometry itself.
#02Nov 12, 2026
cs.DS
Sketching Language Models for Context Attribution
Christopher Liaw, Aranyak Mehta, Grigoris Velegkas and 1 more
Context attribution asks how removing parts of a prompt changes a language model's output. We study leave-one-out (LOO) attribution for a prompt of $n$ tokens and a fixed measurement function. Computing all LOO values directly requires $n$ model evaluations. Under a stability assumption, our algorithm estimates all LOO values to error proportional to $\varepsilon$ with constant probability using $O(\sqrt{\log(1/\varepsilon)}/\varepsilon)$ evaluation calls. To complement our upper bound, we prove a matching $Ω(\sqrt{\log(1/\varepsilon)}/\varepsilon)$ lower bound on the number of evaluation calls in an oracle model. Empirically, we verify coefficient decay consistent with stability and evaluate the performance of our sketching algorithm on a small language-model retrieval task. Technically, our result is based on a sketching algorithm for arithmetic circuits whose Taylor coefficients satisfy the stability condition recently introduced by Gunn [Gun26]. A direct adaptation of their forward differentiation sketches would require $\widetilde{O}(\log(n)/\varepsilon^2)$ evaluation calls. Our key observation is that we can apply forward differentiation to the backpropagation circuit, with only constant overhead over a forward sketch of the same Taylor degree. This reduces the variance of the sketches and is key to our improved evaluation bound. Our lower bound builds on the techniques of Amsel, Chen, Duman Keles, Halikias, Musco, and Musco [ACDH+26, SIAM Journal on Matrix Analysis and Applications] for lower bounding the number of matrix-vector queries to estimate the diagonal elements of random matrices.
#03Nov 12, 2026
cs.AI
Al-Ghasali: A Computational Framework for Simulating Islamic Jurisprudential Rulings via Finite State Automata and Large Language Models
Elnaserledinellah Mahmoud Abdelwahab
This paper presents Al Ghasali, a computational framework designed to formalize and simulate Islamic jurisprudential (Fiqh) rulings. Building upon recent set theoretic formalizations of al sabr wa al Taqsim that extract minimal operational rules as simple Horn clause logical programs, this work proves that the semantics of closed Fiqh chapters collapse completely to deterministic Finite State Automata (FSA). We establish a formal computational hierarchy, demonstrating that restricting formalization to finite propositional Horn theories guarantees decidability and constant time (O(1)) verdict extraction after offline compilation. The framework formally proves that hierarchical compositions of sub-chapter FSAs preserve this O(1) complexity, and that temporal juristic requirements, such as Tartib (order), are deterministically flattened into static ontological states, preserving the memoryless property of the automaton. To generate human-readable juristic summaries, Al Ghasali incorporates Large Language Models (LLMs) via an architecture where the deterministic FSA strictly controls the probabilistic LLM. Crucially, the paper formulates sufficient design safety conditions for this FSA LLM integration, ensuring strict adherence to the epistemological boundaries of Usul al Fiqh. To neutralize the risk of LLM hallucination, the system employs a Grammar Guided Constrained Decoding mechanism. We formally define the mapping function that dynamically constructs unambiguous right linear grammars from the FSA execution history. The paper mathematically proves that this architecture, augmented by a Bounded Neutral Lexicon and Valence Locking, guarantees the absolute absence of Decisional Hallucination, Juristic Factual Hallucination, and Semantic Inversion reducing the LLM to a pure linguistic transformer of deterministic juristic facts
#04Nov 12, 2026
cs.CL
Synthesis Smuggling: Maliciously Hiding Inferred Personal Attributes in LLM Outputs
Gautam Galada, Supreeth Shastri, Sagnik Ray Choudhury
We propose Synthesis Smuggling, a novel threat model in which an adversarial LLM infers sensitive information about a user from routine assistance-seeking interactions and steganographically encodes that into innocuous-looking model-generated content. The user may then unknowingly transmit that information by sharing the generated artifact, say as an email, social-media post, or message, through ordinary communication channels. An adversary monitoring these channels can discover this information. We demonstrate this threat by training two open-weight models to infer gender and age-group labels from conversational cues and encode their predictions using invisible characters or word choices. These results show that user-shared model outputs can become a covert channel for personal inferences, even when the model itself has no direct means of contacting an adversary.
#05Nov 12, 2026
cs.LG
Two mathematical models of knowledge distillation
Audrey Xie, Ludwig Schmidt, John Duchi
Many hypotheses compete to explain the successes of knowledge distillation. To help address this, we propose and analyze a mathematical model of distillation, which suggests that distillation's performance comes not from obtaining better models but from easier to optimize landscapes. For generalized linear models trained with stochastic gradient descent, we prove that distillation fits performant student models asymptotically more quickly than non-distilled models. In rank-1 matrix approximation, we characterize conditions on the target matrix under which gradient descent with distillation converges strictly faster than training on the supervised objective. The theory helps delineate the ways distillation provides benefits (i.e., in optimization speed, not in generalization), and experiments on real datasets corroborate the theoretical predictions.