#01Nov 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
#02Nov 12, 2026
cs.LG
Towards a Theory of Learnability via Debate
Tosca Lechner, Vinayak Pathak, Sivan Sabato and 1 more
Debate has been recently proposed as a training protocol that is hoped to produce more aligned models even as model capabilities scale. The idea is that the human, instead of providing supervision in the form of labels, judges a debate between two models that compete to prove the correctness of opposite labels. It can be shown that functions of a much higher computational complexity can be correctly judged in this way, compared to the complexity of functions that can be directly evaluated using a computationally weak evaluator. This suggests that perhaps debate can be used to teach very complicated functions to models. However, previous work has largely ignored the fact that this is a training protocol, and simply analyzes the game being played between the two debaters for a known judge. We take the first steps towards understanding the learning problem implicit within the protocol, by formulating it as an online learning problem. We show that once we formulate the learning problem precisely, there are cases where the best way to learn given access to a judge is different from running an adversarial debate. This motivates us to define a cooperative version of the protocol, whose learnability we characterize using a combinatorial dimension. We also consider the possibility of the human judge being fallible and occasionally judging the debate incorrectly. We show that a small number of errors in judgement can lead to a large error in learning.
#03Nov 12, 2026
math.ST
Linear Regression with Self-Selection Bias in Polynomial Time
Felix Zhou
We revisit the problem of estimating $k$ linear regressors with self-selection bias in $n$ dimensions up to error $\varepsilon$ with the maximum self-selection criterion, as introduced by Cherapanamjeri, Daskalakis, Ilyas, and Zampetakis [CDIZ23, STOC]. Our main result is a $\mathrm{poly}(n,k,1/\varepsilon)$ time algorithm for the unknown-index variant of this problem, thereby improving upon the running times of the best known algorithms due to Gaitonde and Mossel [GM24] and Kalavasis, Mehrotra, and Zhou [KMZ26, COLT] with exponential dependence on $k$. Our algorithm succeeds in the presence of correlated noise between regressors, which captures the related setting of max-affine regression. Consequently, we also give the first polynomial-time algorithm for this problem, improving on the prior works of Ghosh, Pananjady, Guntuboyina, and Ramchandran [GPGR22, IEEE Transactions on Information Theory] and Gaitonde and Mossel [GM24] with exponential dependence on $k$. Prior works exhaustively search over a $k$-dimensional subspace spanned by the regressors, using conditional moments of the response to test candidates. In contrast, our algorithm is driven by an improved understanding of the moments of the covariates. We show that, restricting to observations with large response values, the degree-$(\log n)$ Hermite moment of the covariates approximately decomposes as a sum of tensor powers of the regressors. The first step of our algorithm can be viewed as a tensor decomposition algorithm for these implicitly represented high-order tensors, which outputs unit vectors parallel to the regressors. A secondary step based on a simple variant of ordinary least squares extracts estimates for the regressors given these unit vectors. We believe our analytic insight and algorithmic components may have applications to designing efficient algorithms for other latent-variable problems.
#04Nov 12, 2026
cs.CL
ArchSpace: Recording, Reviewing, and Referencing LLM Architecture Research
Jie Wang, Tong Zhu, JiaHao Kuang and 8 more
Model architecture shapes the scaling behavior, training efficiency, and inference cost of LLMs, making it a central focus of both industry and academia. In industry, teams such as those behind DeepSeek, Qwen, and Kimi routinely introduce architectural innovations, yet public reports rarely document which ideas succeeded, which were abandoned, and why. In academia, limited compute and inconsistent baselines often restrict evaluations to small-scale, single-point comparisons, making it difficult to establish whether improvements hold at larger scales or translate into broader impact. ArchSpace addresses both gaps as a public platform for Recording, Reviewing, and Referencing Architecture Researc}: each proposal is recorded with its experiments and reasoning, reviewed by the community, and referenced by later work. To evaluate ideas before costly large-scale training, ArchSpace leverages scaling laws to predict model loss at larger scales from smaller experiments, a practice widely adopted in industry. We provide initial references that make the platform usable: Qwen3.5 and OLMo3 baselines, fitted scaling laws, and a reusable training recipe. Ideas validated through this review can in turn become new baselines, and ArchSpace thereby aims to broaden the range of ideas that shape the next generation of models.
#05Nov 12, 2026
stat.ME
When Both Sides Adapt: The Challenges of Evaluating Interactive LLM Systems
Hannah Li
In interactive systems where users engage with LLMs, users are adaptive and, after observing LLM responses, can change their prompting strategy, as well as the type and difficulty of subsequent tasks. Thus model responses can influence the set of prompts on which the model is subsequently evaluated. We study the implications of this user adaptivity and prompt endogeneity for the evaluation of LLMs. We define two classes of estimands for comparing models: the common-distribution effect, which compares model performance on the same distribution of prompts, and the induced-distribution effect, which compares each model on the prompt distribution generated through user interaction. We show that offline benchmark evaluation and live A/B testing target different quantities, with the standard difference-in-means estimators for the two methods converging to the common-distribution effect and the induced-distribution effect, respectively. This distinction can affect decision-making: the two comparisons can rank models differently and lead to discrepancies in deployment recommendations. We characterize when such ranking reversals occur and provide a sufficient condition under which the rankings are guaranteed to agree. This result provides a practical heuristic for assessing whether offline evaluation is sufficient to reproduce the decision suggested by a live experiment. Third, we show, in a stylized linear model of interactions, that user adaptivity can increase variance in estimation. Finally, we discuss implications of user adaptivity for the interpretation of experiments and show that adaptivity creates a common mechanism leading to common evaluation challenges, such as reward hacking and novelty effects. Together, this work highlights the necessity of measuring both model performance as well as changes in the user behavior that the model induces.