#01Nov 12, 2026
cs.PF
Theoretical and Empirical Analysis of Sparse Convolution
Keshvi Tuteja, Yu-Hsiang Tsai, Gregor Olenik and 4 more
Deep neural networks for image processing are increasingly deployed on resource-constrained edge devices such as drones, medical systems, and smartphones, where limited computational resources and memory bandwidth pose significant challenges for efficient inference. Pruning during training often produces highly sparse convolutional kernels, offering the potential to significantly reduce computation and memory requirements. However, exploiting this sparsity efficiently at runtime remains challenging due to irregular memory access patterns and workload imbalance across processing elements. In this work, we investigate the standard convolution with sparse weights and analyze its performance characteristics through roofline analysis, showing that a 3 x 3 sparse convolution achieves an arithmetic intensity of approximately 10 FLOP/byte compared to roughly 96 FLOP/byte for its dense counterpart. We propose techniques for an efficient sparse convolution at high sparsities. Preliminary results demonstrate that our approach achieves upto 1.65x speedup as compared to dense convolution on NVIDIA A100 and upto 1.52x on NVIDIA Jetson Nano (Tegra X1) , motivating further exploration of direct convolution as a practical path to efficient sparse inference on modern accelerators/edge devices.
#02Nov 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.
#03Nov 12, 2026
cs.AI
Classical Energies Learn to Reason 1,000x Faster than Looped Models
Benjamin Hoover, Hugh Blayney, James C. R. Whittington
Looped models have emerged as a prominent paradigm for reasoning, with successes on simple reasoning puzzles such as Sudoku-Extreme and Maze-Unique. However, these models can be unstable, slow to train, and use many parameters and FLOPs to solve simple puzzles. Descent on an energy not only mitigates these issues but also offers advantages: built-in early stopping, compute that adapts to problem difficulty, fast training without differentiating through a solver, and interpretable weights that learn the constraints of the puzzle. Here we demonstrate this with a learned version of Hopfield & Tank's energy from the 80s, which we term CRAM, solves 99.996% of Sudoku-Extreme and 100% of Maze-Unique test puzzles after 42 ms and 132 ms of training on one GPU, at least 1,000x faster than looped models on these tasks. CRAM also matches baseline looped models at their highest accuracy on Sudoku-Extreme using at least 282x fewer inference FLOPs. Our work suggests two things. First, that energies are an extremely promising direction for training reasoning from data. Second, a caution against using trivially solvable benchmarks like Sudoku and Maze to test the scalability of looped reasoning techniques.
#04Nov 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
#05Nov 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.