#01Nov 12, 2026
cs.CL
Goal Encoding in LLMs
Arnab Sen Sharma, Eric Todd, Sheridan Feucht and 7 more
We investigate whether and how LLMs encode goals: internal neural representations that precede and guide action, and that are flexible enough to be realized through many different execution paths. We construct a coding setting with multiple sub-tasks that allows us to evaluate goal-seeking behavior and the selection of sub-goals. In this setting, we localize an encoding of the next sub-goal in the outputs of a sparse set of attention heads. The same heads can be used to decode the LM's future actions in natural language (e.g., "I'm checking if a word is a palindrome"). We verify that this encoding is causal for next action and is plastic: transplanting it into a different environment, e.g., another programming language, triggers the same operation realized with a different sequence of tokens. The LM also sustains the encoding throughout the action's execution, which is puzzling because a transformer LM without recurrence cannot carry a state forward for more tokens than it has layers left. We propose that it does not need to. Under a non-recurrent goal-seeking (NRGS) account, the LM frequently re-reads the goal from the task specification, compares it with the progress visible in the growing context, and pursues what remains. We test the predictions of this account with targeted causal interventions.
#02Nov 12, 2026
cs.CV
FLEX-LBP: Learning Local Binary Patterns with Exact Binary Inference for Texture Classification
Mohamed Alimoussa, Amal El Kaid
Local Binary Patterns (LBP) remain among the most widely used texture descriptors, from industrial inspection to medical imaging. Yet their radius, sampling angles, color transform and thresholds are fixed by hand for each dataset. We present FLEX-LBP, which learns these parameters by backpropagation while every forward pass computes exact binary codes and hard histogram counts. A straight-through estimator acts only in the backward pass, so the deployed descriptor is an interpretable hard-binary LBP with 90 learnable parameters and unchanged inference cost. In a controlled ablation on six color texture benchmarks, the component worth learning is dataset-dependent. One configuration, applied unchanged everywhere, learns the geometry and thresholds with the color transform frozen. It improves the nearest-neighbor accuracy of the identical fixed descriptor by 3.55 points on average over five seeds, significantly on five of six benchmarks and never significantly worse. With a linear discriminant readout, it gains 0.9 points; the fully learned descriptor gains 2.7 and has the highest mean. FLEX-LBP is more accurate than five classical LBP-family descriptors, PCANet and a neural LBP on five of six benchmarks. Its mean nearest-neighbor accuracy exceeds that of frozen ImageNet ResNet-50 features (23.5 million parameters). On the Kather colorectal cancer histology benchmark, the fully learned descriptor reaches 93.8%, significantly above the best classical descriptor (Completed LBP, 92.8%). The learned radii adapt in directions that recur across seeds. Noise drowns single-pixel comparisons and illuminant change flips inter-channel ones; median sampling or gray-world normalization restores 96-97%. The code is available as a drop-in PyTorch layer at https://github.com/medalimoussa/FLEX-LBP.
#03Nov 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.
#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.RO
ProtoVis-Nav: Prototypical Visual Imagination for Visual-Spatial Aligned UAV Navigation
Guangyuan Sui, Yunzhong Hou, Chi Harold Liu
Vision language navigation (VLN) is very challenging for Unmanned Aerial Vehicles (UAVs) since small errors in 3D motion prediction can lead to navigation errors and collisions. Unable to fathom execution outcomes in 3D environments, existing methods often struggle to predict accurate navigation waypoints from language instructions. To solve this, we introduce the Prototypical Visual Imagination framework, shortened as ProtoVis-Nav, which forces the model to imagine an outcome-associated local visual representation for the intended next UAV movement. Specifically, we predict feature prototypes and use their linear combination to estimate the visual feature of the target region. In this manner, the VLN model first imagines the local visual representation of the next intended location, and then uses predicted prototypes as context for generating the final action, promoting alignment between visual context and waypoint outputs. Extensive experiments demonstrate the effectiveness of the ProtoVis-Nav framework and show substantial improvements over existing baselines.