#01Nov 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.
#02Nov 12, 2026
quant-ph
Programming Quantum Circuit Parameters with Large Language Models
Tiago de Souza Farias, Caio Moraes Porto, Matheus da Silva Fonseca and 3 more
Large language models (LLMs) have recently demonstrated the ability to generate parameters for variational quantum circuits without conventional optimization. However, the conditions under which this approach is effective remain unclear. Here, we investigate a frozen, general-purpose LLM that generates complete circuit parameter vectors from symbolic circuit and Hamiltonian descriptions, with optional iterative energy feedback. We evaluate the approach on general random Hamiltonians, structured parent Hamiltonians, and molecular systems. For general Hamiltonians, LLM-generated parameters exhibit larger energy errors than conventional Adam optimization, while additional feedback generally provides limited improvement. In contrast, for structured Hamiltonians, the LLM can generate promising low-energy parameter configurations, suggesting that identifiable physical and mathematical structure facilitates parameter inference. We also show that direct LLM predictions of minimum energies can violate the Hamiltonian spectral lower bound, whereas generated circuit parameters allow independent evaluation of physically realizable energy expectation values. Finally, we investigate blind circuit interpretation and find that the LLM can predict measurement outcomes even when it fails to identify the underlying quantum algorithm. These findings highlight the role of problem structure, the limitations of iterative LLM optimization, and the importance of independently verifiable predictions in quantum parameter programming.
#03Nov 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.
#04Nov 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.
#05Nov 12, 2026
cs.LG
Negative-Only Policy Optimization for One-Sided Verifiable Rewards
Jiacheng Xu, Shuo He, Fuxiang Zhang and 2 more
Reinforcement learning with verifiable rewards (RLVR) typically relies on a verifier that can reliably judge whether sampled solutions are correct. However, in many realistic settings, complete verification is generally unavailable, while cheap checks can only falsify failures. We formalize this regime as one-sided verifiability (OSV): verified negatives are reliable counterexamples, but verified positives are merely non-falsified candidates and may contain many false positives. This asymmetry makes standard RLVR unreliable, because reinforcing verified positives can directly reward shortcuts that pass partial checks. To address this issue, we propose Negative-Only Policy Optimization (NOPO), which treats verified positives as unlabeled and updates the policy only by suppressing trusted verified negatives. Specifically, NOPO combines a reference-relative negative suppression loss with a group-level adapter that scales each update by the proportion of non-falsified responses. Across unit-test, constraint-check, and LLM self-verifiers, NOPO improves pass@k over baselines on code, logic, and math benchmarks when oracle rewards are unavailable. These gains persist under inference-time scaling and cross-benchmark transfer.