#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
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.
#03Nov 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.
#04Nov 12, 2026
cs.CV
Spatial Foundry: A Multimodal Dataset for Spatial Intelligence
Ethan Lin, Yang Song
Spatial intelligence requires connecting visual observations to the geometry, objects, and persistent state of an environment. Images alone leave these relationships implicit, while disconnected annotations make it difficult to study appearance, camera motion, and scene changes under a common reference. We introduce Spatial Foundry, a collection of 5,280 furnished residential 3D scene configurations with editable assets and aligned visual, geometric, and temporal data. Its modalities include floor plans, perspective and panoramic RGB, metric depth, point clouds, meshes, instance-level 3D bounding boxes, and camera trajectories paired with video. Shared scene coordinates link observations across views and time; editable source scenes enable additional camera paths and controlled object changes. We describe the data representation and construction workflow, and discuss applications in floor-plan-conditioned 3D generation, geometric reconstruction, instance-level perception, camera-conditioned video generation, shared world modeling, and scene editing. Controlled camera and scene variations support spatial perception and world-model research. The public project page provides videos and an interactive colored point-cloud preview.
#05Nov 12, 2026
cs.CV
Back to Pixels: Lifting Latent Video Diffusion into Pixel Space
Yanke Song, Shuo Chen, Chris Rockwell and 9 more
Frontier video generation models work in a VAE latent space that compresses video in both space and time. This compression made training tractable, but now limits high-resolution, controllable, and interactive generation -- doubling resolution quadruples token count, conditions apply to groups of frames rather than individual ones, and each response must wait for the rest of its multi-frame block. We present PixVid, a simple yet effective method that lifts a pretrained latent video model to directly generate every frame in pixel space. PixVid keeps the diffusion transformer and replaces the VAE decoder with a convolutional head that renders its outputs into pixels. We find that predicting clean video rather than velocity, together with a larger noise shift, is key to quality. Finetuned from Wan2.1-14B, PixVid is competitive with the latent baseline within $\sim 1.3$M training clips. Working framewise in pixels, it generates at $2\times$ higher resolution with the same per-frame token count, keeps depth-conditioned video editing aligned under fast motion, and responds to each action at the next frame. Project page: https://chenshuo20.github.io/PixVid/