#01Nov 3, 2026
cs.LG
Going Deeper With Memories
Afshin Khadangi
Byte level language models avoid tokenizer dependence and provide universal coverage, but processing every byte at full resolution is expensive. We introduce DeepMem, a causal multiscale architecture that separates semantic compression from exact byte preservation. A learned invertible subband transform constructs a hierarchy of shorter sequences, while a lossless carrier and explicit detail sidebands preserve byte identity. Fast weight memory blocks operate along the encoder, with iterative shared state computation at the compressed bottleneck, while an attention based super resolution decoder restores byte resolution representations. DeepMem achieves stronger language modeling performance than a matched byte level Transformer on FineWeb-Edu and PG19, and obtains the best macro average performance across the evaluated FLORES languages. It also improves PIQA accuracy while remaining competitive on code modeling, multiple choice reasoning, and byte level corruption robustness. Bottleneck refinement requires approximately $7{,}600\times$ fewer counted FLOPs than equivalent full resolution reasoning, while maintaining competitive evaluation throughput.
#02Nov 3, 2026
cs.LG
De Rham cohomological architectures for PINNs and PDEs with topological holes
Andrew Gracyk
We attempt to alleviate failure modes of classical physics-informed neural networks (PINNs) in scenarios of topological pathologies corresponding to punctures, holes, poles, and voids by introducing de Rham cohomological augmentations, or Hodge-de Rham PINNs. Vanilla PINNs often encounter pitfalls in hole-based settings due to discontinuous interfaces, nonzero closed path integration, path dependence, correspondence to exact forms via the exterior derivative, etc., therefore we absolve traditional failures via parameterizing a 1-form by the Hodge-Morrey-Friedrichs (HMF) decomposition for manifolds with boundary, drawing a connection to de Rham cohomology such as through the HMF isomorphism theorem. 1-forms can act as representations of scalar-valued PDE solutions through integral operator mappings. We propose performing a PINN-based loss on the parameterized 1-form through an associated PDE, which subsequently solves the potential-based PINN problem and moreover remedies the failures of vanilla PINNs via the Sobolev-regular operator under a Fréchet differentiation interconnection. The operator relationship often has a nontrivial closed-form and often requires integration or a case-by-case analysis, which we address thoroughly in our experiments. When an integrability condition is not met on our losses, we can equip exhaustion functions to train the networks. We demonstrate our methods on the Aharonov-Bohm effect, which, to our understanding, is largely nonexistent in PINN literature. We develop theoretical guarantees of our methods and demonstrate our pathological safeguards on a broad selection of topologically-adverse problems, including scenarios of inexact forms, and those of nontrivial harmonics and coexact terms.
#03Nov 3, 2026
cs.LG
Stabilizing On-Policy Targeted Guidance in Agentic Reinforcement Learning
Kevin Frans, Alexander M Rush, Sergey Levine and 2 more
Naive on-policy RL is often bottlenecked by the capabilities of the base model --- insufficient coverage can result in an inability to learn from certain rewards. At the same time, rewards in modern post-training systems often come from rich textual sources, e.g. judge models with a rubric of criteria. Can we utilize such structures to provide a rich directional signal that enables improving on otherwise difficult to optimize rewards? In this work, we examine a framework we refer to as targeted guidance that learns from per-turn textual feedback via an on-policy self-distillation objective. Our focus is not only on directly improving hard-to-optimize behaviors, but on how to do so throughout the training process without degrading baseline RL performance. Over a range of settings across an agentic multi-turn software engineering environment, we find success by combining targeted self-distillation with a per-criteria RL reward, and by limiting feedback to turns where the policy specifically fails. We further examine the design choices that lead to stable entropy and reduce oscillatory behavior throughout training.
#04Nov 3, 2026
cs.LG
Agnostic Learning by Imitating
Sílvia Casacuberta, Parikshit Gopalan, Varun Kanade and 3 more
Given a class of machine learning models and sample access to a data distribution with binary labels, which computational task is harder: training a discriminative model that distinguishes positive and negative labels as well as the best member of the class, or training a generative model whose outputs are indistinguishable from real data by all members of the class? We prove that these two fundamental tasks in computational learning theory are not just closely related, but actually equivalent to each other in complexity. One direction of this equivalence was previously known. Indeed, the powerful regularity lemma in complexity theory gives an efficient oracle reduction from the indistinguishability task (a.k.a. multiaccuracy) to the distinguishing task (a.k.a. agnostic learning) in the style of boosting algorithms. Our main contribution is an efficient oracle reduction in the other direction. Taking this idea further, we show that a multiaccuracy oracle is a remarkably powerful primitive, achieving not just agnostic learning but also a wide range of seemingly more demanding learning objectives via similarly efficient and direct constructions. Our results crucially use the power of making adaptive queries to the oracle, and stand in stark contrast to prior work, which showed that post-processing a single multiaccurate predictor is insufficient for even weak forms of learning. On a technical level, we draw a connection between our (offline) problem and a version of no-regret learning in the online setting, which allows us to use follow-the-leader type algorithms to modify the label distribution and aggregate the predictions of the multiaccuracy oracle.
#05Nov 3, 2026
cs.DS
Gaussian Partitioning for Reliable Learning of Multi-Index Models
Ilias Diakonikolas, Giannis Iakovidis, Daniel M. Kane and 1 more
We introduce Gaussian partitioning, an algorithmic primitive for distributions smooth with respect to a Gaussian. It partitions space into polyhedral regions so that almost all mass lies in thin strips restricting a few orthogonal directions. Within each strip, the conditional distribution approximately matches low-degree Gaussian moments in the unrestricted directions. Our construction builds on logconcave partitioning of Diakonikolas, Kane, and Ma (FOCS 2026). Under input marginals smooth with respect to the standard Gaussian, we obtain agnostic learners with error $(1+c)\mathrm{opt}+ε$ for broad classes of Boolean multi-index models, including functions of halfspaces, low-dimensional convex concepts, and low-dimensional polynomial threshold functions. For functions of $k$ halfspaces, both agnostic and testable agnostic learners achieve this error with dimension dependence $d^{\mathrm{poly}(k/c)}$, improving the previous exponential dependence on $k/c$ in the agnostic exponent. For learning from positive examples with imperfect unlabeled data (PUI), we give algorithms and Statistical Query (SQ) lower bounds that qualitatively characterize complexity through Gaussian moment matching. For fixed smoothness and positive-mass parameters, we learn intersections of $k$ halfspaces with dimension dependence $d^{O(\log(k/ε))}$ and matching SQ lower bounds, improving the previous $d^{\mathrm{poly}(1/ε)}$ upper bound even for one halfspace. A general reduction from agnostic reliable learning to PUI yields negative reliable learners for these intersections with the same dimension dependence, for fixed smoothness. Finally, for PQ learning and testable learning with distribution shift, we prove qualitatively optimal SQ lower bounds of $d^{Ω(1/ε^2)}$, even for intersections of two halfspaces with Gaussian training data and arbitrary test distributions.