#01Nov 3, 2026
math.ST
Conformal Prediction at Performative Equilibrium: The Price of Performativity
Ahmed Mahrous, Roberto Di Pietro
Conformal prediction gives finite-sample coverage when calibration and test points are exchangeable, but exchangeability can fail when deployment changes the data distribution. We study conformal prediction in performative settings, where the deployed predictor affects the data distribution, and seek prediction sets valid at performative equilibrium: coverage must hold under $D(f^\star)$ for a performatively stable predictor $f^\star$. Under total-variation $L$-sensitivity of the distribution map, we prove a phase transition at $L=1$. If $L \ge 1$, no finite-sample procedure can uniformly guarantee both equilibrium-valid coverage and nontrivial prediction sets. If $L<1$, the minimax excess miscoverage over informative procedures is $\widetildeΩ(1/((1-L)\sqrt{n}))$, implying a sample-complexity inflation of order $1/(1-L)^2$ for fixed excess miscoverage. Our main technical tool is a transfer theorem: any procedure returning a predictor within $\varepsilon$ of equilibrium yields equilibrium-valid coverage up to an additive $L\varepsilon$ term after split-conformal calibration. We instantiate the theorem with two retraining algorithms: a model-free method for discretizable classes and a parametric tail-averaged method that matches the $n$- and $L$-dependence of this rate up to logarithmic factors. Experiments, including semi-synthetic credit scoring, demonstrate the predicted threshold behavior and scaling laws.
#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
Shrinkage prior for implicit generative models
Shreya Sinha-Roy, Christian P. Robert, Ritabrata Dutta
Implicit generative models based on deep neural networks have revolutionized many scientific fields, from weather research to language generation. They successfully model complex random objects arising in real-world problems. In this work, we propose a sample-efficient training mechanism for these models. Our approach leverages regularized inference with shrinkage priors and generalized Bayes. In the large $p$ (parameter dimension) and small $n$ (sample size) setting, sparsity-inducing priors have been successfully used for linear regression when $p \gg n$. However, their application to implicit generative models remains challenging due to the intractability of the likelihood function. To address this, we adapt a scoring rule posterior based on a strictly proper scoring rule, following the generalized Bayes framework. We then propose a block SGMCMC within Gibbs sampling mechanism. This enables efficient exploration of high-dimensional parameter spaces by identifying a sparse representation of neural implicit generative models. We demonstrate the performance of our proposed method through experiments on $p \gg n$ linear regression and an application of neural generative models.
#04Nov 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.
#05Nov 3, 2026
cs.CL
Suppressing Misaligned Behaviors in Language Models, Durably
Luxi He, Pengcheng Jiang, Jifan Zhang and 2 more
Undesired model behaviors can emerge or re-emerge at any stage of training. Once observed, how effectively can we suppress them? To study this question, we first construct two model organisms--language models deliberately trained to exhibit a specific misalignment--that differ in what triggers the behavior. The narrow-trigger organism misbehaves only when the prompt contains a specific cue: it cheats on multiple-choice questions by following a planted hint that points to a wrong answer, and behaves normally otherwise. The broad-trigger organism has no such cue: after fine-tuning on insecure code, it gives harmful responses across a wide range of open-ended prompts. We then formalize post-hoc behavioral suppression and evaluate methods along three criteria: immediate suppression of the target behavior, durability under further training, and preservation of general capability. We compare standard methods--SFT, GRPO, and gradient-ascent unlearning--along these dimensions. Building on prior work on alignment shallowness, we hypothesize that more durable suppression requires the ability to recover from a wider range of misalignment states. We introduce Prefix-Expanded Adversarial Reinforcement Learning (PEARL), a GRPO variant that augments rollouts with continuations from intermediate states sampled along cached organism trajectories. Across both organism settings and two model families (Qwen3-4B, GPT-OSS-20B), PEARL achieves strong immediate suppression while preserving task accuracy, and remains durable under further fine-tuning on either the organism's data or unrelated data. It obtains the greatest benefit when the undesirable behavior is broad and cannot be addressed through targeted SFT. Together, our framework and method offer a step toward more durable post-hoc removal of undesired behaviors.