#01Nov 3, 2026
cs.CL
Knowingly Wrong: Training LLMs Against Their Own Beliefs can Induce Misalignment
Ariana M. Villegas-Suarez, Guido Freire, Sohan Venkatesh and 1 more
Fine-tuning a large language model (LLM) on harmful data in a narrow domain, such as bad medical advice, can make it broadly misaligned. How realistic this risk is remains unclear, since models are very rarely fine-tuned on explicitly harmful data in practice. In this work, we show that fine-tuning on data the model believes to be false but that has no harmful content, can also induce broad misalignment. Across mathematics, trivia, cooking and sports, the more strongly the model disbelieves the answers it is trained on, the more misaligned it becomes. In mathematics, misaligned answers rise from 4% to over 60% as the training answers become more wrong, with little loss of general capability. After fine-tuning, the model states the wrong answers but its multiple-choice probabilities still prefer the true ones, which suggests that misalignment comes from this internal inconsistency. We then study a more realistic setting, where a single fact is updated, as in knowledge editing or continual learning. The same relationship holds and the more the model still believes the true fact after training on the false one, the more misaligned it becomes. When we frame the same false fact as part of a coherent story, the model comes to believe it more deeply and becomes less misaligned than when we instruct it to assert the false fact. Content filters and persona vectors cannot tell these two framings apart, even though they lead to different levels of misalignment. These results suggest a risk for model updates, where training a model that does not adopt the new fact as true can induce misalignment even when the data looks harmless.
#02Nov 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.
#03Nov 3, 2026
cs.CL
A Circuit for In-Context Learning
Andrew Gao, William Gao
In-context learning (ICL) lets a pretrained language model perform a task specified by demonstrations in its prompt, with no parameter updates. With arbitrary labels the model must acquire a mapping it cannot have memorized, so the learning happens within a single forward pass. Prior work found candidate parts but not how they compose. We give the composition for few-shot sentence classification with arbitrary labels in three 3-4B-parameter transformers. The model implements a key-value memory over label-token positions: each label token's residual stream encodes the label's identity, and middle-layer attention heads write into it the class of the preceding demonstration as its key. At the query, upper-layer heads match the query's class against the stored keys and copy out the matching labels. An early-layer signal encoding whether any label has repeated gates this readout; in its absence the readers attend to the start of the prompt and no label is favored. A separate set of heads suppresses the most recently seen label. Each step is established causally by activation patching, head ablations against random-head baselines, and steering with the model's own signals. A softmax model of the readout with two constants per head, fit on one prompt distribution, predicts another. The computation is conserved across the three models, the named heads alone reproduce the behaviour, and a transformer trained from scratch grows the same parts. The circuit transfers to semantic concepts and to labels with meaning, and the same parts, with a causal gate, appear from 0.6B to 8B in one family and survive instruction tuning. ICL in this setting is a gated associative lookup built from a few identifiable component types, traced causally from demonstrations to prediction.
#04Nov 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.
#05Nov 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.