#01Oct 22, 2026
math.SG
SympFormer: Inertial Attention Blocks from Damped Hamiltonian Dynamics on Spaces of Probability Measures
Viktor Stein, Levin Maier, Wuchen Li and 1 more
The attention mechanism underpins modern large language models, yet their dynamics remain only partially understood. Recent perspectives interpret attention blocks as interacting particle systems, whose mean-field limits correspond to gradient flows of energy functionals on spaces of probability densities on $\mathbb R^d$ equipped with Wasserstein-type metrics. We extend this viewpoint by deriving accelerated attention blocks from inertial, Nesterov-type damped Hamiltonian dynamics on these density spaces, developing the geometry and differential calculus needed to make the construction rigorous. In particular, we introduce a local-mobility geometry for the Otto-Wasserstein and softmax-Wasserstein settings, and a quotient Stein geometry that resolves the degeneracy of the linear-attention kernel to yield a well-defined metric and differential calculus. We provide rigorous foundations when softmax attention admits a gradient-flow formulation and when its inertial counterpart admits a damped Hamiltonian on explicitly characterized domains. For linear attention, we obtain a finite-dimensional solution theory with sharp conditions for global existence versus finite-time second-moment blow-up. We further prove a quantitative link between continuous moment blow-up and the discrete-layer depth at which token norms cross a prescribed threshold. Finally, motivated by the finite-token geometry, we propose geometric corrections to token and momentum updates. In decoder-only, nanoGPT-style experiments on TinyStories and OpenWebText, these corrections lower validation negative log-likelihood on next-token prediction relative to momentum-only controls.
#02Oct 22, 2026
cs.LG
Rethinking Sequence Compression with Test-time Regression
Sihan Yang, Jie Huang, Hanxuan Li and 4 more
Sequence compression is a fundamental operation and a critical information bottleneck in efficient language and multimodal models, and yet prevailing approaches based on pooling or learned projections remain underperforming. We revisit sequence compression through the lens of test-time regression: input tokens define a regression problem whose fitted coefficients form the compressed representation. Importantly, the regression problem is learned end-to-end via backpropagation, while its coefficients are computed efficiently in closed form during the forward pass. This leads to TTR-Compressor, a general alternative to conventional pooling and projection-based compression. We evaluate TTR-Compressor as the compressor for block-wise sparse attention and the visual token merger for multimodal large language models. On block-wise sparse attention, TTR-Compressor improves RULER performance over attention-based compressors by a large margin. For visual token merging, it consistently outperforms the standard MLP merger and matches its performance with 55.6% fewer visual tokens. These results establish test-time regression as an effective primitive for sequence compression in efficient language and multimodal models.
#03Oct 22, 2026
cs.LG
When to Follow the Teacher: Advantage-Based On-Policy Distillation
Mahdi Sabbaghi, George Pappas, Hamed Hassani and 1 more
Online Policy Distillation (OPD) often outperforms offline methods such as Supervised Fine-Tuning (SFT) by training on trajectories sampled directly from the student. However, standard OPD trains the student to follow the teacher at every state of the trajectory, assuming that teacher guidance is always beneficial. We instead distinguish between what the teacher prefers and what actually helps the current student succeed. We introduce Advantage-Based On-Policy Distillation (AOPD), which weights teacher actions by their counterfactual advantage under the student. Teacher actions that improve the student's expected outcome are reinforced, while those that do not are downweighted. Directly computing these advantages requires trying alternative teacher actions at each step and running new rollouts from each. Instead, we show that the AOPD objective can be estimated using only standard student rollouts and their terminal rewards. Our estimator uses teacher importance weights on the student-sampled actions to provide unbiased advantage-weighted supervision, without any additional rollouts or reward evaluations. This allows AOPD to focus teacher supervision on actions that help the current student while preserving the rollout efficiency of standard OPD. Experiments on math, coding, and Medqa show gains over distillation and RL baselines in both external-teacher and self-distillation settings.
#04Oct 22, 2026
cs.LG
CRANE: Post-Hoc Counterfactual Retrieval for Multimodal Classifiers
Franco Rugolon, Ioanna Miliou, Panagiotis Papapetrou
Counterfactual explanation methods have been introduced for unimodal settings, with dedicated frameworks for tabular, timeseries, text, and image data, yet no post-hoc method has been designed for classifiers that learn from multimodal inputs. Existing explainability methods for multimodal classifiers apply modality-specific attribution independently to each input, which fails to yield coherent explanations and does not transfer to arbitrary pre-trained multimodal architectures. To address these shortcomings, we present CRANE (Counterfactual Retrieval via Agnostic Nearest-neighbour Explanations), the first post-hoc, model-agnostic framework for nearest-neighbour multimodal counterfactual generation that retrieves real training examples from the target class as candidate explanations, ensuring plausibility by construction. Across four heterogeneous datasets and three fusion strategies, we show that Multimodal Consensus Retrieval (MC-R), which intersects per-modality neighbour sets to identify instances jointly close to the query in every modality, emerges as the strongest multimodal strategy, achieving the best or joint-best outcome on three of four datasets while grounding every explanation in the joint training distribution. Unimodal strategies remain competitive when a single modality dominates the decision boundary.
#05Oct 22, 2026
cs.CL
Would an LLM Match into a Residency? Uncertainty, Reasoning and Image Use of Open Language Models on the Spanish MIR Examination
Miguel Fernandez-de-Retana, Unai Zulaika, Ruben Sanchez-Corcuera and 2 more
Accuracy on medical examinations is common evidence offered for the clinical use of language models, yet a health system that intends to run an open model on its own hardware needs to know considerably more: whether the model recognizes when it is likely to be wrong, whether medical fine-tuning improves this ability, whether its correct answers rest on sound clinical reasoning, or whether it actually uses the images it is given. We examine these questions for four open models of 8 to 27 billion parameters on the Spanish MIR residency examination, scoring 1,552 questions from eight editions under the exam's own rules. Answering every question, the three larger models would rank among roughly the first 600 to 3,000 candidates, with 41 to 43 specialties still open to them. Abstention, however, never pays, because even their least confident answers are right more often than the 25% break-even. Medical fine-tuning reduced overconfidence at the cost of accuracy, without improving how well confidence separates right from wrong answers. Moreover, 13-38% of correct answers rejected a distractor for a clinically unsound reason that confidence did not reflect, and removing or swapping the provided contextual images left accuracy unchanged.