#01Nov 5, 2026
stat.ML
Unifying Central Flow, Rod Flow, and the Edge Coupling
Eric Regis, Sinho Chewi
At the edge of stability, the iterates of gradient descent oscillate along the sharp directions of the Hessian. This poses a significant challenge for continuous-time models as the usual continuous-time approximation -- the gradient flow -- admits no oscillations. Several continuous-time models have been proposed to capture the behavior at the edge of stability, among them central flow and rod flow. Although both models can be interpreted as performing a coarse-graining in time, the connection between them remains poorly understood. Here we show that both flows can be derived from a third object, the edge coupling: a functional on consecutive iterates whose critical points are the fixed points and period-two orbits of gradient descent. It is revealed that the two flows correspond to coarse-grainings at different time scales. Rod flow coarse-grains over only the fastest time scale, while central flow coarse-grains over both the fast and intermediate time scales. Furthermore, using the edge coupling, we derive rod flows and central flows for momentum methods such as heavy ball and Adam. We verify the derived flows experimentally on representative neural network architectures, where they track the discrete iterates throughout all phases of training -- including the transition from the stable regime to the edge of stability.
#02Nov 5, 2026
cs.LG
Synthesis of Ovarian Cancer Multi-Omics Datasets: A Biology-Informed Evaluation Framework
Déborah Boyenval, Alina Malyutina, Jaana Oikkonen and 2 more
Paired multi-omic cancer cohorts are costly to assemble and difficult to share, motivating synthetic cohorts as a complementary resource. As generative model development accelerates, we shift the focus from proposing yet another architecture to defining evaluation criteria that determine whether synthetic data preserve biologically relevant structure. We introduce a biology-informed and patient-disjoint framework for evaluating the generation of paired RNA expression and copy-number variation (CNV) profiles, and apply it to the longitudinal DECIDER high-grade serous ovarian cancer cohort. The framework assesses modality-specific fidelity and coherence between RNA and CNV pairs using agreement between real training and held-out data as a reference, alongside complementary training-data proximity diagnostics. We adapt three multi-omic integration architectures based on variational autoencoders to generate paired profiles. The model leading several fidelity and coherence measures also shows the strongest training-data proximity. The protocol and case study offer the community a reference for comparing future multi-omic generators.
#03Nov 5, 2026
cs.LG
Interpretable many-body interaction laws for collective motion from few trajectories
Timon S. Gutleb
Models of collective motion usually reduce social interactions to pairwise forces, despite empirical evidence for many-body effects. We introduce the directional atomic cluster expansion (dACE), which adapts the atomic cluster expansion (ACE) of interatomic potentials to self-propelled agents. dACE provides a systematically improvable, exactly equivariant expansion of an agent's acceleration that splits uniquely into 1-, 2-, 3-body and higher contributions, along with a self term for the agent's own past motion that is fitted so that it does not absorb the interactions. On simulated collectives in two and three dimensions with known rules, dACE recovers the interaction law body order by body order from little data, while the neural model SocialNet, the current closest competitor, needs more data, has much larger errors on many-body or chiral rules and is restricted to 2D. On real data sets of tracked zebrafish and golden shiners, the laws learned by dACE agree better between disjoint halves of the data than SocialNet's. The learned laws are interpretable, and in the shiners the 3-body term opposes the pairwise response as neighbourhoods get dense. Finally, we show that next-step prediction accuracy mostly measures self-propulsion and noise rather than the interactions, and suggest more robust combinations of error measures for interaction learning.
#04Nov 5, 2026
cs.LG
Muir: Linear Attention with Sensitivity-Allocated Gating and Matched-Filter Readout
Tushaar Gangavarapu, Gil Tabak, Clemens JS Schaefer
Linear attention compresses context into a fixed-size key-value state for linear-time training and constant-memory inference. Gated delta-rule models decay this state and erase its prediction for an incoming key before writing a new value; Gated DeltaNet-2 (GDN-2) generalizes this with channel-wise decay and decoupled, full-rank erase and write gates. However, we show that state updates are far less sensitive to erasure than to writes: key activation and unit normalization concentrate key energy onto a sparse subset of channels, whereas value writes scale all channels, so the erase gate can be parameterized at lower rank. Furthermore, slow-decaying state rows accumulate much larger norms than fast rows, dominating unweighted readout and forcing stronger write-time erasure to suppress interference. Guided by this analysis, we introduce Muir, which fuses all gates into a sensitivity-allocated low-rank projection, re-weights state rows with a matched-filter readout gate, and reinvests the saved parameters in a wider feed-forward network. Because standard chunkwise algorithms become numerically unstable at the large chunk sizes needed to saturate wide matrix units, we design a parallel update for stable, efficient training. Across 166M-1.34B parameters, Muir lowers perplexity by 1.8-2.0% over GDN-2 and 2.5-3.6% over Transformer, raises commonsense accuracy by up to 1.9 points, and improves extractive recall over GDN-2. At 1.34B, Muir outperforms both baselines on multi-hop and multi-needle recall, extrapolates 2,560x from its 4K training length to 10M-token streams without perplexity drift, and maintains near-100% passkey retrieval to 1M tokens with static readout. Muir achieves these gains while matching GDN-2 throughput, reaching its 100B-token validation loss 1.2x faster, and training 2.7x faster than Transformer at 32K.
#05Nov 5, 2026
cs.CL
Label-Wording Augmentation in a Typed-Decision Encoder: Gains on Unfamiliar Words, Not on Abbreviations or Codes
Vladimir Beskorovainyi
Typed-decision models score options that the caller supplies at request time, so their accuracy depends on label wording that the model's developer does not control. We compare two releases of a 307M-parameter multilingual cross-encoder, Ru-Jev, trained on thirteen Russian-language tasks; the later release adds an augmentation that presents labels in several surface forms. Holding questions fixed and varying only how eighteen routing labels are worded, we evaluate ten label vocabularies, produced by three separate processes and checked for overlap with the training data, with five candidates per question and, for eight of them, also with eighteen. On held-out vocabularies made of ordinary or borrowed words (English-derived jargon, office slang, department names), the augmented release is more accurate in every setting, by up to 0.24. Eleven of these fourteen gains survive a Holm correction (slang with eighteen candidates and descriptive sentences with five do not), and for jargon on all labels the label-level interval excludes zero in both settings. On abbreviations and opaque codes it gives no usable gain: on abbreviations it is not better, and worse on the clean slice, and on opaque codes both releases stay at or below chance once labels related to training options are removed. In most cells where accuracy rises, the risk-coverage area falls, but with eighteen candidates confident errors rise on jargon and slang. On two datasets neither release saw, accuracy moves by -8.4 and +5.6 points. We also report four evaluation hazards from comparing the two releases.