#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.AI
Scientist World: Grow a Research World for AI-Scientists
Taiming Lu, Sachin Konan, Zhuang Liu
AI-Scientists arrived, but a world for them to grow in did not. Human scientists take theirs for granted $-$ centuries of open problems and shared ideas, waiting in the scientific literature. To AI-Scientists, that world is readable but not runnable, so we build Scientist World for them: every research paper becomes an executable environment. Our autonomous pipeline extracts each paper's open-ended research question and reproduces its proposed method as the baseline; an AI-Scientist entering the environment is evaluated against what the human authors achieved. We release the first 1,000 verified environments. With the world as an evaluation, we found that frontier AI-Scientists can already surpass the human researchers 74% of the time. As a record of how AI does science, it contains 6,400 hours of research traces, with every idea, experiment, failure, and success. As a training ground, we are able to raise (+158%) a small model to match frontier models in research ideation. At last, AI-Scientists' own world has arrived, grown from and growing with science itself.
#03Nov 5, 2026
cs.LG
Towards interpreting any residual stream direction by scaling activation inversion
Celeste De Schamphelaere, Juan J. Vazquez, Ari Spiesberger and 4 more
To interpret a direction in a language model's residual stream, we can look for text that strongly activates it. But when such text is found by scanning a corpus, it is limited to what that corpus contains. We develop Maximally-Activating Example Metamodels (MAEMs), language models which map residual stream directions from a subject model to text exemplars that strongly activate those directions. Our objective is to maximise the cosine similarity of a supplied residual stream direction with the activations of the text generated by the MAEM. This label-free RL objective helps to scale MAEMs on diverse sources of residual stream directions. Empirically, we find the resultant metamodel produces informative exemplars: a Qwen3.6-27B MAEM inverts held-out activations better than corpus search or a natural-language autoencoder (NLA), beats corpus search (at 10M tokens) on a majority of held-out languages/domains, and activates 89% of held-out SAE features. It also identifies concepts behind steering vectors about as well as NLAs, recovers the payloads of LoRA backdoors more often than corpus search, and can even verbalise some model workspace inner monologue. Unlike explanations produced by other metamodels (e.g. NLAs), MAEM exemplars can be verified with a forward pass on the subject model, making the MAEM objective a grounded alternative for scaling the training of metamodels.
#04Nov 5, 2026
cs.CV
4D Point Splatting for mmWave Radar Micro-Doppler Differentiable Rendering
Adnan Armouti, Guanyue Qian, Rajalakshmi Nandakumar
Millimeter-wave radar resolves the micrometer displacements of a moving body as micro-Doppler, enabling gait, gesture, activity, pose and vital-sign sensing. Each task relies on a downstream model trained on real data, yet radar datasets lag orders of magnitude behind vision and language. Brute-force collection will not close that gap, and existing synthesis methods (forward-only simulators, learned generators and static-scene inverse renderers) cannot fit a real capture of a moving body, leaving a sim2real gap. We present 4D Point Splatting (4DPS), a physics-based differentiable renderer that fits an explicit moving scene to a real capture. Using the synchronized camera to initialize the room and body, we represent the scene as oriented points carrying material, normal and velocity, and splat each point into range and Doppler bins. Our output is the raw complex return a real radar records, so we apply the same signal processing on the rendered data to obtain any representation for training any SOTA downstream model. We fit 235 sequences on HuPR and 100 on RT-Pose, two datasets with different radars. Our reconstructions set the state of the art, with median correlations of 0.940 and 0.830 on range-azimuth, 0.829 and 0.695 on range-Doppler, and 0.988 and 0.966 on micro-Doppler. Our renders also set the state of the art in downstream sim2real gap. On RT-Pose, a pose model trained on them reaches 21.9 cm MPJPE on real data, against 16.7 cm for real training and 127.6 cm for the RF-Genesis baseline, where both the rendered- and real-trained models learn nearly the same features. Our custom CUDA kernels fit a sequence in 5.7 minutes on HuPR and 12.9 on RT-Pose on one H100, making dataset-scale inverse rendering of mmWave radar possible for the first time. This work can enable synthetic data generation for any human-centered downstream task and model, and scene editing for data augmentation.
#05Nov 5, 2026
cs.LG
Module-Aware Optimization for Graph Neural Networks
Guy Hadad, Haggai Roitman, Moshe Eliasof and 1 more
Different optimizers impose different geometries on parameter updates. Adaptive methods such as Adam and AdamW use coordinate-wise updates, while matrix-aware optimizers such as Muon utilize weight-matrix structure through orthogonalized updates. For Graph Neural Networks (GNNs), however, the effective geometry of its weight matrices is shaped not only by its learned channel-mixing weights, but also by the graph-propagated representations it acts on. Thus, even if an update is well normalized as a matrix, its effect on the layer output can be amplified when applied to graph-propagated features. To address this gap, we introduce GraphMuon, a graph-aware optimizer that adapts Muon's matrix updates to the covariance structure of graph-propagated layer inputs. GraphMuon performs orthogonalization in a metric defined by these propagated representations and normalizes step sizes according to the update's induced effect on the layer representation. We show that theoretically, vanilla Muon can suffer from graph-induced update amplification, while our GraphMuon can mitigate this effect. As such, our GraphMuon yields a graph-metric analogue of Muon's polar update step. Empirically, GraphMuon achieves $1.32\times$-$2.42\times$ validation-loss time-to-target speedups over AdamW on three large-scale OGB benchmarks. Across 15 dataset-architecture configurations spanning node classification, inductive graph classification, and graph regression, it achieves lower time-to-target in 13 cases, while maintaining competitive or superior predictive performance. Code is available at https://github.com/guy-hadad/GraphMuon.