#01Oct 19, 2026
math.NA
Polar Switch: Fast Muon Orthogonalization with Polynomial Circuits
Zhehang Du, Weijie Su
Muon, a 2024-born optimizer for language models, differs from the 2015-born spectral gradient descent mainly in its fast, GPU-friendly Newton--Schulz polynomial for orthogonalizing the gradient matrix. Accordingly, a line of research proposes faster polynomial iterations for gradient orthogonalization, such as Polar Express and Gram Newton--Schulz, both built on quintic polynomials. In this paper, we introduce Polar Switch, a new approach to polynomial gradient orthogonalization. Using simple polynomial circuits, Polar Switch reaches a given high polynomial degree at a lower FLOP cost than quintic iterations. We define a circuit as a short sequence of symmetric matrix products on a few square buffers, and circuits with $k$ products form a restricted family of odd polynomials of degree up to $2^{k+1}+1$. We choose the sequence of products in each circuit, their coefficients, and how the circuits are composed by numerically minimizing a worst-case bound on the polar approximation error. This minimization is subject to a FLOP budget that accounts for symmetric matrix multiplication kernels and a rounding constraint for numerical stability in half precision. Our two recommended Polar Switch methods have 15.5--18.7\% lower runtime than Polar Express on square matrices and 8.6--16.2\% lower runtime than Gram Newton--Schulz on rectangular matrices with aspect ratios 3.25, 3.5, and 8, with comparable approximation accuracy. In pretraining Modded-NanoGPT \#91, Qwen3-0.6B, and Gemma 3-1B, Polar Switch reaches final validation losses similar to those of established orthogonalization methods. Across the more than 14 million matrices that each of the two recommended methods orthogonalized in these runs, the estimated output spectral norms never exceed the designed bounds by more than 3\%, demonstrating their numerical stability.
#02Oct 19, 2026
quant-ph
Supervised Learning with Quantum Hamiltonian Embeddings
Riccardo Molteni, Minjun Jeon, Paolo Braccia and 8 more
Machine learning is widely regarded as a promising application in which quantum computing could offer a computational advantage. However, general quantum machine learning models with provable guarantees on performance, trainability, and efficient inference remain limited. In this work, we introduce quantum Hamiltonian embeddings, a supervised learning framework in which a classical training dataset is encoded into a single effective, parameterized Hamiltonian. Training optimizes the parameters of this data-dependent Hamiltonian, whose approximate ground state defines the classification rule. Once the ground state has been approximated using a quantum algorithm, inference can be performed either classically using a classical representation of the learned state, or with a quantum representation of the state. We establish efficient methods for gradient estimation and prove favorable generalization guarantees. Furthermore, under standard cryptographic assumptions, we show that Hamiltonian embeddings can realize hypothesis functions beyond the reach of efficient classical algorithms. We then demonstrate the framework at scale on IBM Heron processors using a standard benchmark dataset. Together, these results establish Hamiltonian embeddings as a new framework for quantum machine learning, combining theoretical guarantees with a path for experimental investigations at scale on quantum hardware.
#03Oct 19, 2026
cs.RO
CoopUQ: Robust Multi-Robot Social Navigation via Uncertainty-Aware Cooperative Forecasting
Zehao Wang, Jianpeng Yao, Yuping Wang and 9 more
Reinforcement learning enables mobile robots to make fast and scalable navigation decisions in constrained human-shared environments. However, directly extending single-robot approaches to multi-robot settings often fails to ensure safety and efficiency, especially under occlusions and out-of-distribution (OOD) scenarios, where individual robots may overlook potential risks or make inaccurate predictions. Leveraging cooperation effectively for both prediction and navigation remains a major challenge. We propose CoopUQ, a multi-robot social navigation framework that bridges uncertainty-aware cooperative occupancy forecasting and robust decision making. CoopUQ predicts future occupancy grid maps through cross-robot spatiotemporal feature fusion and further leverages forecasts and their uncertainty to guide policy via constrained multi-agent reinforcement learning, where the cost penalizes navigation through regions predicted to be occupied or highly uncertain. This design enables the policy to adapt its risk sensitivity under distribution shifts. Experimental results across multiple Unity3D-based simulation environments with both in-distribution and OOD settings, including diverse layouts, pedestrian densities, and rushing behavior, demonstrate improved prediction performance and safety over representative baselines. Real-robot experiments further demonstrate its robustness across various scenes. Our code and videos are available at https://coopuq.github.io/.
#04Oct 19, 2026
cs.LG
WeAct: Dynamic Weight Switching as Agent Actions
Rui Shi, Xunjian Yin, Jiacheng Sang and 2 more
Long-horizon agents must learn heterogeneous capabilities from interleaved trajectories. Updating shared parameters to learn new capabilities can degrade previously acquired ones, resulting in catastrophic forgetting. As a trajectory unfolds, different stages may require different capabilities, yet conventional joint training and static adapter merging maintain a fixed parameter configuration throughout execution. We introduce WeAct (Weight-level Internal Actions), which trains independent capability-specific LoRA adapters over a frozen backbone and adds adapter selection to the agent's action space. These internal actions use the model's native tool-calling interface for on-demand capability composition in a shared context. Across eight deep-research benchmarks, Qwen3-32B with WeAct improves average accuracy by 6.2% relative to full fine-tuning counterparts despite using less compute, and by 27.5% relative to the strongest static LoRA-merging method. WeAct also supports modular continual adaptation, by adding a new code computation adapter to expand the agent's capabilities and updating the existing writing adapter to improve report quality. Both updates leave the backbone and other adapters unchanged, supporting modular continual adaptation in agents.
#05Oct 19, 2026
stat.ME
Dirichlet-Tree Allocation Priors for Bayesian Causal Forests
Javier Enrique Aguilar, Daniel Klippert, Yusufhan Balci and 1 more
Bayesian Causal Forests (BCF) estimate heterogeneous treatment effects with a separate ensemble of treatment trees. The prior on the leaf values of the treatment trees determines whether sampling variability is attributed to the treatment effect. Independent shrinkage priors exert no control over how a tree allocates variability across its leaves, and their total prior variance grows as leaves are added. We propose the Dirichlet-Tree Bayesian Causal Forest, which jointly regularizes the leaf values of each treatment tree through a Dirichlet-Tree prior on their variance shares, generated by stick-breaking along the tree topology. We characterize the spike and tails of the marginal leaf prior, show that the prior adaptively bounds the number of regions of effect heterogeneity, and establish posterior consistency for the forest. In simulations, the model outperforms BCF when heterogeneity is confined to a few regions and reduces spurious heterogeneity elsewhere, and, unlike independent shrinkage priors, its accuracy does not deteriorate as the trees grow. We also evaluate the model on real data, including a pancreatic cancer survival study.