#01Oct 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.
#02Oct 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.
#03Oct 19, 2026
cs.LG
Kronecker Delta Rule for Long Context Linear Attention
Anamaria-Roberta Hartl, Levente Zólyomi, Michael List and 3 more
We propose KronLSTM, a linear attention architecture based on the Kronecker Delta Rule, a novel update rule for associative matrix memories. KronLSTM extends the xLSTM family with a memory-revision mechanism that corrects targeted associations while modifying the memory only along a single direction in matrix space. This minimally invasive memory revision reduces interference with previously stored information compared with delta-rule updates, making it particularly well suited for long-context language modeling. The resulting memory dynamics can be mathematically described as a Markov chain that converges to a steady-state distribution, while the expected norm of the memory matrix remains uniformly bounded throughout the entire input sequence. Hence, KronLSTM ensures stable memory dynamics without requiring additional normalization and stabilization mechanisms for the memory state. Experiments show that KronLSTM is competitive with, and often outperforms, existing linear attention architectures, including models of the (Gated) DeltaNet family, with particularly strong performance on long context benchmarks. These results establish the Kronecker Delta Rule as an effective and analytically tractable foundation for stable associative memory in recurrent linear attention architectures. Our code (https://github.com/NX-AI/KronLSTM) and models (https://huggingface.co/collections/NX-AI/kronlstm) are open-source.
#04Oct 19, 2026
stat.ML
Teacher Supervision, Fixed Representations and Calibration: Exact Risk Calculations for Candidate-Scoring Decision Models
Agus Sudjianto, Denis Burakov
Candidate-scoring decision models return a probability distribution over a presented set of answers. Public documentation of one such system, Jev, and of an open counterpart, JevAny, describes three training ingredients that determine what these probabilities estimate: soft targets from larger models, a frozen pretrained backbone and temperature calibration. We analyze each ingredient in Gaussian surrogates where the finite-sample risk can be computed exactly. A student trained on teacher targets inherits the teacher's bias, which more student data does not remove and agreement with the teacher does not reveal. A fixed representation lowers the risk only below an explicit sample-size threshold. In a probit model the exact recalibration map is a temperature scaling, which removes all excess risk only when the teacher's coefficient has the correct direction and otherwise leaves a residual that calibration diagnostics do not detect. Under Luce's choice axiom, candidate scores are coherent across refinements of an event if and only if they aggregate by log-sum-exp. On 231,521 credit card complaints from the Consumer Financial Protection Bureau, where the decision is whether a complaint ends in monetary relief, a student trained on a logistic teacher's probabilities ends at the teacher's decision cost while a student trained on outcomes goes 8% below it, a 30B model read zero-shot remains worse than the teacher after recalibration, and that model departs from the coherence condition by 17.5 decibans. Pretrained representations reduce the labeled data required and calibration corrects the scale of the probabilities, but neither corrects a biased teacher, so the probabilities have to be checked against realized outcomes.
#05Oct 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.