#01Oct 19, 2026
cs.LG
Trajectory Replay: Continuous-Time Mixture Transport for Lifelong Generative Models
Alessandro Palma, Charles Jones, Tristan Cinquin and 2 more
Adapting pre-trained continuous-time generative models to sequentially incoming data without forgetting earlier tasks is a central challenge in lifelong learning. A leading strategy, generative replay, uses a generative model trained on historical tasks to augment its own continual update with synthetic samples from experience. However, it requires full trajectory simulations at every training step, which accumulate discretization errors and can degrade the replayed historical distribution. Here, we propose trajectory replay, which bypasses sample generation by training an updated velocity field to match both a frozen historical velocity along its trajectories and the incoming task's velocity field, weighted by a stability-plasticity coefficient. Through the lens of continuous-time transport, we show the resulting optimum averages the two task velocities by their respective densities and generates the mixture of their probability paths. Combined with mean velocity distillation, trajectory replay accesses historical trajectories using only a few network evaluations per continual update. Empirically, it outperforms generative replay and distillation baselines on class-incremental image generation. In two biological case studies, trajectory replay extends generative perturbation models to new contexts and experimental batches across two data modalities while preserving treatment-effect prediction.
#02Oct 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.
#03Oct 19, 2026
cs.LG
Scaling Parameter-Efficient Fine-Tuning for Brain Encoding
Zhuofan Josh Ying, Guanglong Sun, Nolan Ho and 6 more
Brain encoding models aim to predict neural responses to stimuli. The most widely used approach fits readouts from frozen pretrained backbones. Using neural data to train large models from scratch or fully fine-tune them after task-pretraining has proven difficult because neural data is costly and limited. We show that parameter-efficient fine-tuning (PEFT) enables us to effectively adapt very large pretrained backbones for brain encoding with a small number of trainable parameters. To make it computationally practical, we exploit the backbone's causal structure to predict multiple timepoints in a single pass instead of using sliding windows, significantly reducing feature-extraction cost. This enables efficient fine-tuning of multimodal backbones with up to 104B parameters, the largest model adapted for brain encoding to our knowledge. Trained with a low-rank adapter (LoRA) and a lightweight readout, our approach consistently improves brain encoding performance across nine diverse multimodal backbones. On the same Qwen3-Omni backbone as the prior state-of-the-art (SoTA), our method BrainLoRA achieves the best published performance on the Algonauts 2025 Challenge. We also show the adapted multimodal backbones remain interpretable: modality attribution recovers the canonical sensory topography that prior work often obtains by construction from separate unimodal encoders, and neural adaptation increases the contribution of audio inputs and cross-modal mixing within the backbone. To scale out the number of adapted models, we develop a multi-LoRA kernel that accelerates joint training of multiple LoRAs on a shared backbone. This enables an ensemble of 200+ adapted models that ranks first on the public Algonauts post-challenge leaderboard at the time of writing. Together, our results highlight PEFT as an efficient and powerful paradigm for brain encoding.
#04Oct 19, 2026
cs.LG
Next Best Action: Causal Constrained Offline RL for Business Action Targeting
Surya Ramachandiran, Yiming Li, Juan Mancilla-Caceres and 2 more
Next Best Action (NBA) systems must select among customer interventions (e.g., discounts, promotions, and lifecycle actions), maximize long-term economic value, satisfy complex operational constraints, and remain causally grounded. Existing approaches lack a rigorous framework for meeting these requirements jointly. We address this gap by formulating NBA as a Constrained Markov Decision Process (CMDP). We then integrate off-policy causal correction of the estimated customer dynamics directly into the Linear Programming (LP) formulation of the CMDP. The resulting policy selects actions based on customer states to maximize long-term value while explicitly enforcing business guardrails. Furthermore, the LP formulation yields shadow prices that quantify the economic trade-offs of operational constraints (e.g., fairness and user welfare), enhancing policy interpretability. We validate our proposed offline Reinforcement Learning (RL) framework on an industry case study involving rideshare coupon targeting, where customer states are defined by Recency, Frequency, and Monetary (RFM) stages. We evaluate performance using model-based off-policy evaluation, with causal dynamics estimated from a temporal holdout. Under the observed coupon budget and RFM state representation, our optimized policy improves customer lifetime value (LTV) by 19% over the estimated behavior policy and 8% over a myopic baseline. Although the demonstrated action space is binary, the proposed framework is action-agnostic, yielding a general-purpose decision module for targeting systems that manage multiple interventions.
#05Oct 19, 2026
cs.LG
Simulation Priors for Rapid Adaptation in Model-Based RL for Autonomous Racing
Adrian Remonda, Jiajun Xi, Nicklas Hansen and 5 more
Reinforcement learning enables learning high-performance control policies, but its reliance on extensive interaction limits deployment on physical systems where data collection is costly, and failures are unsafe. We introduce Prior-Informed Adaptation (PIA), an offline-to-online model-based RL framework that uses structured simulation priors for rapid adaptation. PIA pretrains a world model on heterogeneous low- and high-fidelity simulated trajectories, then adapts it with limited target-domain interaction using uncertainty-regularized planning. Rather than requiring an accurate simulator for policy transfer, PIA treats simulated trajectories as biased priors whose residual mismatch is corrected during online adaptation. We evaluate PIA in autonomous racing using high-fidelity simulation and on a real full-size autonomous race car. In simulation, PIA adapts faster across track and surface shifts than strong baselines, achieving lower lap times and fewer failures. On hardware, PIA achieves reliable few-shot adaptation with less than one hour of on-vehicle interaction.