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arXiv:2508.15659v2 Announce Type: replace Abstract: Accurate dose-response forecasting under sparse sampling is central to precision pharmacotherapy. We present the Amortized In-Context Mixed-Effect Transformer (AICMET) model, a transformer-based latent-variable framework that unifies mechanistic compartmental priors with amortized in-context Bayesian inference. AICMET is pre-trained on hundreds of thousands of synthetic pharmacokinetic trajectories with Ornstein-Uhlenbeck priors over the parameters of compartment models, endowing the model with strong inductive biases and enabling zero-shot adaptation to new compounds. At inference time, the decoder conditions on the collective context of previously profiled trial participants, generating calibrated posterior predictions for newly enrolled patients after a few early drug concentration measurements. This capability collapses traditional model-development cycles from weeks to hours while preserving some degree of expert modelling. Experiments across public datasets show that AICMET attains state-of-the-art predictive accuracy and faithfully quantifies inter-patient variability -- outperforming both nonlinear mixed-effects baselines and recent neural ODE variants. Our results highlight the feasibility of transformer-based, population-aware neural architectures as offering a new alternative for bespoke pharmacokinetic modeling pipelines, charting a path toward truly population-aware personalized dosing regimens.

arXiv:2509.05732v1 Announce Type: new Abstract: How do we enable AI systems to efficiently learn in the real-world? First-principles models are widely used to simulate natural systems, but often fail to capture real-world complexity due to simplifying assumptions. In contrast, deep learning approaches can estimate complex dynamics with minimal assumptions but require large, representative datasets. We propose SimPEL, a method that efficiently combines first-principles models with data-driven learning by using low-fidelity simulators as priors in Bayesian deep learning. This enables SimPEL to benefit from simulator knowledge in low-data regimes and leverage deep learning's flexibility when more data is available, all the while carefully quantifying epistemic uncertainty. We evaluate SimPEL on diverse systems, including biological, agricultural, and robotic domains, showing superior performance in learning complex dynamics. For decision-making, we demonstrate that SimPEL bridges the sim-to-real gap in model-based reinforcement learning. On a high-speed RC car task, SimPEL learns a highly dynamic parking maneuver involving drifting with substantially less data than state-of-the-art baselines. These results highlight the potential of SimPEL for data-efficient learning and control in complex real-world environments.

arXiv:2303.14694v3 Announce Type: replace-cross Abstract: We define bigraded persistent homology modules and bigraded barcodes of a finite pseudo-metric space X using the ordinary and double homology of the moment-angle complex associated with the Vietoris-Rips filtration of X. We prove a stability theorem for the bigraded persistent double homology modules and barcodes.

arXiv:2509.05735v1 Announce Type: new Abstract: Data collection is crucial for learning robust world models in model-based reinforcement learning. The most prevalent strategies are to actively collect trajectories by interacting with the environment during online training or training on offline datasets. At first glance, the nature of learning task-agnostic environment dynamics makes world models a good candidate for effective offline training. However, the effects of online vs. offline data on world models and thus on the resulting task performance have not been thoroughly studied in the literature. In this work, we investigate both paradigms in model-based settings, conducting experiments on 31 different environments. First, we showcase that online agents outperform their offline counterparts. We identify a key challenge behind performance degradation of offline agents: encountering Out-Of-Distribution states at test time. This issue arises because, without the self-correction mechanism in online agents, offline datasets with limited state space coverage induce a mismatch between the agent's imagination and real rollouts, compromising policy training. We demonstrate that this issue can be mitigated by allowing for additional online interactions in a fixed or adaptive schedule, restoring the performance of online training with limited interaction data. We also showcase that incorporating exploration data helps mitigate the performance degradation of offline agents. Based on our insights, we recommend adding exploration data when collecting large datasets, as current efforts predominantly focus on expert data alone.

arXiv:2406.16032v2 Announce Type: replace-cross Abstract: We consider a variant of the stochastic gradient descent (SGD) with a random learning rate and reveal its convergence properties. SGD is a widely used stochastic optimization algorithm in machine learning, especially deep learning. Numerous studies reveal the convergence properties of SGD and its theoretically favorable variants. Among these, the analysis of convergence using a stationary distribution of updated parameters provides generalizable results. However, to obtain a stationary distribution, the update direction of the parameters must not degenerate, which limits the applicable variants of SGD. In this study, we consider a novel SGD variant, Poisson SGD, which has degenerated parameter update directions and instead utilizes a random learning rate. Consequently, we demonstrate that a distribution of a parameter updated by Poisson SGD converges to a stationary distribution under weak assumptions on a loss function. Based on this, we further show that Poisson SGD finds global minima in non-convex optimization problems and also evaluate the generalization error using this method. As a proof technique, we approximate the distribution by Poisson SGD with that of the bouncy particle sampler (BPS) and derive its stationary distribution, using the theoretical advance of the piece-wise deterministic Markov process (PDMP).