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arXiv:2504.06372v3 Announce Type: replace-cross Abstract: Inference and estimation are fundamental in statistics, system identification, and machine learning. When prior knowledge about the system is available, Bayesian analysis provides a natural framework for encoding it through a prior distribution. In practice, such knowledge is often too vague to specify a full prior distribution, motivating the use of default 'uninformative' priors that minimize subjective bias. Jeffreys prior is an appealing uninformative prior because: (i) it is invariant under any re-parameterization of the model, (ii) it encodes the intrinsic geometric structure of the parameter space through the Fisher information matrix, which in turn enhances the diversity of parameter samples. Despite these benefits, drawing samples from Jeffreys prior is challenging. In this paper, we develop a general sampling scheme using the Metropolis-Adjusted Langevin Algorithm that enables sampling of parameter values from Jeffreys prior; the method extends naturally to nonlinear state-space models. The resulting samples can be directly used in sampling-based system identification methods and Bayesian experiment design, providing an objective, information-geometric description of parameter uncertainty. Several numerical examples demonstrate the efficiency and accuracy of the proposed scheme.

arXiv:2508.20614v1 Announce Type: new Abstract: Amortized Bayesian model comparison (BMC) enables fast probabilistic ranking of models via simulation-based training of neural surrogates. However, the reliability of neural surrogates deteriorates when simulation models are misspecified - the very case where model comparison is most needed. Thus, we supplement simulation-based training with a self-consistency (SC) loss on unlabeled real data to improve BMC estimates under empirical distribution shifts. Using a numerical experiment and two case studies with real data, we compare amortized evidence estimates with and without SC against analytic or bridge sampling benchmarks. SC improves calibration under model misspecification when having access to analytic likelihoods. However, it offers limited gains with neural surrogate likelihoods, making it most practical for trustworthy BMC when likelihoods are exact.

arXiv:2508.01228v2 Announce Type: replace-cross Abstract: Modeling forest dynamics under novel climatic conditions requires a careful balance between process-based understanding and empirical flexibility. Dynamic Vegetation Models (DVM) represent ecological processes mechanistically, but their performance is prone to misspecified assumptions about functional forms. Inferring the structure of these processes and their functional forms correctly from data remains a major challenge because current approaches, such as plug-in estimators, have proven ineffective. We introduce Forest Informed Neural Networks (FINN), a hybrid modeling approach that combines a forest gap model with deep neural networks (DNN). FINN replaces processes with DNNs, which are then calibrated alongside the other mechanistic components in one unified step. In a case study on the Barro Colorado Island 50-ha plot we demonstrate that replacing the growth process with a DNN improves predictive performance and succession trajectories compared to a mechanistic version of FINN. Furthermore, we discovered that the DNN learned an ecologically plausible, improved functional form of the growth process, which we extracted from the DNN using explainable AI. In conclusion, our new hybrid modeling approach offers a versatile opportunity to infer forest dynamics from data and to improve forecasts of ecosystem trajectories under unprecedented environmental change.

arXiv:2507.11535v2 Announce Type: replace Abstract: Standard Bayesian approaches for linear time-invariant (LTI) system identification are hindered by parameter non-identifiability; the resulting complex, multi-modal posteriors make inference inefficient and impractical. We solve this problem by embedding canonical forms of LTI systems within the Bayesian framework. We rigorously establish that inference in these minimal parameterizations fully captures all invariant system dynamics (e.g., transfer functions, eigenvalues, predictive distributions of system outputs) while resolving identifiability. This approach unlocks the use of meaningful, structure-aware priors (e.g., enforcing stability via eigenvalues) and ensures conditions for a Bernstein--von Mises theorem -- a link between Bayesian and frequentist large-sample asymptotics that is broken in standard forms. Extensive simulations with modern MCMC methods highlight advantages over standard parameterizations: canonical forms achieve higher computational efficiency, generate interpretable and well-behaved posteriors, and provide robust uncertainty estimates, particularly from limited data.

arXiv:2507.04441v3 Announce Type: replace Abstract: Conformal prediction (CP) is an Uncertainty Representation technique that delivers finite-sample calibrated prediction regions for any underlying Machine Learning model. Its status as an Uncertainty Quantification (UQ) tool, though, has remained conceptually opaque: While Conformal Prediction Regions (CPRs) give an ordinal representation of uncertainty (larger regions typically indicate higher uncertainty), they lack the capability to cardinally quantify it (twice as large regions do not imply twice the uncertainty). We adopt a category-theoretic approach to CP -- framing it as a morphism, embedded in a commuting diagram, of two newly-defined categories -- that brings us three joys. First, we show that -- under minimal assumptions -- CP is intrinsically a UQ mechanism, that is, its cardinal UQ capabilities are a structural feature of the method. Second, we demonstrate that CP bridges the Bayesian, frequentist, and imprecise probabilistic approaches to predictive statistical reasoning. Finally, we show that a CPR is the image of a covariant functor. This observation is relevant to AI privacy: It implies that privacy noise added locally does not break the global coverage guarantee.

arXiv:2508.20103v1 Announce Type: cross Abstract: The optimal asset allocation between risky and risk-free assets is a persistent challenge due to the inherent volatility in financial markets. Conventional methods rely on strict distributional assumptions or non-additive reward ratios, which limit their robustness and applicability to investment goals. To overcome these constraints, this study formulates the optimal two-asset allocation problem as a sequential decision-making task within a Markov Decision Process (MDP). This framework enables the application of reinforcement learning (RL) mechanisms to develop dynamic policies based on simulated financial scenarios, regardless of prerequisites. We use the Kelly criterion to balance immediate reward signals against long-term investment objectives, and we take the novel step of integrating the Time-series Dense Encoder (TiDE) into the Deep Deterministic Policy Gradient (DDPG) RL framework for continuous decision-making. We compare DDPG-TiDE with a simple discrete-action Q-learning RL framework and a passive buy-and-hold investment strategy. Empirical results show that DDPG-TiDE outperforms Q-learning and generates higher risk adjusted returns than buy-and-hold. These findings suggest that tackling the optimal asset allocation problem by integrating TiDE within a DDPG reinforcement learning framework is a fruitful avenue for further exploration.

arXiv:2508.20755v1 Announce Type: cross Abstract: Tool-augmented language models, equipped with retrieval, memory, or external APIs, are reshaping AI, yet their theoretical advantages remain underexplored. In this paper, we address this question by demonstrating the benefits of in-tool learning (external retrieval) over in-weight learning (memorization) for factual recall. We show that the number of facts a model can memorize solely in its weights is fundamentally limited by its parameter count. In contrast, we prove that tool-use enables unbounded factual recall via a simple and efficient circuit construction. These results are validated in controlled experiments, where tool-using models consistently outperform memorizing ones. We further show that for pretrained large language models, teaching tool-use and general rules is more effective than finetuning facts into memory. Our work provides both a theoretical and empirical foundation, establishing why tool-augmented workflows are not just practical, but provably more scalable.

arXiv:2508.20102v1 Announce Type: cross Abstract: Signal control in urban corridors faces the dual challenge of maintaining arterial traffic progression while adapting to demand variations at local intersections. We propose a hierarchical traffic signal coordination and control scheme that integrates model-based optimization with reinforcement learning. The system consists of: (i) a High-Level Coordinator (HLC) that selects coordination strategies based on observed and predicted demand; (ii) a Corridor Coordinator that derives phase constraints from the selected strategy-either Max-Flow Coordination (MFC) or Green-Wave Coordination (GWC); and (iii) Hybrid Signal Agents (HSAs) that determine signal phases via reinforcement learning with action masking to enforce feasibility. Hierarchical reinforcement learning with Proximal Policy Optimization (PPO) is used to train HSA and HLC policies. At the lower level, three HSA policies-MFC-aware, GWC-aware, and pure agent control (PAC) are trained in conjunction with their respective coordination strategies. At the higher level, the HLC is trained to dynamically switch strategies using a multi-objective reward balancing corridor-level and network-wide performance. The proposed scheme was developed and evaluated on a SUMO-RLlib platform. Case results show that hybrid MFC maximizes throughput under heavy demand; hybrid GWC consistently minimizes arterial stops and maintains progression across diverse traffic conditions but can reduce network-wide efficiency; and PAC improves network-wide travel time in moderate demand but is less effective under heavy demand. The hierarchical design enables adaptive strategy selection, achieving robust performance across all demand levels.

arXiv:2508.19507v2 Announce Type: replace-cross Abstract: In e-commerce, where users face a vast array of possible item choices, recommender systems are vital for helping them discover suitable items they might otherwise overlook. While many recommender systems primarily rely on a user's purchase history, recent multi-behavior recommender systems incorporate various auxiliary user behaviors, such as item clicks and cart additions, to enhance recommendations. Despite their overall performance gains, their effectiveness varies considerably between visited items (i.e., those a user has interacted with through auxiliary behaviors) and unvisited items (i.e., those with which the user has had no such interactions). Specifically, our analysis reveals that (1) existing multi-behavior recommender systems exhibit a significant gap in recommendation quality between the two item types (visited and unvisited items) and (2) achieving strong performance on both types with a single model architecture remains challenging. To tackle these issues, we propose a novel multi-behavior recommender system, MEMBER. It employs a mixture-of-experts framework, with experts designed to recommend the two item types, respectively. Each expert is trained using a self-supervised method specialized for its design goal. In our comprehensive experiments, we show the effectiveness of MEMBER across both item types, achieving up to 65.46% performance gain over the best competitor in terms of Hit Ratio@20.

arXiv:2508.20097v1 Announce Type: cross Abstract: We investigate whether large language models can discover and analyze U.S. tax-minimization strategies. This real-world domain challenges even seasoned human experts, and progress can reduce tax revenue lost from well-advised, wealthy taxpayers. We evaluate the most advanced LLMs on their ability to (1) interpret and verify tax strategies, (2) fill in gaps in partially specified strategies, and (3) generate complete, end-to-end strategies from scratch. This domain should be of particular interest to the LLM reasoning community: unlike synthetic challenge problems or scientific reasoning tasks, U.S. tax law involves navigating hundreds of thousands of pages of statutes, case law, and administrative guidance, all updated regularly. Notably, LLM-based reasoning identified an entirely novel tax strategy, highlighting these models' potential to revolutionize tax agencies' fight against tax abuse.