Artificial intelligence (AI) systems increasingly influence safety-critical aspects of society, from medical diagnosis to autonomous mobility, making uncertainty awareness a central requirement for trustworthy AI. We present a photonic Bayesian machine that leverages the inherent randomness of chaotic light sources to enable uncertainty reasoning within the framework of Bayesian Neural Networks. The analog processor features a 1.28 Tbit/s digital interface compatible with PyTorch, enabling probabilistic convolutions processing within 37.5 ps per convolution. We use the system for simultaneous classification and out-of-domain detection of blood cell microscope images and demonstrate reasoning between aleatoric and epistemic uncertainties. The photonic Bayesian machine removes the bottleneck of pseudo random number generation in digital systems, minimizes the cost of sampling for probabilistic models, and thus enables high-speed trustworthy AI systems.

Timely assessment of current conditions is essential especially for small, open economies such as Singapore, where external shocks transmit rapidly to domestic activity. We develop a real-time nowcasting framework for quarterly GDP growth using a high-dimensional panel of approximately 70 indicators, encompassing economic and financial indicators over 1990Q1-2023Q2. The analysis covers penalized regressions, dimensionality-reduction methods, ensemble learning algorithms, and neural architectures, benchmarked against a Random Walk, an AR(3), and a Dynamic Factor Model. The pipeline preserves temporal ordering through an expanding-window walk-forward design with Bayesian hyperparameter optimization, and uses moving block-bootstrap procedures both to construct prediction intervals and to obtain confidence bands for feature-importance measures. It adopts model-specific and XAI-based explainability tools. A Model Confidence Set procedure identifies statistically superior learners, which are then combined through simple, weighted, and exponentially weighted schemes; the resulting time-varying weights provide an interpretable representation of model contributions. Predictive ability is assessed via Giacomini-White tests. Empirical results show that penalized regressions, dimensionality-reduction models, and GRU networks consistently outperform all benchmarks, with RMSFE reductions of roughly 40-60%; aggregation delivers further gains. Feature-attribution methods highlight industrial production, external trade, and labor-market indicators as dominant drivers of Singapore's short-run growth dynamics.

Reinforcement Learning (RL) following Supervised Fine-Tuning (SFT) has become the standard paradigm for post-training Large Language Models (LLMs). However, the mechanism by which RL contributes to reasoning capabilities-- whether it incentivizes the synthesis of new skills or merely amplifies existing behaviors--remains a subject of intense debate. In this work, we investigate this question through the lens of Complementary Reasoning, a complex task that requires integrating internal parametric knowledge with external contextual information. Using a controlled synthetic dataset of human biographies, we strictly decouple this ability into two atomic skills: Parametric Reasoning (relying on internal knowledge encoded in model parameters) and Contextual Reasoning (depending on novel information provided in the context window). To rigorously assess capability boundaries, we evaluate generalization across three distinct levels of difficulty: I.I.D., Composition, and Zero-shot settings. We find that while SFT is sufficient for in-distribution performance, it struggles with out-of-distribution generalization, particularly in Zero-shot settings where relational combinations are novel. Crucially, we identify the SFT Generalization Paradox: Models supervised solely on the composite task achieve near-perfect in-distribution accuracy (90%) but collapse on out-of-distribution generalization (18%), indicating their reliance on rote memorization of path shortcuts. In contrast, we find that RL acts as a reasoning synthesizer rather than a probability amplifier. However, we uncover a strict atomic prerequisite: RL can only synthesize these complex strategies if the base model has first mastered the independent atomic skills (Parametric and Contextual) via SFT. These findings challenge the view of RL as a mere amplifier, suggesting that given sufficient atomic foundations, RL can actively synthesize complex reasoning strategies from learned primitives without explicit supervision on such complex strategies. This indicates that decoupled atomic training followed by RL offers a scalable path to generalization for complex reasoning tasks. Code and data will be at https://github.com/sitaocheng/from The rapid evolution of Large Language Models (LLMs) has been fundamentally driven by advanced post-training strategies, specifically an initial Supervised Fine-Tuning (SFT) stage followed by a Reinforcement Learning (RL) stage (Achiam et al., 2023; Team et al., 2024; Guo et al., 2025). While SFT is effective at establishing behavioral norms and imparting foundational knowledge, it fundamentally relies on maximum likelihood estimation, which tends to favor the memorization of the training distribution.

Dynamic feature selection (DFS) offers a compelling alternative to traditional, static feature selection by adapting the selected features to each individual sample. This provides insights into the decision-making process for each case, which makes DFS especially significant in settings where decision transparency is key, i.e., clinical decisions. However, existing DFS methods use opaque models, which hinder their applicability in real-life scenarios. DFS also introduces new own sources of uncertainty compared to the static setting, which is also not considered in the existing literature. In this paper, we formalize the additional sources of uncertainty in DFS, and give formulas to estimate them. We also propose novel approach by leveraging a rule-based system as a base classifier for the DFS process, which enhances decision interpretability compared to neural estimators. Finally, we demonstrate the competitive performance of our rule-based DFS approach against established and state-of-the-art greedy and reinforcement learning methods, which are mostly considered opaque, compared to our explainable rule-based system.

Correctness is an emergent property of systems where exposing error is cheaper than committing it. In dynamic, low-trust environments, autonomous AI agents benefit from delegating work to sub-agents, yet correctness cannot be assured through upfront specification or centralized oversight. We propose a protocol that enforces correctness through collateralized claims in a recursive verification game. Tasks are published as intents, and solvers compete to fulfill them. Selected solvers carry out tasks under risk, with correctness checked post hoc by verifiers. Any challenger can challenge a result by staking against it to trigger the verification process. Incorrect agents are slashed and correct opposition is rewarded, with an escalation path that penalizes erroneous verifiers themselves. When incentives are aligned across solvers, challengers, and verifiers, falsification conditions make correctness the Nash equilibrium.

Learning the structure of a Bayesian network from decentralized data poses two major challenges: (i) ensuring rigorous privacy guarantees for participants, and (ii) avoiding communication costs that scale poorly with dimensionality. In this work, we introduce Fed-Sparse-BNSL, a novel federated method for learning linear Gaussian Bayesian network structures that addresses both challenges. By combining differential privacy with greedy updates that target only a few relevant edges per participant, Fed-Sparse-BNSL efficiently uses the privacy budget while keeping communication costs low. Our careful algorithmic design preserves model identifiability and enables accurate structure estimation. Experiments on synthetic and real datasets demonstrate that Fed-Sparse-BNSL achieves utility close to non-private baselines while offering substantially stronger privacy and communication efficiency.

Foundation models, and in particular large language models, can generate highly informative responses, prompting growing interest in using these ''synthetic'' outputs as data in empirical research and decision-making. This paper introduces the idea of a foundation prior, which shows that model-generated outputs are not as real observations, but draws from the foundation prior induced prior predictive distribution. As such synthetic data reflects both the model's learned patterns and the user's subjective priors, expectations, and biases. We model the subjectivity of the generative process by making explicit the dependence of synthetic outputs on the user's anticipated data distribution, the prompt-engineering process, and the trust placed in the foundation model. We derive the foundation prior as an exponential-tilted, generalized Bayesian update of the user's primitive prior, where a trust parameter governs the weight assigned to synthetic data. We then show how synthetic data and the associated foundation prior can be incorporated into standard statistical and econometric workflows, and discuss their use in applications such as refining complex models, informing latent constructs, guiding experimental design, and augmenting random-coefficient and partially linear specifications. By treating generative outputs as structured, explicitly subjective priors rather than as empirical observations, the framework offers a principled way to harness foundation models in empirical work while avoiding the conflation of synthetic ''facts'' with real data.

Differential privacy is increasingly formalized through the lens of hypothesis testing via the robust and interpretable $f$-DP framework, where privacy guarantees are encoded by a baseline Blackwell trade-off function $f_{\infty} = T(P_{\infty}, Q_{\infty})$ involving a pair of distributions $(P_{\infty}, Q_{\infty})$. The problem of choosing the right privacy metric in practice leads to a central question: what is a statistically appropriate baseline $f_{\infty}$ given some prior modeling assumptions? The special case of Gaussian differential privacy (GDP) showed that, under compositions of nearly perfect mechanisms, these trade-off functions exhibit a central limit behavior with a Gaussian limit experiment. Inspired by Le Cam's theory of limits of statistical experiments, we answer this question in full generality in an infinitely divisible setting. We show that suitable composition experiments $(P_n^{\otimes n}, Q_n^{\otimes n})$ converge to a binary limit experiment $(P_{\infty}, Q_{\infty})$ whose log-likelihood ratio $L = \log(dQ_{\infty} / dP_{\infty})$ is infinitely divisible under $P_{\infty}$. Thus any limiting trade-off function $f_{\infty}$ is determined by an infinitely divisible law $P_{\infty}$, characterized by its Levy--Khintchine triplet, and its Esscher tilt defined by $dQ_{\infty}(x) = e^{x} dP_{\infty}(x)$. This characterizes all limiting baseline trade-off functions $f_{\infty}$ arising from compositions of nearly perfect differentially private mechanisms. Our framework recovers GDP as the purely Gaussian case and yields explicit non-Gaussian limits, including Poisson examples. It also positively resolves the empirical $s^2 = 2k$ phenomenon observed in the GDP paper and provides an optimal mechanism for count statistics achieving asymmetric Poisson differential privacy.

We study the problem of learning disentangled signals from data using non-linear Independent Component Analysis (ICA). Motivated by advances in self-supervised learning, we propose to learn self-sufficient signals: A recovered signal should be able to reconstruct a missing value of its own from all remaining components without relying on any other signals. We formulate this problem as the minimization of a conditional KL divergence. Compared to traditional maximum likelihood estimation, our algorithm is prior-free and likelihood-free, meaning that we do not need to impose any prior on the original signals or any observational model, which often restricts the model's flexibility. To tackle the KL divergence minimization problem, we propose a sequential algorithm that reduces the KL divergence and learns an optimal de-mixing flow model at each iteration. This approach completely avoids the unstable adversarial training, a common issue in minimizing the KL divergence. Experiments on toy and real-world datasets show the effectiveness of our method.

Many tasks require mapping continuous input data (e.g. images) to discrete task outputs (e.g. class labels). Yet, how neural networks learn to perform such discrete computations on continuous data manifolds remains poorly understood. Here, we show that signatures of such computations emerge in the representational geometry of neural networks as they learn. By analysing the Riemannian pullback metric across layers of a neural network, we find that network computation can be decomposed into two functions: discretising continuous input features and performing logical operations on these discretised variables. Furthermore, we demonstrate how different learning regimes (rich vs. lazy) have contrasting metric and curvature structures, affecting the ability of the networks to generalise to unseen inputs. Overall, our work provides a geometric framework for understanding how neural networks learn to perform discrete computations on continuous manifolds.