Optimisation of functions on graphs is challenging.

Recently, considerable research effort has been devoted to developing deep architectures for topic models to learn topic structures.

A loose signal wire caused the cargo ship Dali to crash into Baltimore's Francis Scott Key Bridge, with NTSB blaming Maryland officials for failing to assess bridge vulnerability.

Federated Learning (FL) enables collaborative learning without exposing clients' data. While clients only share model updates with the aggregator, studies reveal that aggregators can infer sensitive information from these updates. Secure Aggregation (SA) protects individual updates during transmission; however, recent work demonstrates a critical vulnerability where adversarial aggregators manipulate client selection to bypass SA protections, constituting a Biased Selection Attack (BSA). Although verifiable random selection prevents BSA, it precludes informed client selection essential for FL performance. We propose Adversarial Robust Federated Learning (AdRo-FL), which simultaneously enables: informed client selection based on client utility, and robust defense against BSA maintaining privacy-preserving aggregation. AdRo-FL implements two client selection frameworks tailored for distinct settings. The first framework assumes clients are grouped into clusters based on mutual trust, such as different branches of an organization. The second framework handles distributed clients where no trust relationships exist between them. For the cluster-oriented setting, we propose a novel defense against BSA by (1) enforcing a minimum client selection quota from each cluster, supervised by a cluster-head in every round, and (2) introducing a client utility function to prioritize efficient clients. For the distributed setting, we design a two-phase selection protocol: first, the aggregator selects the top clients based on our utility-driven ranking; then, a verifiable random function (VRF) ensures a BSA-resistant final selection. AdRo-FL also applies quantization to reduce communication overhead and sets strict transmission deadlines to improve energy efficiency. AdRo-FL achieves up to $1.85\times$ faster time-to-accuracy and up to $1.06\times$ higher final accuracy compared to insecure baselines.

Causal discovery combines data with knowledge provided by experts to learn the DAG representing the causal relationships between a given set of variables. When data are scarce, bagging is used to measure our confidence in an average DAG obtained by aggregating bootstrapped DAGs. However, the aggregation step has received little attention from the specialized literature: the average DAG is constructed using only the confidence in the individual edges of the bootstrapped DAGs, thus disregarding complex higher-order edge structures. In this paper, we introduce a novel theoretical framework based on higher-order structures and describe a new DAG aggregation algorithm. We perform a simulation study, discussing the advantages and limitations of the proposed approach. Our proposal is both computationally efficient and effective, outperforming state-of-the-art solutions, especially in low sample size regimes and under high dimensionality settings.

Generative models on curved spaces rely on charts to map Euclidean spaces to manifolds. Exponential maps preserve geodesics but have stiff, radius-dependent Jacobians, while volume-preserving charts maintain densities but distort geodesic distances. Both approaches entangle curvature with model parameters, inflating gradient variance. In high-dimensional latent normalizing flows, the wrapped exponential prior can stretch radii far beyond the curvature scale, leading to poor test likelihoods and stiff solvers. We introduce Radial Compensation (RC), an information-geometric method that selects the base density in the tangent space so that the likelihood depends only on geodesic distance from a pole, decoupling parameter semantics from curvature. RC lets radial parameters retain their usual meaning in geodesic units, while the chart can be tuned as a numerical preconditioner. We extend RC to manifolds with known geodesic polar volume and show that RC is the only construction for geodesic-radial likelihoods with curvature-invariant Fisher information. We derive the Balanced-Exponential (bExp) chart family, balancing volume distortion and geodesic error. Under RC, all bExp settings preserve the same manifold density and Fisher information, with smaller dial values reducing gradient variance and flow cost. Empirically, RC yields stable generative models across densities, VAEs, flows on images and graphs, and protein models. RC improves likelihoods, restores clean geodesic radii, and prevents radius blow-ups in high-dimensional flows, making RC-bExp a robust default for likelihood-trained generative models on manifolds.

Neural Differential Equations (NDEs) excel at modeling continuous-time dynamics, effectively handling challenges such as irregular observations, missing values, and noise. Despite their advantages, NDEs face a fundamental challenge in adopting dropout, a cornerstone of deep learning regularization, making them susceptible to overfitting. To address this research gap, we introduce Continuum Dropout, a universally applicable regularization technique for NDEs built upon the theory of alternating renewal processes. Continuum Dropout formulates the on-off mechanism of dropout as a stochastic process that alternates between active (evolution) and inactive (paused) states in continuous time. This provides a principled approach to prevent overfitting and enhance the generalization capabilities of NDEs. Moreover, Continuum Dropout offers a structured framework to quantify predictive uncertainty via Monte Carlo sampling at test time. Through extensive experiments, we demonstrate that Continuum Dropout outperforms existing regularization methods for NDEs, achieving superior performance on various time series and image classification tasks. It also yields better-calibrated and more trustworthy probability estimates, highlighting its effectiveness for uncertainty-aware modeling.

Small and medium-sized enterprises (SMEs) represent 99.9% of U.S. businesses yet remain systematically excluded from AI due to a mismatch between their operational scale and modern machine learning's data requirements. This paper introduces SmallML, a Bayesian transfer learning framework achieving enterprise-level prediction accuracy with datasets as small as 50-200 observations. We develop a three-layer architecture integrating transfer learning, hierarchical Bayesian modeling, and conformal prediction. Layer 1 extracts informative priors from 22,673 public records using a SHAP-based procedure transferring knowledge from gradient boosting to logistic regression. Layer 2 implements hierarchical pooling across J=5-50 SMEs with adaptive shrinkage, balancing population patterns with entity-specific characteristics. Layer 3 provides conformal sets with finite-sample coverage guarantees P(y in C(x)) >= 1-alpha for distribution-free uncertainty quantification. Validation on customer churn data demonstrates 96.7% +/- 4.2% AUC with 100 observations per business -- a +24.2 point improvement over independent logistic regression (72.5% +/- 8.1%), with p < 0.000001. Conformal prediction achieves 92% empirical coverage at 90% target. Training completes in 33 minutes on standard CPU hardware. By enabling enterprise-grade predictions for 33 million U.S. SMEs previously excluded from machine learning, SmallML addresses a critical gap in AI democratization. Keywords: Bayesian transfer learning, hierarchical models, conformal prediction, small-data analytics, SME machine learning

Scientific applications continue to rely on legacy Fortran codebases originally developed for homogeneous, CPU-based systems. As High-Performance Computing (HPC) shifts toward heterogeneous GPU-accelerated architectures, many accelerators lack native Fortran bindings, creating an urgent need to modernize legacy codes for portability. Frameworks like Kokkos provide performance portability and a single-source C++ abstraction, but manual Fortran-to-Kokkos porting demands significant expertise and time. Large language models (LLMs) have shown promise in source-to-source code generation, yet their use in fully autonomous workflows for translating and optimizing parallel code remains largely unexplored, especially for performance portability across diverse hardware. This paper presents an agentic AI workflow where specialized LLM "agents" collaborate to translate, validate, compile, run, test, debug, and optimize Fortran kernels into portable Kokkos C++ programs. Results show the pipeline modernizes a range of benchmark kernels, producing performance-portable Kokkos codes across hardware partitions. Paid OpenAI models such as GPT-5 and o4-mini-high executed the workflow for only a few U.S. dollars, generating optimized codes that surpassed Fortran baselines, whereas open-source models like Llama4-Maverick often failed to yield functional codes. This work demonstrates the feasibility of agentic AI for Fortran-to-Kokkos transformation and offers a pathway for autonomously modernizing legacy scientific applications to run portably and efficiently on diverse supercomputers. It further highlights the potential of LLM-driven agentic systems to perform structured, domain-specific reasoning tasks in scientific and systems-oriented applications.

Current AI alignment through RLHF follows a single directional paradigm that AI conforms to human preferences while treating human cognition as fixed. We propose a shift to co-alignment through Bidirectional Cognitive Alignment (BiCA), where humans and AI mutually adapt. BiCA uses learnable protocols, representation mapping, and KL-budget constraints for controlled co-evolution. In collaborative navigation, BiCA achieved 85.5% success versus 70.3% baseline, with 230% better mutual adaptation and 332% better protocol convergence. Emergent protocols outperformed handcrafted ones by 84%, while bidirectional adaptation unexpectedly improved safety (+23% out-of-distribution robustness). The 46% synergy improvement demonstrates optimal collaboration exists at the intersection, not union, of human and AI capabilities, validating the shift from single-directional to co-alignment paradigms.