Traditional concentration indices like the Herfindahl-Hirschman Index ($HHI = \sum_i w_i^2$) measure weight dispersion but ignore network topology, meaning two systems with identical weight distributions can exhibit different effective concentration. This paper introduces the Network Concentration Index (NCI), defined as $\psi(w,A) = \frac{w^{\top}Aw}{1-\sum_i w_i^2}$, which measures the fraction of potential weighted interconnection realized along observed network links. The framework unifies weight distributions with interaction structures, providing a theoretically grounded tool for assessing systemic risk in financial networks, supply chains, and economic production systems.

This paper develops a neural operator framework for approximating mappings defined on constrained Wasserstein spaces $\mathcal{M}_\lambda$, consisting of probability measures on $I \times \mathbb{R}^d$ with prescribed marginal $\lambda$ on the label space $I$. The core contribution is the DeepONetCyl architecture, which combines cylindrical moment approximations $\Phi_J(\mu) = (\langle \varphi_1, \mu \rangle, \ldots, \langle \varphi_J, \mu \rangle)$ with a DeepONet-type branch–trunk structure to preserve the marginal constraint. This enables learning of heterogeneous (non-exchangeable) mean-field control problems where agent interactions depend on labels, extending prior neural methods beyond the exchangeable case.

Multifidelity surrogate modeling aims to leverage cheap low-fidelity simulations to improve predictions of expensive high-fidelity models when training data is scarce. This paper proposes MAGPI, a Gaussian process regression method that augments the high-fidelity input space with features derived from recursively-trained low-fidelity surrogate models. The approach unifies desirable properties from cokriging and autoregressive estimators while allowing non-GP models for low-fidelity levels, achieving superior accuracy and computational efficiency.

Bayesian neural networks (BNNs) suffer from fragmented, high-dimensional posteriors due to weight-space symmetries, raising doubts about the practicality of sampling-based inference. This paper demonstrates that overparametrization—using more hidden units than necessary—actually transforms the posterior geometry in beneficial ways. The authors identify three key phenomena induced by redundancy: balancedness (norm equalization across layers), weight reallocation on equal-probability manifolds (following Dirichlet distributions), and prior conformity (marginals aligning with zero-mean Gaussian priors). Through theory for ReLU networks and extensive experiments with up to 10 million posterior samples, the work explains why recent sampling methods succeed and provides a principled foundation for understanding weight priors in overparametrized regimes.

While most bias mitigation research targets binary classification, multi-class fairness remains under-explored. This paper proposes Generalised Exponentiated Gradient (GEG), an in-processing method that extends the Exponentiated Gradient framework to multi-class settings and enables simultaneous optimization of multiple fairness constraints via positive-label moment conditions. Evaluated on ten datasets against six baselines, GEG achieves fairness improvements up to 92% with moderate accuracy trade-offs, filling a critical gap in fair machine learning toolboxes.

This paper tackles the memory explosion problem in high-rank DoRA fine-tuning. At $d_{in}=8192$ and rank $r=384$, computing the row-wise norm $\|\mathbf{W}+s\mathbf{B}\mathbf{A}\|_{\text{row}}$ via standard materialization consumes ~512 MB per module—prohibitive for large models with hundreds of adapted layers. The authors propose a factored norm decomposition that reduces the computation to $\mathcal{O}(d_{out}r+r^2)$ intermediates plus fused Triton kernels that collapse the composition into a single pass. On 8–32B vision-language models, this yields 1.5–2.0× speedups and up to 77 GB VRAM savings without numerical drift.

This paper addresses conditional distribution estimation for regression by proposing a non-parametric binning approach. Observations sorted by a one-dimensional covariate are partitioned into contiguous bins via dynamic programming, minimizing a closed-form leave-one-out CRPS cost function. The method produces conformal prediction sets with finite-sample marginal coverage guarantees and connects to Venn predictors, offering substantially narrower intervals than standard split-conformal methods on heteroscedastic and bimodal benchmarks.

The paper addresses functional Gaussian Process regression on compact Riemannian manifolds, proposing a time-adaptive Empirical Bayes framework that exploits invariance of covariance kernels under isometries and spectral decomposition via Laplace–Beltrami eigenfunctions. The core idea is to work in the time-varying angular spectral domain, truncating the infinite-dimensional expansion based on functional sample size (typically logarithmic) to balance computational cost with approximation accuracy. This matters because it extends GP regression to infinite-dimensional functional settings on non-Euclidean domains while attempting to maintain computational tractability through spectral truncation schemes.

Time-dependent reliability analysis for nonlinear dynamical systems under stochastic loading is computationally prohibitive with Monte Carlo simulation. CoNBONet proposes a surrogate combining DeepONet operator learning with Variable Spiking Neurons (VSNs) for sparse computation, Bayesian variational inference for uncertainty, and split conformal prediction for calibration. The goal is fast, energy-efficient inference with theoretical guarantees on reliability estimates.

The paper proposes a non-parametric classifier based on the Nadaraya-Watson (NW) estimator that achieves linear $O(n)$ computational complexity while providing frequentist uncertainty bounds on predictions. By reformulating kernel regression for multi-class classification and deriving error bounds under Lipschitz continuity or separability assumptions, the authors bridge the gap between efficient "black box" methods and computationally expensive approaches like Gaussian Processes that offer formal guarantees. The method achieves $>96\%$ accuracy on MIT-BIH ECG data with uncertainty intervals that flag low-confidence predictions, making it suitable for safety-critical applications.

The paper tackles Constrained Online Convex Optimization with Memory (COCO-M), where both losses and constraints depend on a window of past decisions, capturing realistic scenarios like smart-grid budgets and battery health limits. The authors propose the first algorithms achieving sublinear regret and cumulative constraint violation (CCV) under adversarial, time-varying constraints, both with and without unreliable predictions of future gradients. This work bridges the gap between classical constrained OCO and practical memory-dependent control problems.

This paper proposes a training-free conditional diffusion model for Bayesian filtering in data assimilation. Instead of learning the score function via neural networks, the authors leverage kernel density estimation (KDE) to represent the joint distribution of states and measurements, yielding a closed-form expression for the score that enables analytical sampling from the posterior. The method targets nonlinear, non-Gaussian filtering problems where traditional ensemble Kalman filters (EnKF) make restrictive Gaussian approximations and particle filters suffer from weight degeneracy in small-ensemble regimes.

Diffusion language models (DLMs) enable parallel token generation, but their efficiency depends critically on the decoding strategy that determines which tokens to unmask and when. This paper investigates confidence-based decoding—specifically an entropy sum strategy that adaptively batches tokens until cumulative prediction uncertainty exceeds a threshold—and proves it achieves $\varepsilon$-accurate sampling in KL divergence with expected iteration complexity $\widetilde{O}(H(X_0)/\varepsilon)$. When the data distribution has low entropy ($H(X_0) \ll L$), this yields sublinear complexity in sequence length, providing the first theoretical foundation for why confidence-based methods accelerate sampling without sacrificing fidelity.

This paper extends stochastic approximation (SA) theory to non-Markovian driving noise that is also non-ergodic, establishing that the ergodic decomposition of the original process corresponds to a Doeblin decomposition of an equivalent Markov chain. The core insight is that iterates retain memory of the distant past through the tail $\sigma$-field at $-\infty$, offering a theoretical lens on how learning algorithms might encode long-term dependencies. The author proposes this framework as a paradigm for understanding transformer attention mechanisms and continual learning, where the entire history influences current updates.

This paper studies how batch size and sequence length should scale with the total token budget in stochastic conditional gradient methods for LLM training. Under a $\mu$-Kurdyka-\L ojasiewicz condition, the authors derive a BST (Batch-Sequence-Token) scaling rule $BS \asymp T^{2/3}$ that predicts three distinct regimes: noise-dominated, batch-independent optimal, and iteration-starved. The theory yields actionable guidelines for adaptive batch size scheduling and is validated on NanoGPT models up to 1B parameters.

Vector Diffusion Maps (VDM) capture pairwise connection relationships in complex datasets via the Graph Connection Laplacian, but eigenvalue decomposition costs $O(n^{2.81})$, prohibiting large-scale applications. This paper proposes LA-VDM (Landmark Accelerated VDM), which constrains diffusion through landmark points and introduces a novel two-stage normalization scheme with parameters $\alpha$ and $\beta$ to handle non-uniform sampling densities in both data and landmarks. Under a manifold model with the frame bundle structure, the authors prove that LA-VDM asymptotically converges to the connection Laplacian while reducing complexity to $O(nm^2)$, enabling applications to datasets with millions of points.

ALMAB-DC unifies Gaussian process active learning, multi-armed bandit scheduling, and asynchronous distributed computing to tackle expensive black-box optimization in sequential experimental design. The framework targets dose-finding, spatial field estimation, and ML/engineering tasks, claiming superior sample efficiency and near-linear parallel speedups up to $K=16$ agents. While the modular architecture and ablation analyses are rigorous, all empirical results derive from calibrated surrogate emulators rather than live systems, substantially limiting external validity.

This paper studies nonparametric regression for learning degree-$k_0$ spherical polynomials on the unit sphere $\mathbb{S}^{d-1}$ using over-parameterized two-layer neural networks. The authors propose a novel Gradient Descent with Projection (GDP) algorithm that constrains learning to the top $r_0 = \Theta(d^{k_0})$ eigenspaces of the Neural Tangent Kernel (NTK). The main result establishes a nearly minimax optimal risk bound of order $\log(4/\delta) \cdot \Theta(d^{k_0}/n)$, improving the sample complexity from previous polynomial-in-$1/\varepsilon$ rates to linear $1/\varepsilon$ scaling.

Constraint-based causal discovery algorithms like PC require exponentially many conditional independence (CI) tests in the worst case---specifically $p^{\mathcal{O}(d)}$ where $d$ is the maximum degree. This paper establishes that the fundamental complexity parameter is actually $s$, the maximum undirected clique size in the essential graph, which can be much smaller than $d$ (e.g., $s=2$ vs $d=p-2$ in Figure 1). The authors propose Greedy Ancestral Search (GAS), which achieves $p^{\mathcal{O}(s)}$ CI tests, and prove a matching lower bound of $2^{\Omega(s)}$, establishing exponent-optimality up to a logarithmic factor.

Rule-State Inference (RSI) addresses compliance monitoring in domains like taxation where authoritative rules are known a priori but observations are partial, noisy, or strategically distorted. The paper proposes a Bayesian framework that inverts the standard ML paradigm: instead of learning rules from data, RSI encodes regulatory rules as structured priors and infers latent rule states (activation, compliance rate, parametric drift) via posterior inference. This enables zero-shot compliance assessment without labeled training data—a critical capability for low-resource environments where non-compliance labels are scarce or legally sensitive.