Modern data analysis usually gives a prediction without showing whether the evidence behind it is clear, conflicting, or stable. Two cases can have the same fitted confidence even when one has mostly agreeing evidence and the other has strong support and strong opposition. We propose Signed Evidence Flow (SEF), which combines a fitted prediction rule with signed feature attributions to measure support, opposition, conflict, and perturbation stability. We prove that confidence determines conflict exactly when it also determines total evidence mass, derive the remaining conditional variance, and state when conflict can improve loss prediction beyond confidence and other audit variables. We also connect conflict to geometric decision fragility. Across healthcare, Covertype, black-box, finance, and ten external data sets, conflict sometimes separates risk among predictions that already appear confident. Cross-fitted tests show added error-ranking information beyond confidence and attribution entropy on several data sets, including two large finance tasks. The direction is not universal: in some tasks, lowconflict cases are riskier. We therefore introduce ScopeGate, a held-out permutation diagnostic that checks the direction before SEF is used for review triage. SEF is consequently an audit tool rather than a universal risk score: it describes evidence structure, while an independent calibration sample determines whether that structure is useful in the target population.

One of the powerful techniques in data modeling is accounting for features that are available at the training stage, but are not available when the trained model is used to classify or predict test data -- the Learning Using Privileged Information paradigm (LUPI). Sequential Minimal Optimization (SMO) methods have been developed for supervised Support Vector Machines (SVM), unsupervised one-class SVM, and SVM with privileged information (SVM+). The missing brick in this research has long been a one-class SVM with privileged information (OC-SVM+). In this paper, we propose an SMO algorithm for OC-SVM+ that significantly outperforms non-sequential algorithms for training the OC-SVM+ model. Its finite-time convergence is established. The experiments show how privileged information affects a descriptive domain in the space of original features. Comparative benchmark tests demonstrate that our algorithm is superior over interior point algorithms.

Agentic LLMs must continuously decide whether newly extracted facts should be added, merged with existing memories, or ignored, yet prior work has focused more on retrieval and storage than on principled write-side control. We frame memory evolution as a novelty-detection problem and propose SAGE, a Spherical Adaptive Gate for memory Evolution that scores candidate facts with a von Mises-Fisher-based density estimator over memory embeddings and routes them with an adaptive threshold that tracks memory-store geometry. SAGE resolves clearly novel facts as ADD, clearly redundant facts as NOOP, and sends only uncertain cases to an LLM merge step, reducing expensive write-time reasoning. On LoCoMo, SAGE achieves the best average token-F1 against Mem0 on all seven open-weight backbone comparisons, while on GPT-4o-mini it reduces add-phase API cost by 3.4$\times$ and add-phase latency by 2.5$\times$ with only a small average judge-score gap. As a drop-in binary gate for A-Mem, SAGE skips roughly 16-18% of LLM calls across five models with minimal quality change on open-weight backbones. These results suggest that novelty-aware write control is a practical lever for improving both memory quality and system efficiency in long-term agentic memory. The source code for our approach is accessible at https://github.com/swang1024/SAGE.

Accurately estimating treatment effects in time series is essential for evaluating interventions in real-world applications, especially when treatment assignment is biased by unobserved factors. In many practical settings, interventions are adopted at different times across individuals, leading to staggered treatment exposure and heterogeneous pre-treatment histories. In such cases, aggregating outcome trajectories across treated units is ill-defined, making individual treatment effect (ITE) estimation a prerequisite for reliable causal inference. We therefore study the problem of estimating the average treatment effect for the treated (ATT) by first recovering individual-level counterfactuals. We introduce a neural framework that learns simultaneously low-dimensional latent representations of individual time series and propensity scores. These estimates are then used to approximate the individual treatment effects through a flexible matching procedure that avoids classical convexity constraints commonly used in synthetic control methods. By operating at the individual level, our approach naturally accommodates staggered interventions and improves counterfactual estimation under latent bias, without relying on explicit temporal modeling assumptions. We illustrate our approach on both real-world energy consumption data and clinical time series, including high-frequency electricity demand-response programs and semi-synthetic data for individuals in intensive care unit (ICU), where hidden confounding, staggered treatment adoption, and non-stationary dynamics are prevalent.

In this paper we prove some concentration inequalities for two types of error probabilities in the Empirical Risk Principle (ERP) in statistical learning, which provide a lower bound and an upper bound for the minimal risk (in terms of the minimal empirical risk) with non-asymptotic high confidence. The usual boundedness condition of the empirical risk function is relaxed to the Gaussian or exponential integrability condition. The confidence of the lower bound of the minimal risk is shown to be independent of the number of training parameters and the dimension of the input vectors, allowing one to detect the deficiency of a learning machine efficiently; and the confidence of the upper bound of the minimal risk is proved to be high provided that the sample size $n$ is much greater than the box dimension of the parameter set $Θ$ in the Orlicz metric $d_{ψ_1}$ associated with the risk functions. Our work is based on Talagrand's concentration inequalities (the sharp versions by Bousquet and Klein-Rio), transport-entropy inequalities and the recent progress in the theory of empirical processes and statistical learning.

Frameworks for ensuring fairness in machine learning typically focus on learning fair models from existing data. But this endeavor is often undermined by biases already present in that data. We therefore look to modify the data acquisition process itself to help gather fairer data that is inherently more suitable for training fair predictors. To this end, we introduce FairBED, which provides novel formulations for quantifying the fairness of datasets themselves based on the idea that fair datasets should be uninformative about sensitive attributes. We then use this to construct practical fairness-aware Bayesian experimental design (BED) objectives that maximize expected information gain about the target quantity of interest while minimizing expected information gain about sensitive attributes. We further derive a theoretical link between FairBED and demographic parity, and show empirically that models trained on data gathered using FairBED provide improved fairness-accuracy trade-offs compared to randomly acquired data and conventional BED.

This paper investigates convergence properties of regularized Nystr om subsampling applied to the unsupervised domain adaptation problem under covariate shift. We focus on the low-smoothness (misspecified) case where the target function lies outside the reproducing kernel Hilbert space. By combining Tikhonov regularization with Nystr om projection onto a subsampled subspace, we obtain upper bounds on the excess risk that hold with high probability and are expressed in terms of the source condition, the effective dimension, and the sample sizes. We further extend the analysis to the setting where the Radon-Nikodym derivative between the target and source marginal distributions is unknown and must be approximated, and we identify the minimal additional sample sizes required to maintain the same convergence rate as in the oracle case.

Diffusion models are known to exploit unknown low-dimensional structure to accelerate sampling. However, existing convergence theory under low-dimensional data structure has largely focused on update rules with narrowly prescribed coefficient choices. This raises a fundamental question: is adaptation to low-dimensional structure sensitive to the precise choice of update coefficients? In this paper, we show that such adaptation is a robust property of diffusion models. For a broad class of update coefficients, we prove that $\widetilde{O}(k/\varepsilon)$ iterations suffice to generate an $\varepsilon$-accurate sample in total variation (TV) distance, independently of the ambient dimension. Our framework substantially broadens the class of diffusion samplers known to enjoy low dimensional adaptation and applies to several commonly used methods in practice. These results provide a theoretical justification for the empirical effectiveness of diffusion samplers across different coefficient choices when applied to structured, high-dimensional data.

We show that replacing the standard MSE denoising loss in diffusion models with a nonlinear transformation induced by an f-divergence yields a simple robust training surrogate that empirically improves performance under data contamination, with small additional computational overhead. The theoretical foundation rests on a local divergence construction: under the Gaussian reverse-kernel structure of DDPM, each per-step likelihood ratio follows a lognormal distribution parameterized by a scalar mismatch, so the conditional f-divergence at each step reduces to a one-dimensional function of the denoising error. Summing these local divergences yields a training objective that unifies diffusion training as divergence induced weighted denoising, where the derivative of the induced divergence acts as a residual-space influence weight that controls the contribution of each sample. Bounded-influence divergences (Hellinger, negative exponential) suppress large error samples, with Hellinger yielding an explicit exponential weight, connecting the framework to robust M-estimation. Empirically, on CIFAR-10 under 30% contamination, NED reduces FID from 93.0 (KL) to 77.5, while also outperforming standard robust losses such as Huber and clipped MSE.

Existing multi-view clustering methods employ various strategies to address datalevel sparsity and view-level dynamic fusion. However, we identify a critical yet overlooked issue: varying sparsity across views. Cross-view sparsity variations lead to encoding discrepancies, heightening sample-level semantic heterogeneity and making view-level dynamic weighting inappropriate. To tackle these challenges, we propose Adaptive Sparse Autoencoders for Multi-View Clustering (SparseMVC), a framework with three key modules. Initially, the sparse autoencoder probes the sparsity of each view and adaptively adjusts encoding formats via an entropymatching loss term, mitigating cross-view inconsistencies. Subsequently, the correlation-informed sample reweighting module employs attention mechanisms to assign weights by capturing correlations between early-fused global and viewspecific features, reducing encoding discrepancies and balancing contributions. Furthermore, the cross-view distribution alignment module aligns feature distributions during the late fusion stage, accommodating datasets with an arbitrary number of views. Extensive experiments demonstrate that SparseMVC achieves state-of-theart clustering performance.