Federated learning (FL) remains highly vulnerable to adaptive backdoor attacks that preserve stealth by closely imitating benign update statistics. Existing defenses predominantly rely on anomaly detection in parameter or gradient space, overlooking behavioral constraints that backdoor attacks must satisfy to ensure reliable trigger activation. These anomaly-centric methods fail against adaptive attacks that normalize update magnitudes and mimic benign statistical patterns while preserving backdoor functionality, creating a fundamental detection gap. To address this limitation, this paper introduces FeRA (Federated Representative Attention) -- a novel attention-driven defense that shifts the detection paradigm from anomaly-centric to consistency-centric analysis. FeRA exploits the intrinsic need for backdoor persistence across training rounds, identifying malicious clients through suppressed representation-space variance, an orthogonal property to traditional magnitude-based statistics. The framework conducts multi-dimensional behavioral analysis combining spectral and spatial attention, directional alignment, mutual similarity, and norm inflation across two complementary detection mechanisms: consistency analysis and norm-inflation detection. Through this mechanism, FeRA isolates malicious clients that exhibit low-variance consistency or magnitude amplification. Extensive evaluation across six datasets, nine attacks, and three model architectures under both Independent and Identically Distributed (IID) and non-IID settings confirm FeRA achieves superior backdoor mitigation. Under different non-IID settings, FeRA achieved the lowest average Backdoor Accuracy (BA), about 1.67% while maintaining high clean accuracy compared to other state-of-the-art defenses. The code is available at https://github.com/Peatech/FeRA_defense.git.

To bridge this gap, (i) we postulate a set of natural axioms that we expect a measure of potential correlation to satisfy; (ii) we show that the rate of information bottleneck, i.e., the hypercontractivity coefficient, satisfies all the proposed axioms;

Given samples lying on any of a number of subspaces, subspace clustering is the task of grouping the samples based on the their corresponding subspaces. Many subspace clustering methods operate by assigning a measure of affinity to each pair of points and feeding these affinities into a graph clustering algorithm. This paper proposes a new paradigm for subspace clustering that computes affinities based on the corresponding conic geometry. The proposed conic subspace clustering (CSC) approach considers the convex hull of a collection of normalized data points and the corresponding tangent cones. The union of subspaces underlying the data imposes a strong association between the tangent cone at a sample $x$ and the original subspace containing $x$. In addition to describing this novel geometric perspective, this paper provides a practical algorithm for subspace clustering that leverages this perspective, where a tangent cone membership test is used to estimate the affinities. This algorithm is accompanied with deterministic and stochastic guarantees on the properties of the learned affinity matrix, on the true and false positive rates and spread, which directly translate into the overall clustering accuracy.

The machine learning community has become increasingly concerned with the potential for bias and discrimination in predictive models. This has motivated a growing line of work on what it means for a classification procedure to be fair. In this paper, we investigate the tension between minimizing error disparity across different population groups while maintaining calibrated probability estimates. We show that calibration is compatible only with a single error constraint (i.e.

We propose a novel adaptive test of goodness-of-fit, with computational cost linear in the number of samples. We learn the test features that best indicate the differences between observed samples and a reference model, by minimizing the false negative rate. These features are constructed via Stein's method, meaning that it is not necessary to compute the normalising constant of the model. We analyse the asymptotic Bahadur efficiency of the new test, and prove that under a mean-shift alternative, our test always has greater relative efficiency than a previous linear-time kernel test, regardless of the choice of parameters for that test. In experiments, the performance of our method exceeds that of the earlier linear-time test, and matches or exceeds the power of a quadratic-time kernel test. In high dimensions and where model structure may be exploited, our goodness of fit test performs far better than a quadratic-time two-sample test based on the Maximum Mean Discrepancy, with samples drawn from the model.

In this study, we attempt to place a full size color image within another image of the same size.

In this paper, we aim to answer three key open questions: (i) whether and how brain networks are cross-correlated at different time scales with long-range dependencies ("long-memory" process,

As datasets grow richer, an important challenge is to leverage the full features in the data to maximize the number of useful discoveries while controlling for false positives. We address this problem in the context of multiple hypotheses testing, where for each hypothesis, we observe a p-value along with a set of features specific to that hypothesis. For example, in genetic association studies, each hypothesis tests the correlation between a variant and the trait.

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Estimation of mutual information from observed samples is a basic primitive in machine learning, useful in several learning tasks including correlation mining, information bottleneck, Chow-Liu tree, and conditional independence testing in (causal) graphical models.