Outliers

Outliers are important for stress-testing algorithms and understanding system behaviour under rare conditions. Despite being commonly described as low-likelihood events, existing generative approaches rarely control likelihood explicitly. In this work, we introduce a measure-theoretic notion of outliers based on the distribution of log-likelihood values, which is guaranteed to assign higher probability mass to low-likelihood events with a specifiable magnitude. Building on this formulation, we derive how likelihood reweighting modifies the diffusion score and use this relation to motivate a controlled modification of the reverse-time dynamics. In particular, likelihood reweighting implies a scaling of the score function with a control term derived from the Radon-Nikodym derivative of the likelihood distributions. Correspondingly, the updated score function can be obtained with no retraining of the diffusion model. We exploit the Ornstein-Uhlenbeck semigroup underlying diffusion models to motivate an exponentially interpolated controller which approximates the true control. Experiments demonstrate controlled generation of low-likelihood samples while remaining consistent with the data geometry.

Despite their strong multimodal understanding ability, multimodal large language models (MLLMs) incur substantial computational overhead when processing long visual token sequences. To reduce inference costs, recent studies have explored visual token pruning through vision-centric or text-guided strategies. However, these methods often overlook high-norm outlier tokens, i.e., tokens with abnormally large feature norms, leading to suboptimal pruning decisions. In this work, we show that such high-norm outlier tokens are highly redundant in both feature and spatial dimensions, yet are often mistakenly preserved as informative cues by existing methods. Motivated by this observation, we propose SinkPruner, a training-free visual token pruning framework for efficient MLLM inference. SinkPruner follows a coarse-to-fine design with two key modules: a visual sanitizer that filters high-norm redundancies and alleviates attention sink and attention dispersion, and a text-guided pruner that further retains tokens semantically aligned with the text query. Extensive experiments on twelve image-language and four video-language benchmarks demonstrate the effectiveness, efficiency, and generalizability of our framework. Notably, SinkPruner preserves 96.5% (91.8%) of the original performance of LLaVA-1.5 (Qwen2.5-VL) under an 89% token reduction. Experiments further indicate that our visual sanitizer exhibits promising transferability in enhancing the performance of existing pruning methods. Our code is available at https://github.com/LaVi-Lab/SinkPruner.

Broad Learning System (BLS) offers an efficient alternative to deep architectures by enabling fast learning through randomized feature mapping and closed-form solutions. However, its reliance on squared error loss makes it highly sensitive to noise, outliers, and corrupted labels, limiting its reliability in real-world scenarios. To address this limitation, we propose Wave-BLS, a robust broad learning framework that integrates the wave loss function, which is asymmetric, bounded, and smooth, enabling controlled penalization of large errors. The proposed formulation replaces the standard least-squares objective with a wave-loss-based optimization problem, solved efficiently using a Nesterov accelerated gradient (NAG)-based scheme without requiring matrix inversion, thereby improving scalability. Extensive experiments on 30 UCI benchmark datasets demonstrate that Wave-BLS consistently outperforms classical BLS and several robust variants. Statistical validation using Friedman and Nemenyi post-hoc tests confirms the significance of the observed improvements. Furthermore, robustness evaluations under controlled noise and outlier injection reveal that Wave-BLS exhibits substantially slower performance degradation compared to BLS, even in challenging contamination settings. These results establish Wave-BLS as a stable and robust alternative to existing broad learning models for learning under data uncertainty.

Given a dataset where a portion of the samples are contaminated, our goal is to recover the underlying clean population distribution. To this end, we propose Wasserstein Filtering (WF), a novel sample selection framework that discards a fraction of suspicious samples and estimates the target distribution using the empirical measure of the remaining data. The core insight is to select a subset of samples whose empirical distribution maximizes its Wasserstein distance to the fully contaminated empirical distribution, thereby preferentially isolating and removing geometrically influential outliers. To render this optimization computationally tractable, we introduce three algorithms: a marginal screening scheme, SinkMarg, and two joint optimization algorithms, SinkWF and SlicedWF, leveraging entropic optimal transport and sliced Wasserstein approximations, respectively. On the theoretical front, we introduce the Far Exclusion and Local Projection (FELP) contamination model, which characterizes corruptions consisting of well-separated outliers and locally indistinguishable perturbations. Under this model, we prove that the WF estimator achieves minimax optimality over distribution families with bounded covariance. Extensive numerical experiments on synthetic datasets, benchmark anomaly detection suites, and robust generative learning with diffusion models demonstrate that WF serves as a highly practical, model-agnostic preprocessing tool. It delivers competitive outlier detection performance and provides substantial downstream benefits for generative modeling under heavy contamination.

In this paper, we test different methods for multivariate detection of outliers in the data of transmitted heat energy in the selected substation of local District Heating System, by also considering outside ambient temperature, namely Z-score (univariate, as a benchmark), Mahalanobis distances, Principal Component Analysis (PCA), Isolation Forest and Hotelling's T-squared test. The overall research aims at uncovering irregular plant operation, with a wider objective of identifying the opportunities for reducing the consumption of gas in central heating plants as well as the CO2 emission. The proposed approach considers specific domain circumstances, such as irrelevance of zero transmit-ted energy timepoints as indication of off-grid plant. The outcomes of the different methods are discussed with domain experts. It was concluded that PCA, Isolation Forest and Hotelling method provide relevant results. Finally, we adopt the ensemble method (selection based on the agreement of all three methods on the detected outliers) as the final approach.

In LLM pre-training, synchronization propagates rank-local stalls, slowdowns, and numerical errors into job-wide symptoms, obscuring their origin. Existing diagnosis often relies on in-process monitors that cannot report after the trainer blocks or terminates, or on post-mortem logs that preserve only synchronized symptoms; offline health tests lose the workload and operating conditions that triggered the failure. We present SCOUT, a unified runtime failure-localization framework built on one design principle: identify outliers through strict-majority consensus among equivalent replicas. SCOUT aligns replica progress, timing, and numerical evidence, then uses its Consensus Collective Communication (C3) abstraction to identify ranks whose compact signatures disagree with their peers. An out-of-band CPU observer remains responsive when training hangs, whereas in-situ replay exercises recurring stragglers and silent data corruption (SDC) beside the live job with its model state, kernels, allocations, communication path, and thermal and memory pressure present. Collective fingerprints expose rank-local protocol divergence. Clean replay coverage certifies checkpoint numerical integrity, preventing recovery from selecting state corrupted by SDC. SCOUT integrates with PyTorch, TorchTitan, Megatron-Core, and DeepSpeed without training-loop or framework-source modifications. SCOUT is open source at https://github.com/LMResiliency/lm-resiliency.

Outlier detection in decentralized data environments is a challenging task for many machine learning implementations, particularly in settings where data cannot be shared. Recently, there have been advances in federated outlier detection, some of which are based on the use of autoencoder networks. The introduction of attention mechanisms to autoencoders boosts their efficiency. However, the application of attention-based models in federated learning remains underdeveloped due to the absence of proper aggregation functions for these types of networks. In our work, we propose two novel aggregation functions tailored for attention-based autoencoders, which better preserve the learned information stored within the memory modules of these networks. We evaluated our approach on the KDDCUP10 dataset, and we showed that the proposed methods achieve up to 2.9% and 5.1% better results for F1 score and AUC ROC respectively when compared to traditional autoencoders.

We apply Marchenko-Pastur (MP) random matrix theory to pre-trained attention weights in order to separate each projection matrix into a random-like bulk and a set of spectral outliers. We validate this decomposition causally: zeroing the MP-identified outliers (signal) in Mistral-7B drives HellaSwag, MMLU, and PIQA close to random-chance performance, whereas zeroing a count-matched subset of bulk singular values causes smaller but non-negligible degradation. Across 11 pre-trained transformers we identify five recurring patterns: spectral outliers encode a dominant component of the learned structure; Q projections carry the most outliers; V projections under grouped-query attention lack a clean signal/noise separation; entry-level outliers form structured row-bands in Q and column-bands in O; and specific residual-stream dimensions persist as band outliers across layers in K and O. We close by outlining how these observations could inform parameter-efficient fine-tuning and structured pruning.

Joint Energy-Based Models (JEM) unify classification and generation within a single network and support out-of-distribution (OOD) detection. Canonical JEM training relies on stochastic gradient Langevin dynamics (SGLD); a theoretically motivated alternative, the Predictor-Corrector (PC) sampler, has not previously undergone a systematic replication test on the canonical model. We reproduce canonical JEM on WideResNet-28-10 without normalisation layers on two independent runs and test a fixed-noise PC adaptation - with the degenerate annealed-noise predictor replaced by a deterministic gradient step - across three protocols: the adapted sampler replacing SGLD throughout the full training trajectories (115-132 epochs); cold-start generation (FID); and refinement-style multi-OOD detection (AUROC). The reconstruction reaches 92.88% test accuracy and buffer-FID 44.46 (canonical: 92.9% and 38.40). We document two failure modes: catastrophic late-training divergence with the signature of the canonical outlier-buffer mechanism (all four runs), and run-dependent SVHN OOD-discrimination dynamics. No consistent method-level advantage of the adaptation over SGLD is observed on any protocol: refinement AUROC differences stay below 0.007 across ten checkpoint-OOD pairs; seeded cold-start generation favours SGLD by about five FID points; on the training protocol a hierarchical seed-by-image bootstrap gives a 95% confidence interval on the macro-averaged AUROC difference that contains zero, while a seed-level equivalence test with two runs per method cannot establish formal equivalence. The training-protocol data are consistent both with equivalence and with a small directional effect. This outcome is consistent with theory: the guarantees of the annealed-noise PC framework do not transfer to the constant-noise regime of canonical JEM.

Attention layers are the backbone of today's most powerful and impactful models. Models with multi-million and billion parameters rely on contextual knowledge provided by attention layers. However, their use goes well beyond just being the core component of large language models. One particularly interesting application is in Memory Augmented Autoencoders (MemAE), specifically for unsupervised representation learning in outlier detection tasks. It was shown that attention helps these models be more effective in centralized learning scenarios. Our work aims to address the lack of specialized aggregation techniques in Federated Learning (FL) when it comes to MemAE models. In this paper we analyze the intricacies of the architecture behind Memory Augmented Autoencoders, and propose novel, guided approaches to effectively aggregate these models in federated scenarios. We demonstrate our approach on non-IID datasets and show that these novel aggregation schemes are more robust when dealing with numerous edge nodes in environments with unbalanced datasets, specifically for unsupervised anomaly detection scenarios. This approach improves the performance of even very shallow autoencoders, allowing them to be used in resource constrained environments.

Detecting a change in a multivariate series answers only the first of two questions; the operational question is which coordinates changed. Existing answers are incomplete. Block-level procedures certify predefined groups of coordinates under an additive union bound, high-dimensional variable-selection methods return interpretable rankings without error guarantees, and the post-detection inference literature controls error along the time axis rather than across coordinates. We propose ARM (Attribution by Rank Maxima), a wrapper that accepts a changepoint located by an arbitrary detector and returns the set of coordinates certified to have changed, each carrying a location or scale type label. ARM scores each coordinate by a max-over-splits rank statistic. Because this statistic dominates the corresponding statistic at the estimated split, the resulting certificate is invariant to the manner, and to the accuracy, of the changepoint estimate. Three finite-sample guarantees follow from within-coordinate ranks alone: per-coordinate validity under any detector; exact family-wise error control through a Westfall--Young joint permutation that preserves cross-coordinate dependence, with a fully distribution-free Holm fallback; and false discovery rate control under arbitrary coordinate dependence in high dimensions through Benjamini--Yekutieli and e-BH. In simulations, naive per-coordinate testing at the estimated changepoint inflates its family-wise error beyond $0.66$ as the dimension grows, whereas ARM maintains the nominal level while retaining validity under heavy tails, power in high dimensions, and accurate type labels. On five financial series surrounding the 2008 collapse, ARM attributes a scale change to every asset class and excludes injected control coordinates.

Detecting when the statistical behavior of an engineered system changes, and identifying which component is responsible, are core problems in the monitoring of telecommunication networks, robotic platforms, security infrastructure, and multi-agent systems. In safety- and mission-critical deployments, such decisions must be accompanied by statistical reliability guarantees rather than by point estimates alone. Conformal changepoint localization (CONCH) and conformal root cause analysis (CROC) meet this need by returning confidence sets that contain the true changepoint, or the true root-cause stream, with a user-specified probability, without parametric assumptions on the data-generating process. In practice, however, observations are frequently corrupted, e.g., by outliers, sensor faults, or adversarial perturbations. While the finite-sample coverage of these procedures is preserved under contamination, the resulting confidence sets can become uninformatively large. Adopting a Huber-type contamination model, this paper proposes weighted CONCH (W-CONCH) and weighted CROC (W-CROC), which downweight observations that are likely to be corrupted with the goal of reducing confidence set size when data may be corrupted. The weighting mechanism, derived from a formal bound on the unknown corrupted data densities, leverages pre-existing second-order classifier-based uncertainty signals, such as those produced by evidential deep learning or Bayesian learning. W-CONCH and W-CROC are further generalized by introducing a meta-learning procedure for the weights that optimizes a differentiable surrogate of the confidence set size. Experiments on image-based and real-world changepoint and root-cause benchmarks show that uncertainty-based weighting substantially reduces confidence set size while maintaining the target coverage.

In this work, we explore how the inference time of a Transformer Neural Network can be efficiently optimized with applications to real-time anomaly detection in financial time series. The financial time series are price series such as asset prices. Unfortunately, the data is often with errors or outliers that make the downstream data processing tasks useless, unstable or even harmful. Moreover, the amount of financial time-series data has been significantly increasing. Hence, there is a need for better data-cleaning methods in terms of accuracy and in terms of processing speed. Transformers as a neural network architecture have achieved superior performances in many tasks such as Natural Language Processing and Computer Vision. Time series modelling and especially anomaly detection tasks can benefit from the features of transformers architecture in multiple ways, including the capacity to capture long-range dependencies and interactions. Increasingly powerful hardware, such as field-programmable gate arrays (FPGAs), have seen increasing usage in recent years due to their reconfigurability and high performance. They can be efficiently utilized to speed up the computations of the Transformer architecture. We explore different Transformer architectures for time series modelling and how they can be efficiently implemented on an FPGA board (PYNQ-Z2). In particular, we examine the application of Transformers to detect anomalies in time series and we show how they can be efficiently implemented on an FPGA board to minimize latency. The code is available at https://github.com/thxi/icl_thesis

Transformers are known to have internal continuous symmetries that leave outputs invariant, while modifying quantization. GaugeQuant leverages this in-training by introducing a LogSumExp term to the loss that breaks the symmetries, thus selecting a basis that minimizes activation outliers. A stop-gradient operator ensures that only rotation matrices are updated, yielding the language modeling objective completely unaltered. Our requires no specific calibration data, no quantization simulation, and adds negligible training overhead. With the LLaMA-2 7B model under W4A4 quantization with group size 128, perplexity drops from 8.22 to 6.73, competing with post-training methods that require frozen models and calibration datasets. Under W4A16, perplexity drops from 11.16 to 5.45. Code is available at https://github.com/MPedraBento/gauge-quant.

Recent detection-free approaches have shown significant efficacy in image-to-point cloud (I2P) registration by employing a coarse-to-fine matching pipeline. In the coarse stage, down-sampled image features and voxelized point cloud features are typically fused to establish initial coarse correspondences for subsequent refinement. However, existing methods largely overlook the critical role of point cloud density, which fundamentally dictates the quality of coarse correspondences and the final registration results. Specifically, excessively sparse point clouds lead to an insufficient number of inliers, while overly dense ones often introduce a high outlier ratio. Consequently, this creates an inherent density trade-off, thereby significantly limiting the registration accuracy of current approaches. For mitigating this trade-off, we propose a novel Cross-Coordinate Correspondences Pruning (CCP) strategy to acquire sufficient inliers while ensuring a low outlier ratio. To minimize interference from inter-modal coordinate discrepancies, we first project cross-coordinate coarse correspondences to the 2D image coordinate system for spatial unification. Subsequently, a lightweight pruning network is responsible for predicting the inlier confidences, which are used to filter coarse outliers, from coordinate geometric and modal feature dimensions. To maximize inlier recall, we further design a Multi-Density Point Ensemble (MDPE) strategy that consolidates and deduplicates pruned coarse correspondences across varying point cloud densities. Our method achieves a significant performance improvement, surpassing existing state-of-the-art methods by at least 8.6% in Registration Recall across various benchmarks.

LiDAR place recognition supports loop closure, relocalization, and multi-agent map management. As robotic platforms increasingly combine LiDARs with different fields of view, resolutions, and scanning patterns, existing descriptors degrade because they are tightly coupled to sensor-specific characteristics. We present InLiER, a learning-free pipeline based on an intermediate tokenization step. Height-sliced keypoints from structural elements receive mixed-radix token IDs encoding height, radial distance, local shape, and azimuth from local 3D geometry, in a compact sub-2KB representation. The same vocabulary is reorganized across three retrieval stages: height-ceiling histogram intersection for fast rotation-invariant shortlisting, binary bitmask alignment for yaw estimation and reranking, and token-guided geometric verification for 6-DoF pose estimation. InLiER achieves state-of-the-art performance on the HeLiPR dataset and in real-world field experiments, among modern handcrafted methods and outperforms the learning-based baseline on most cross-sensor configurations.

Reconstruction-based methods are a cornerstone of unsupervised image anomaly detection, but they remain vulnerable to \emph{outlier leakage}, where standard mean squared error (MSE) loss drives the model to faithfully reconstruct anomalous patterns. We propose a Non-linear Reconstruction Loss that applies a sigmoid-based squashing function to suppress high-magnitude features, preventing outliers from dominating optimization while preserving sensitivity to normal patterns. In addition, we introduce a statistical calibration scheme that selects the scaling factor $k$ from the confidence interval (CI) of the normal feature distribution, enabling data-driven control of the suppression strength. Our approach achieves competitive or superior anomaly detection performance compared to state-of-the-art methods, reaching 99.0% Image-AUROC and 97.3% Pixel-AUROC on MVTec-AD, and 95.3% Image-AUROC and 99.0% Pixel-AUROC on VisA. These results indicate that non-linear gradient suppression is an effective mechanism for mitigating outlier leakage and improving anomaly localization in unified industrial inspection settings. The implementation is available at https://github.com/mintii13/Statistical-Non-linear-Reconstruction-Loss.git.

True causal relationships are rarely known, and inferring causal graphs from data is hard. A fundamental challenge is how to assess whether a given causal graph is good in the absence of a ground truth. We propose falsifying candidate causal graphs based on whether they can explain the propagation of an outlier event. Our approach leverages a key principle: weak outliers rarely cause strong ones. While this principle has previously been used in root cause analysis to identify root causes without prior knowledge of the graph, we turn it on its head and use it to falsify candidate causal graphs whose implied outlier propagation is inconsistent with the data. To this end, we present the first statistical tests for the hypothesis that a candidate graph is the true causal graph, and show they have false positive control, power guarantees against incorrect causal graphs, and can operate with a single outlier sample.

Integrating information across related tasks can improve estimation and prediction in transfer, multi-task, and federated learning, but contamination and heterogeneity make robust borrowing challenging. We study a contaminated multi-task empirical risk minimization (ERM) framework in which an $ε$ fraction of $K$ tasks, each with sample size $n$, may be arbitrarily contaminated while the remaining tasks are heterogeneous. Our goal is to estimate both the global minimizer of the average risk and the clean task-specific minimizers, thereby combining robustness and personalization. In the Gaussian mean model, we show that several common paradigms, including adaptive and robust regularization around a shared center, global matrix regularization, decomposition-based regularization, and score-based outlier-task detection, all suffer from a worst-case contamination error of order $ε\sqrt{d/n}$, which is suboptimal compared to the lower bound $ε/\sqrt{n}$. This identifies a dimension-dependent barrier for these approaches. We then establish minimax lower bounds for a general heterogeneous ERM setting and propose a computationally efficient filtering-based robust multi-task gradient descent method. Under local strong convexity, smoothness, and sub-Gaussian gradient assumptions, the proposed method attains high-probability upper bounds matching the minimax rates up to logarithmic factors over a broad regime. In particular, it removes the extra $\sqrt{d}$ contamination dependence of many regularization-based methods and score-based outlier detection, while achieving personalization to local tasks under strong heterogeneity. Simulations and a real-data analysis demonstrate strong robustness and personalization relative to a broad range of benchmark methods.

For clinical deployment, it is essential that automated diagnostic systems remain reliable when confronted with previously unseen cases, yet deep models routinely misclassify out-of-distribution (OOD) inputs with high confidence, underscoring the need for more robust OOD detection methods. Although substantial effort has been devoted to improving model robustness, most of the existing literature assumes balanced datasets, evaluates OOD detection on coarse or non-clinical OOD sources, or lacks comprehensive assessment across diverse OOD scenarios. To address the gaps, we propose a novel methodology trained on diverse and imbalanced medical datasets and evaluated across a clinically reflective OOD spectrum. Our framework comprises three key components: (1) a Nonlinear von Mises-Fisher (NvMF) classifier capable of learning non-linear decision boundaries, with theoretical proof of its asymptotic connection to cosine classifiers; (2) a multi-expert framework in which margin-aware NvMF classifiers specialise in different regions of label distribution to better handle imbalance; and (3) an outlier expert trained explicitly to distinguish inlier from outlier data, thereby strengthening OOD detection. Evaluation on RFMiD, ISIC2019, and NCTCRC datasets demonstrates consistent improvements over state-of-the-art methods, achieving mean FPR95 reductions of 8.45%, 13.02%, and 36.90% respectively. These gains are further supported by comprehensive ablations that validated the contributions of each component. This enables reliable identification of unfamiliar cases for deferral to clinicians, supporting safer AI-assisted diagnosis in real-world workflows. Our code is available at https://github.com/redboxup/MARVEL.

Outlier detection (OD) aims to identify anomalous instances by learning the underlying structure of normal data (inliers), and is particularly challenging in fully unsupervised settings where no information about anomalies is available during training. Recent advances have leveraged the inlier-memorization (IM) effect, a phenomenon in which deep models memorize inlier patterns earlier than those of outliers, as a powerful signal for distinguishing outliers. However, despite its empirical success, the theoretical understanding of the IM effect remains limited. In this work, we present a theoretical study of the IM effect. Focusing on a simple autoencoder, we show that, under mild assumptions, the model can successfully memorize inliers while failing to memorize outliers during certain stages of early training. In particular, we characterize not only the emergence of the IM effect, but also its strength and persistence, and analyze how these properties depend on the data distribution and parameter initialization. In addition, building on these insights, we derive simple yet practical guidelines for enhancing the IM effect, including data preprocessing and parameter initialization schemes, achieving state-of-the-art performance on the ADBench datasets. Our findings provide a theoretical foundation for the IM effect and offer actionable directions for improving IM-based outlier detection methods.

Standard NLP pipelines for occupational clustering discard the 10-15% of job postings that density-based methods assign to noise. We argue this is an error: in rapidly evolving domains, low posting density signals novelty, not incoherence. We formalize this as the Emergence-Density Inversion (EDI) hypothesis and test it longitudinally on 84,988 job postings across eight quarters (Q4 2022-Q3 2024). EDI is partially confirmed: high-EOS outlier groups transition to stable clusters in 1.4 +/- 0.6 quarters vs. 4.1 +/- 1.2 for low-EOS groups (p < 0.001), though the signal fails in approximately 19% of cases, which we characterize as a failure analysis. We extend the Emerging Occupation Score (EOS) with Temporal Velocity and Cross-Platform Convergence, improving 2-quarter cluster-formation prediction from F1 = 0.61 to 0.74, outperforming Isolation Forest, LOF, GLOSH, and BERTrend baselines. A retrospective study on three now-established roles (MLOps Engineer, DevOps/SRE, Data Engineer) confirms EOS signalled 2-3 quarters before cluster formation, providing held-out validation. A held-out annotator panel (kappa = 0.74) rates EOS > 0.75 as coherent emerging occupations with 77% precision. Prompt Engineer, AI Safety Researcher, Foundation Model Engineer, and Agent Systems Engineer, all absent from O*NET, are top-4 in Q3 2024 and form stable clusters by Q1 2025.

Most real-world datasets used for training supervised learning models are contaminated with noisy data and outliers leading to large prediction errors. This paper proposes a new approach for achieving robustness where the learning rate is modulated by a factor that is sensitive to outliers. In this approach a reduction of the learning rate is shown to be achieved by using alternate loss functions that are infinitely differentiable, strictly convex or quasiconvex and more closely approximate the absolute error than Huber and log-cosh losses. A comparison of the performance of regression models trained with different loss functions on a wide variety of benchmarks and datasets is presented to demonstrate the superior performance of the Square Root Loss (SRL) and Smooth Mean Absolute Error (SMAE) losses proposed in this paper. Two new robust linear regression models are presented. Highly vectorized robust parameter update formulae that take advantage of modern GPUs for both stochastic and batch gradient descent are presented.

Trained transformers reliably develop massive activations, a small number of hidden dimensions whose magnitude is far above the median and which concentrate on the sequence-start token. Whether these outliers are a removable artifact of the residual stream's overloaded read and write role, or instead a functional necessity, is actively debated. We test the artifact hypothesis directly, with an architectural intervention. Our architecture, Ledger Residuals, splits the residual stream into a mutable scratch stream (Deliberation) that intermediate computation may freely overwrite and a protected, decode-only accumulator (Commitment) that holds the representation the model reads out. If massive activations exist only because one stream is forced to be both scratchpad and answer, then a dedicated answer channel should remove the need for them. We find that it does not. In matched-loss language models at the 160M and 290M scales, the model rebuilds the canonical fixed-dimension, start-token outlier inside the protected channel. The rebuilt feature is smaller in magnitude than in a standard transformer but more sharply concentrated on the start token, and a stronger sparsity penalty makes it more persistent and more concentrated still, rather than removing it. Massive activations therefore look architecturally robust: they re-emerge in whichever representation the model decodes from, which is what we would expect if they are functional rather than incidental. We release our architecture and measurement code.

The increasing use of machine learning algorithms in social applications has raised concerns about fairness and transparency, leading to the development of counterfactual explanations. These explanations supports individuals to understand and potentially alter unfavorable decisions in areas such as loan applications, job selections, and more, by providing actionable changes to input features that would lead to a desired outcome. Existing methods often struggle to balance feasibility, plausibility, and computational efficiency. To address this, we introduce P$^2$CE, an algorithm for generating plausible Pareto-optimal counterfactual explanations, offering users a diverse set of optimal trade-offs between different notions of feasibility. P$^2$CE employs an auxiliary isolation forest outlier detector to ensure that explanations are in accordance with the data distribution and leverages SHAP values to obtain optimal results with short computing times, regardless of the underlying model. Our algorithm was empirically evaluated on three datasets, demonstrating superior performance in terms of both solution quality and computational efficiency compared to related techniques.

While Multimodal Retrieval-Augmented Generation (M-RAG) enhances Large Vision-Language Models, it remains highly susceptible to cross-modal hallucinations, causal fabrications, and sycophancy. Furthermore, existing mitigation pipelines often face an intervention paradox: static rules tend to unnecessarily disrupt accurate generations, whereas leaving the multi-modal reasoning completely unguided allows existing mismatches to cascade into severe logical fabrications. To quantify and mitigate these hallucinations, we propose a Multi-Agent system, MODE-RAG, driven by Variational Free Energy (VFE) and internal attention states to dynamically gate interventions. High-risk queries are routed to five stage-specific agents, integrating Monte Carlo Tree Search (MCTS) for rigorous causal derivation and logit perturbations to penalize sycophancy. Dedicated Correction and Overseer agents ensure formatting stability and perform post-hoc factual verification. To objectively evaluate our approach, we introduce ModeVent, a challenging subset derived from the MultiVent dataset. Extensive experiments indicate that our system effectively reduces hallucination rates and logical fabrication, significantly improving the robustness of M-RAG systems.

A certificate that removes outliers sees the data only through its low-degree moments, and an adversary exploits exactly this, hiding corruption where the clean data already looks typical, in the blind spot no bounded-degree test resolves. That blind spot turns out to have an exact size: the Christoffel function of the clean marginal, the very quantity modern data analysis thresholds to detect outliers, here read from the adversary's side as the corruption a bounded-degree certificate cannot remove. We turn this inversion into the organizing principle of the reweighted-hinge approach to robustly learning $γ$-margin halfspaces under malicious noise (Shen, 2025; Zeng and Shen, 2025): the governing resource is the Sum-of-Squares degree of the outlier-removal certificate, and the resolution principle states that the maximal corruption mass which can hide at a center $c$ from a degree-$2t$ certificate is exactly the Christoffel function $λ_{t+1}(c)$ of the clean marginal. Three consequences follow, all against the certificate method (not information-theoretic). A margin-degree tradeoff: certifying the dense pancake to error $ε$ costs SoS degree $Ω(\log(1/ε))$ or margin $Ω(\sqrt{\log(1/ε)}/\sqrt{d})$, explaining why the $\log(1/ε)$ margin Shen (2025) records is forced, with a weighted-Chebyshev reduction making the threshold $2t=Θ((|c|/s)^2)$ tight modulo one classical weighted-extremal estimate. A degree-$2$ outlier barrier: the resolution principle realized as an explicit instance on which degree $2$ is stuck at $η^{1/2}$ while degree $4$ escapes, locating the method's small breakdown rate in the degree, not the analysis. And a degree-$2t$ algorithm tracing the frontier $η^{1-1/2t}$ (recovering Shen (2025) at $t=1$), whose gain is an explicit constant, capped by the pancake density and shown unimprovable by the degree-$2$ barrier.

Do different LLM architectures encode high-level concepts in structurally compatible ways? We systematically characterize a geometric-functional universality dissociation: across multiple concept domains and architectural families, moderate geometric convergence coexists with near-perfect functional transfer. Using contrastive-difference CKA (CKA_Delta), a training-free diagnostic that computes kernel alignment on per-sample contrastive differences, we isolate concept-specific convergence from generic similarity -- achieving significant discrimination where standard CKA cannot. The dissociation replicates across all six concept domains we test (five with p <= 0.017 geometric discrimination and safety as a converging-functional trend, p = 0.08), including two non-instruction concepts (code-vs-NL, reasoning-vs-recall) validated without system prompts; a single 70B--70B pair provides an observational note that universality may strengthen with scale, requiring replication with additional >=70B models. We position CKA_Delta as a practical regime classifier and architectural outlier detector (Gemma: d = 1.08, AUC = 0.79) rather than an absolute transfer-accuracy predictor, providing a training-free diagnostic for cross-architecture concept monitoring.

Evaluating representation similarity is fundamental to representation learning. However, existing metrics suffer from significant limitations: they lack interpretability due to shifting baselines, lack robustness to outliers, and are computationally intractable for large datasets, forcing reliance on heuristic approximations. To address this, we develop an ordinal-similarity framework, instantiated by the Triplet (TSI) and Quadruplet (QSI) Similarity Indices, which measure alignment by quantifying the consistency of ordinal relationships. We theoretically demonstrate this formulation is inherently interpretable, robust to outliers, and computationally efficient. Finally, we establish a formal equivalence between TSI and local neighborhood alignment, measured by Mutual Nearest Neighbors. Empirically, we validate these properties and show that ordinal similarity offers a scalable approach to measuring alignment, enabling practitioners to better understand and design representations.

4-bit quantization significantly reduces the memory footprint and accelerates the inference of large language models (LLMs). However, its limited bit-width representation struggles to faithfully capture both dense common values (\emph{inliers}) and rare large-magnitude values (\emph{outliers}), causing substantial accuracy degradation. Existing mixed-precision methods mitigate this by retaining outliers in high precision, but at the cost of breaking the uniformity of low-bit execution, introducing precision conversion and extra data movement that undermine practical speedup. We propose \textbf{MosaicQuant}, a unified 4-bit LLM quantization paradigm built on a novel principle of \emph{inlier--outlier disaggregation}. Rather than elevating outlier precision, MosaicQuant quantizes the full weight matrix into a dense 4-bit base component, where inliers are captured faithfully while outlier are inevitably quantized. A sparse 4-bit residual component is then introduced to compensate for these quantization errors, selectively targeting the most error-critical weight blocks where output distortion is shown to be concentrated. However, a unified representation alone is insufficient, as naïvely executing the sparse residual as a separate kernel still breaks the unified low-bit inference pipeline. To bridge this gap, we introduce \textbf{ZipperEngine}, which fuses sparse block computation into the dense 4-bit GEMM kernel via an overlapped pipeline, unifying not only the representation but also the execution into a single coherent low-bit inference pipeline. Extensive experiments on LLaMA3 and Qwen3 demonstrate that MosaicQuant preserves near-FP16 accuracy while achieving up to $1.24\times$ speedup over the W16A16 baseline.

The signed integer alphabet contains one more negative representable value than positive. Yet, by convention, the standard symmetric integer quantizer fixes its scale to be strictly positive, which assigns this extra representable value to the negative tail and can force clipping of positive outliers. In this work, we show that, at few-bit precision, such clipping is a non-trivial source of quantization error. Asymmetric quantization addresses this problem with a zero point, shifting the grid toward the observed data range; however, this flexibility is well-known to carry a runtime penalty. For example, in llama.cpp on an AMD EPYC(TM) "Turin" CPU, a 4-bit symmetric format uses up to 9% less memory with up to 2.45$\times$ higher throughput than its asymmetric counterpart. We highlight signed symmetric quantization as a third option that retains the runtime profile of symmetric quantization without the penalty of the asymmetric format: our signed absmax grid places the extra representable value on the dominant-outlier tail through a principled and lightweight sign selection rule while keeping the zero point at zero. Our theoretical analysis offers two main results. First, we establish the signed absmax grid as conditionally bound-optimal on $\ell_2$ quantization error, and show that the condition holds for 88-99% of weight groups across pre-trained large language models (LLMs) at low bit widths. Second, we show that negating the scale of a standard symmetric quantizer is analytically equivalent to a unit zero point shift on the same signed integer alphabet. We empirically validate our proposal on models from the Qwen3, Qwen3.5, and Llama3 families, and observe improvement in perplexity and downstream few-shot accuracy over the standard unsigned symmetric quantizer at no extra inference cost

The most widely used RANSAC variants score candidate models by counting inliers or summing per-point scores that saturate beyond a residual threshold. Every such score requires a user-supplied parameter that is a function of the inlier scale, which must itself be estimated from contaminated data. We remove this dependence by reversing the usual order of inference: rather than estimating the scale and then scoring against it, we marginalize the inlier scale analytically in closed form under a conjugate Inverse-Gamma prior for a fixed inlier partition, then optimize over partitions. A single closed-form expression spans the non-informative Jeffreys limit and informative empirical-Bayes priors, so the same score adapts across data-rich and data-scarce regimes without any change to the algorithm. The proposed RANSAC score is the first in which the inlier scale is genuinely absent from the formula. The score admits O(N log N ) computation via sort-and-sweep. On a benchmark of nearly 70 000 image pairs spanning different two-view estimation problems and both engineered and learned feature pipelines, the proposed score exceeds the state of the art (RANSAC, MSAC, GaU, MAGSAC): it stays nearly flat under threshold miscalibration where baselines degrade, reaches near-optimal accuracy from as few as two validation pairs where baselines need ont he order of 100 times more,. and tightens its prior regularization as validation data grows scarce.

We develop a new, differentially private mean estimator called the balloon mean. The main features of the balloon mean are that it is computationally tractable and enjoys robustness to outlying observations. It is based on an iterative clipping procedure over expanding Mahalanobis balls, or ``balloons.'' The method satisfies zero-concentrated differential privacy and depends on a small number of interpretable tuning parameters. We provide theoretical guarantees under heavy-tailed and contaminated elliptical models, characterizing its statistical performance and robustness to outliers. Extensive simulations demonstrate that the balloon mean is robust to heavy-tailed and contaminated data, and outperforms existing differentially private mean estimators in contaminated settings.

Continual anomaly detection in tabular data is challenging and remains largely underexplored, particularly in settings with heterogeneous feature schemas, distribution shifts, and severe class imbalance. In many real-world applications, data arrive sequentially from diverse domains, rendering conventional continual learning methods ineffective due to their reliance on a fixed input space. We propose a continual learning (CL) method, which can overcome these challenges and continually learn from different tasks. Our method consists of three main parts: our AGF model, Taskfusion augmentation, and outlier exposure. The AGF-model maps task-specific features into a shared space, then aligns distributions to reduce representation drift, and learns anomaly decision boundaries in the aligned space. To improve stability, we introduce Taskfusion augmentation, combining boundary-aware interpolation within tasks to refine the model anomaly boundaries and cross-task mixing to transfer anomaly structure across datasets. To handle class imbalance and memory constraints, we employ tabular dataset distillation to store compact synthetic replay samples, which are jointly used with augmented data in an outlier exposure objective for robust anomaly detection. We evaluate the approach on 21 heterogeneous datasets across multiple domains. Results show that our approach substantially improves continual anomaly detection performance over sequential fine-tuning and other CL baselines while reducing catastrophic forgetting and maintaining stable detection across heterogeneous datasets.

Large Language Models frequently hallucinate in precision-critical domains such as technical diagramming and mechanical design, where outputs must satisfy strict geometric constraints. We study open-ended geometric synthesis from natural language: translating free-form descriptions into precise constructions whose entities must simultaneously satisfy dozens of interacting constraints. To make this tractable, we release PyGeoX, a programmable geometric DSL that compiles declarative constraints into a differentiable loss, and PyGeoX-Bench, a stratified suite of 300 problems with per-constraint verifiable rewards. Using PyGeoX as a verifier, we identify a failure mode we call Outlier Gradient Masking: under global-norm rewards (any scheme that aggregates residuals through a single norm, for example, $\exp(-\mathrm{MSE})$), a single outlier constraint can nullify the learning signal across all others. To address this, we propose Saturating Additive Rewards (SAR), which decompose the reward into bounded per-constraint terms, preserving partial progress and ensuring consistent gradients even under severe violations. Against MSE-based rewards, the natural baseline for geometry solvers, SAR improves the hard-tier solving rate by $2.3\times$, and the resulting 8B model is competitive with much larger frontier systems on this benchmark. We release the engine, benchmark, and data at https://github.com/Huawei-AI4Math/PyGeoX.

Low-bit quantization has been widely adopted to accelerate the inference of large language models (LLMs) by significantly reducing computational cost and memory usage. However, activation outliers pose a major challenge to effective quantization, often leading to notable performance degradation. In this paper, we introduce OffQ, a method designed to mitigate activation outliers in low-bit quantization through a novel offsetting mechanism. Specifically, OffQ first identifies a low-dimensional outlier subspace in the activations using a proposed top-1 PCA, and then concentrates high-magnitude activations into 1 channel via rotation. OffQ then absorbs this concentrated outlier channel by converting its magnitude into a shared offset, thereby reducing the standard deviation of the activations. This offsetting strategy enables effective W4A4KV4 quantization of LLMs using deployment-friendly uniform-grid and uniform-precision quantization. Extensive experiments across diverse LLM architectures and benchmarks demonstrate that OffQ outperforms state-of-the-art baselines, consistently improving model accuracy while preserving low-bit efficiency.

Imitation-learning policies inherit the quality of the demonstrations they are trained on, and a growing set of curation metrics promise to score and filter low-quality demonstrations automatically. These metrics are each validated on different data with different protocols, so it is unclear which of them actually identify the demonstrations that harm a policy. We build a controlled testbed in which demonstration defects are injected with known type, and audit seven curation metrics along two axes: how well each separates defective from clean demonstrations, and whether training a behavior-cloning policy on each metric's curated subset improves task success. We study two defect regimes. Subtle perturbations (correlated action noise, tremor, truncation) are detectable by multivariate outlier scoring and, once removed, recover the full downstream gap. Structural errors, where the demonstration executes a wrong action at a key moment, are invisible to every action-only metric we test, and two of them are inverted: they score defective demonstrations as higher quality and, used for curation, tend to leave the policy at or below the uncurated baseline rather than above it. Only metrics that examine the state trajectory detect structural errors, and even the best of them recovers just a third of the downstream gap. High detection accuracy does not guarantee downstream improvement. We release the testbed and all curation implementations.

Correspondence pruning aims to identify inliers from an initial set of correspondences. Most existing Graph Neural Network (GNN)-based methods rely on geometric features mapped from coarse Euclidean coordinates, which struggle to capture the subtle geometric consistencies presented by inliers. While Mamba-based methods possess global receptive fields and long sequence modeling capabilities, they tend to accumulate substantial inconsistent features within the hidden state space, making it difficult to distinguish inliers from outliers. In this paper, we integrate frequency domain perception into this task for the first time and propose SFMambaNet, a novel Spectral-Frequency enhanced Mamba-based two-view correspondence pruning network. Our method is collaboratively composed of two components: First, we design a Local Spectral-Geometric Attention (LSGA) block. LSGA incorporates spectral positional encoding into local graph interactions and introduces multi-scale Mamba processing to enhance the capture of subtle geometric consistencies and improve local feature discriminability. Building upon this, we design a Spectral-Integrated Global Mamba (SIGM) block. SIGM embeds a frequency gating mechanism within the state space, utilizing the frequency information provided by LSGA to explicitly suppress high-frequency noise accumulation within hidden states and mitigate the propagation of inconsistent features. This enhances inlier-outlier separability and achieves robust global context modeling capabilities with nearly linear complexity. Extensive experiments demonstrate that SFMambaNet outperforms current state-of-the-art methods on several challenging tasks. The code is available at https://github.com/Kirito14IT/SFMambaNet.

Accurate registration of CAD models to CT scans is essential for establishing ground truth geometry in volumetric imaging. Obtaining reliable object masks is of growing importance in machine learning settings; as recent architectures grow more capable, huge datasets are required to fully utilise their capabilities. Traditional intensity-based methods fail when CT grayscale values lack calibration references, while point-based algorithms (e.g., ICP, RANSAC) require feature correspondence unavailable between idealized CAD geometry and noisy volumetric CT data. We propose a two-stage geometric registration method for cylindrical objects (ionization chambers) that takes advantage of the distinctive geometric features of the objects. First, we estimate the 3D rotation axis by detecting elliptical cross-sections across CT slices, fitting ellipses to edge-detected contours, and performing PCA on the fitted ellipse centers after RANSAC outlier removal. Second, we voxelize the CAD model, orient it along the detected axis, and maximize volumetric overlap with the CT scan through translational adjustment. This approach achieves robust registration with tilt and orientation errors below $0.1^\circ$ without intensity calibration or feature matching. Once registered, the aligned CAD model provides ground truth geometry for applications including machine learning-based object localization and automated analysis in industrial CT workflows.

Key-value (KV) cache quantization is widely used to reduce Large Language Model (LLM) inference memory, yet existing evaluations solely focus on measuring perplexity and accuracy without assessing the safety impact. In this study, we explore alignment preservation under KV cache quantization. Across eleven instruction-tuned models (3.8B-72B) and five benchmarks (1,894 prompts), we find that low-bit quantization can silently destroy safety alignment: Mistral-7B loses 15.2% of its refusals at only 1.03x perplexity, and no universal safe bit-width exists, with sharp model-specific phase transitions invisible to standard metrics. We identify that the root cause is geometric: safety features occupy a low-dimensional activation subspace 10^2-10^3x more vulnerable to quantization noise than the full representation space perplexity averages over. Inspired by this observation, we propose Per-Channel Reduction (PCR), a diagnostic that classifies each model into one of three mechanistic failure modes: outlier-crushes-safety, where safety lives in non-outlier channels collaterally damaged by outlier-driven scale factors; outlier-as-safety, where safety overlaps outlier channels and finer granularity cannot rescue it; and multi-layer dilution, where safety is distributed across many layers and per-layer fixes fail. PCR predicts the correct mitigation direction on all nine primary models and one held-out model from an independent family using 20 calibration prompts. PCR generalizes across unseen prompts, models, and production quantizers, including KIVI with up to 97.2% recovery, succeeding where attention-based allocation methods fail. The resulting training-free protocol, requiring approximately 35 GPU-minutes, recovers up to 97% of lost alignment at minimal memory overhead, addressing vulnerabilities confirmed in production vLLM serving with FP8 KV cache on NVIDIA GPUs.

Single-score translation metrics can conflate legitimate variation with error, a problem especially acute for classical languages where multiple defensible English renderings of the same passage coexist. We audit Pali-to-English output from four flagship large language models (LLMs): GPT-5.5, Claude Sonnet 4.6, Gemini 3.1 Pro, and Grok 4.3, on 1,700 passages from the Pali Canon, using three established human translations by Bhikkhu Sujato, Thanissaro Bhikkhu, and Bhikkhu Bodhi as a local reference envelope rather than a single gold standard. Each candidate's normalized embedding drift from the reference centroid serves as a triage signal, not an error label; the 1,203 candidates above a 1.5 drift threshold are then adjudicated by a blinded three-model LLM judge panel, calibrated against a 300-instance author-adjudicated validation set. Two results stand out. First, drift predicts severity rather than error per se: the major-error rate among adjudicated high-drift candidates rose monotonically from 7.9% in the 1.5-2.0 band to 51.6% above 3.0, while approximately 80% of 1.5-2.0 outliers were judged valid translation variations. Second, model differences were clearest in the high-drift tail: GPT-5.5 had the lowest adjudicated high-drift major-error rate, with confidence intervals overlapping those of Claude Sonnet 4.6 and Gemini 3.1 Pro; Grok 4.3 had both the largest outlier volume and the highest tail major-error rate (27.6% overall, 74.4% above drift 3.0). The dominant major-error categories (e.g. omission or truncation, doctrinal term errors) are precisely the failures most likely to mislead readers of doctrinal text. The contribution is a reusable audit design for classical-to-modern translation: define a local reference envelope from multiple human translators, use embedding drift to prioritize review, and adjudicate the flagged tail rather than treating outlier status as error.

Sparse autoencoders (SAEs) decompose neural network activations into interpretable features, but many learned features never activate, a problem called feature death that wastes dictionary capacity and can reintroduce superposition. Death rates vary dramatically between models: near-zero on GPT-2, over 70% on AlphaFold3 with identical configurations. We find that dimension-level activation outliers (dimensions whose mean magnitude is large relative to per-token variation) cause this by shifting pre-activations at initialization based on each feature's alignment with the activation mean. Features anti-aligned with the mean receive permanently negative pre-activations and never fire. We formalize outlier severity as $γ= \|μ\|/\|σ\|$; it predicts initial death rates (Spearman $ρ= 0.89$ for dead-by-TopK, $0.82$ for dead-by-ReLU) across 454 model-layer combinations spanning language, vision, protein, and genomic models. Dead features can revive during training, but recovery requires the SAE bias to learn the activation mean, a process that is prohibitively slow at high $γ$. Mean-centering (subtracting the activation mean) sidesteps this and eliminates outlier-induced death across all tested models, confirming the mechanism and providing a principled basis for when and why this preprocessing step is necessary.

Large Vision-Language Models have achieved unprecedented success in zero-shot recognition by aligning visual features with broad semantic concepts. However, this semantic abstraction creates a critical vulnerability in open-world deployment: the Hubris of Semantics'', where models force-fit unknown anomalies into known categories with high confidence due to the lack of explicit negative knowledge. To address this \textit{Open-World Trustworthiness Paradox}, we propose \textbf{Immuno-VLM}, a bio-inspired framework that adapts the biological principle of \textbf{Immunological Negative Selection} to high-dimensional latent spaces. Departing from traditional Open-Set Recognition methods that rely on passive density estimation or inefficient pixel-space outlier generation, Immuno-VLM leverages the generative reasoning of Large Language Models to actively hallucinate Semantic Antibodies'', textual descriptions of near-distribution outliers (e.g., look-alikes, contextual anomalies) that effectively bound the decision space of known classes.Extensive experiments on ImageNet-1K and four challenging OOD benchmarks reveal that Immuno-VLM establishes a new state-of-the-art.

Out-of-distribution (OOD) detection is essential for deploying machine learning models in open-world and safety-critical scenarios, where test inputs may deviate from the training distribution and overconfident predictions on unknown samples can lead to unreliable decisions. Outlier Exposure (OE) has emerged as a promising OOD detection paradigm by introducing auxiliary outliers during training to enlarge the margin between in-distribution (ID) and OOD samples. Existing OE-based methods typically enlarge this margin by employing uniform labels to maximize the entropy of OOD samples over ID categories. However, we theoretically show that uniform labels inevitably disregard the relations between OOD samples and ID categories, termed the over-softening effect, leading to a suboptimal margin bound. Our theoretical analysis further reveals that explicitly exploiting such relations can instead yield improved OOD detection performance. Motivated by this insight, we propose \underline{A}daptive Confidence \underline{OE} (AOE), a simple yet effective method that leverages temperature scaling to recalibrate outlier labels. Specifically, AOE generates adaptive soft targets from temperature-scaled model predictions for OOD samples, where the learnable temperature smooths the prediction distribution without fully erasing class-wise relational information. By supervising OOD samples with these adaptive soft targets, AOE preserves the semantic proximity between OOD samples and ID categories while encouraging the softened targets to approach a high-entropy distribution, thereby suppressing overconfident OOD predictions and enlarging the separation margin. Extensive experiments across diverse benchmarks demonstrate the effectiveness of AOE.

Time series anomaly detection (TSAD) has long been a hot research topic in data mining due to its various applications. Recent studies challenge the effectiveness of popular deep learning methods for TSAD, suggesting their failure in detecting subtle and prolonged anomalies. Outlier Exposure (OE) and Masked Autoencoder (MAE) emerge as two promising paradigms (classification and reconstruction) for solving the above problems. However, OE-based methods are constrained by poor generalization, while MAE-based methods are limited by masking misalignment issues. To address these limitations, this paper proposes a novel framework, CoAD, which unifies the two paradigms to leverage their complementary strengths while mitigating their respective weaknesses. In this framework, the classification module generates probability-informed soft masks for the reconstruction module, which in turn alleviates the generalization problem of the classification module. This cooperative design enables CoAD to effectively detect subtle and complex anomalies that are often overlooked by existing methods. Additionally, the classification module is carefully designed to resolve issues related to improper classification granularity and the neglect of frequency information. Extensive experiments on high-quality benchmark datasets, conducted under rigorous evaluation protocols, demonstrate that CoAD significantly outperforms both state-of-the-art deep learning and traditional data mining methods, highlighting the potential of deep learning in TSAD. Moreover, CoAD is lightweight and substantially faster than existing SOTA methods, demonstrating its practical value for large-scale, real-time applications.

Low-bit activation quantization remains a major bottleneck in efficient large language model (LLM) deployment. The difficulty is not only that activations contain outliers, but that their distributions are often poorly matched to a low-bit uniform quantizer. Existing post-training quantization (PTQ) methods suppress peaks, balance channels, or minimize reconstruction error, yet they rarely specify what activation distribution is actually easy to discretize. As a result, activations may appear numerically smoother while still incurring large quantization error because the quantization range remains wide or most values collapse into a few levels near the mean. We recast activation transformation as quantizer-facing distribution design and analyze quantization error from an information-theoretic perspective. Our analysis shows that quantization-friendly activations should jointly have a smaller numerical range and sufficient dispersion within that range. Guided by this analysis, we propose InfoQuant, a train-free method that employs Peak Suppression Orthogonal Transformation (PSOT) to shape activations into more quantization-friendly distributions. We further introduce adaptive outlier-token selection to improve the robustness of PSOT during optimization. Across multiple LLM families, InfoQuant consistently outperforms prior PTQ and end-to-end training baselines. Under W4A4KV4, it preserves 97% of floating-point accuracy on average and reduces the LLaMA-2 13B performance gap by 42% over the previous state of the art. Code is available at https://github.com/LLIKKE/InfoQuant

Real-world time-series data in industrial sensing, healthcare, and energy systems is often corrupted by a mixture of Gaussian noise and occasional large-magnitude impulse outliers. For tasks that depend on local shape, such as ECG morphology analysis and battery degradation monitoring, the main requirement is not only low reconstruction error but also preservation of derivative peaks and task-critical features. We propose Cascade-KDE, a training-free restoration framework for corrupted time series. The method first estimates a two-dimensional temporal-amplitude density, then applies a Density-Truncated Robust Expectation to limit the influence of distant abnormal points, and finally refines the sequence through an exponential cascade with adaptive stopping. This design aims to improve robustness under out-of-distribution impulse corruptions while keeping the restored trajectory close to the original local structure. Across several benchmark datasets, the proposed method shows consistent gains over classical filters and representative learning-based baselines on curve fidelity, derivative preservation, downstream classification, and runtime efficiency. These results suggest that bounded density-based restoration is a practical option for feature-preserving preprocessing in noisy time-series pipelines.

Unsupervised anomaly detection is widely used in transaction fraud detection where labels are scarce. Isolation Forest (IF) is among the most popular classical methods due to its scalability and ease of deployment. We propose SilIF, an augmentation of Isolation Forest that adds a silhouette-based scoring layer computed in a representation space induced by the trees of the forest. For each point, we extract a vector of per-tree path lengths, cluster these "fingerprints" into structural groups, and compute a silhouette score that measures how well the point fits its assigned group versus the nearest alternative. The silhouette signal is combined with the base IF score via a single hyperparameter alpha. On the IEEE-CIS Fraud Detection benchmark (~590K transactions, 3.5% fraud), SilIF with alpha=1.0 improves over plain Isolation Forest by +0.0080 AUC-PR on average across five seeds, with SilIF winning on all five seeds (paired t-test p=0.046). We also report results on a synthetic credit-card dataset (Sparkov) where the silhouette augmentation does not improve over plain IF, and we characterize the conditions that distinguish the two outcomes. The paper presents SilIF as a tunable, easy-to-deploy enhancement to Isolation Forest with honest reporting of when it helps and when it does not. Code at https://github.com/venkat15vk/silif-anomaly-detection.

Federated learning faces increasing threats from model poisoning attacks, which harms its application to improve privacy. Existing defense methods typically rely on fixed thresholds or perform clustering with a fixed number of clusters to distinguish malicious gradients from benign ones. However, these methods are difficult to adapt to dynamic poisoning strategies of malicious clients, and often result in the loss of benign gradients due to the heterogeneity of clients' local datasets. To address these problems, we propose a novel robust aggregation method that leverages a small number of known benign clients as references, enabling accurate identification and filtering of malicious gradients while retaining as many benign gradients as possible, even when the number of malicious clients is unknown and variable. First, we introduce a density-based low-dimensional gradient clustering method, which projects gradients onto the two most divergent dimensions and applies density-based clustering to identify malicious gradients while retaining clustered benign gradients and potentially benign outliers. Second, we design an enhancing clustering low-dimensional gradient generator model, which learns to generate pseudo-gradients aligned with the boundary of the benign cluster. These pseudo-gradients act as bridges to connect sparse benign gradient outliers. Third, we introduce low-dimensional gradient re-clustering that clusters the generated pseudo-gradients together with real gradients to recover benign gradients misclassified as noise points, enabling more benign gradients to participate in aggregation. Extensive experiments on the MNIST, CIFAR-10, and MIND datasets demonstrate that our method exhibits superior fidelity and robustness under dynamic poisoning scenarios.

Deep neural networks (DNNs) experience significant performance degradation when processing noisy labels, primarily due to overfitting on mislabeled data. Current mainstream approaches attempt to mitigate this issue by passively filtering clean samples during training. However, simple sample filtering within feature spaces degraded by noise struggles to distinguish between challenging samples and noisy samples, creating a bottleneck for model performance. We highlight for the first time the fundamental importance of actively reshaping feature space geometry for learning from noisy data. We propose a novel Geometry-aware Manifold Regularization Paradigm whose core idea is to explicitly construct energy barriers between data manifolds by actively synthesizing virtual outlier samples. By imposing geometric constraints that promote intra-class compactness and inter-class separation, this approach enhances the discriminability between hard and noisy samples, leading to the learning of more robust representations. Our regularization mechanism exhibits high universality, with effectiveness independent of any prior assumptions about noise patterns. It can be integrated as a standalone mechanism into existing sample selection frameworks, providing stronger robustness against diverse noisy environments. Experiments demonstrate that our paradigm achieves performance surpassing current state-of-the-art (SOTA) methods on multiple benchmarks, including CIFAR-10, with particularly pronounced advantages under more challenging asymmetric noise conditions. Furthermore, this paradigm significantly enhances the model's capability in Out-of-Distribution (OOD) detection, ensuring superior reliability and safety for deployment in open-world scenarios.

Modern applications of conformal inference to multiple testing problems, such as outlier detection and candidate selection, often involve selecting test samples whose conformal p-values fall below a threshold. The quality of such methods is often measured by the false discovery proportion (FDP), defined as the fraction of incorrect selections. Existing approaches typically control the expected value of the FDP, using methods such as the Benjamini-Hochberg procedure. This approach fails to provide high-probability bounds on the realized false discovery proportion and invalidates statistical guarantees if the rejection threshold is selected after inspecting the data. This paper establishes finite-sample, distribution-free upper bounds on the FDP that hold simultaneously over all possible rejection thresholds, enabling arbitrary post hoc selection of the threshold. Simultaneous validity is achieved by constructing a high-probability envelope for the empirical distribution function of null conformal p-values by sampling from their joint distribution. Furthermore, our framework allows practitioners to modulate the envelope's shape, thereby producing tight bounds in rejection regions of primary interest. We use this flexible approach to derive simultaneous FDP upper bounds for both outlier detection and conformal selection. We demonstrate through synthetic and real-data experiments that the resulting bounds are both valid and substantially less conservative than those derived from existing approaches.

We propose OASIS, an outlier- and sink-aware technique built on inter-layer null signaling. As AttnResidual architectures introduce an additional depth-wise normalization channel, they improve inter-layer routing flexibility but also exacerbate attention sinks, activation outliers, and the resulting degradation in inference stability and quantization robustness. OASIS addresses this issue by introducing a Softmax1-based null space and coupling token-level null evidence to depth routing through an inter-layer null signal, thereby reducing sink-dominated routing and improving structural robustness. Theoretically, we show that the dual-normalization design of AttnResidual intensifies sink formation and quantization brittleness. Experimentally, we compare OASIS against five baselines on three real-world datasets and observe consistent improvements in both attention sink and post-quantization performance. Notably, OASIS achieves an average reduction of 9.26% in maximum infinity norm and 2.60% in average kurtosis across the evaluated settings, while lowering perplexity by 75.85% under W8A8 and improving GSM8K Pass@1 by 12.42% under W4A4.

We study the multi-task linear regression problem in the presence of contaminated tasks. We address the setting where the unknown parameters of a majority of tasks are close in the $\ell_2$-norm, while a fraction of tasks are arbitrary outliers. Existing theoretical frameworks for this problem rely heavily on the assumption that the empirical second moment of each task has a minimum eigenvalue bounded away from zero (order $Ω(1)$). Crucially, this assumption fails in many high-dimensional scenarios, rendering prior guarantees vacuous. To overcome this limitation, we propose an estimator based on matrix-weighted norm regularization. We also introduce a relative balancedness condition, quantified by a balancedness constant, that compares each task's second moment with the average inlier geometry and relaxes the need for taskwise second-moment lower bounds. In favorable regimes with moderate balancedness, our prediction MSE bounds match the rate of Duan and Wang (2023) under substantially weaker spectral assumptions; the resulting task-overall MSE is minimax optimal up to logarithmic factors. Furthermore, we demonstrate that our estimator enjoys a safety guarantee: when the relevant balancedness constant is large or infinite, or when tasks are unrelated, the method performs no worse than independent task learning.

Unsupervised outlier detection is attractive because it eliminates the need for labeled data. Moreover, forming multi-model ensembles can improve detection robustness. However, composing an ensemble without labeled data is challenging. Naively composed ensembles can suffer from ensemble saturation, where redundant or unreliable detection models degrade performance and incur unnecessary computation. We propose MetaEns, an automatic unsupervised framework for selecting ensembles of outlier detection models. Using labeled meta-datasets, MetaEns learns a model that predicts marginal ensemble gains, estimating the expected improvement from adding a candidate model to a partially constructed ensemble. At test time, this learned signal is combined with a submodular-inspired proxy objective that enforces diminishing returns through diversity-aware discounting and family-level risk regularization, thereby enabling greedy sequential selection with adaptive early stopping. As a result, MetaEns constructs compact, high-quality ensembles without access to ground-truth labels. Experiments on 39 real-world datasets show that MetaEns consistently outperforms state-of-the-art unsupervised selectors and ensemble baselines, achieving higher average precision while using fewer models.

Vision Transformers (ViTs) are known to exhibit high-norm patch-token outliers that degrade feature map quality, a problem effectively mitigated by register tokens. As diffusion models increasingly adopt transformer architectures and move toward pixel-space training, they become closer in form to ViTs, raising the question of whether register tokens are also useful for Diffusion Transformers (DiTs). In this work, we show that DiTs differ from ViTs in a key respect: they do not exhibit patch-token outliers but still benefit from registers. Interestingly, registers are more effective in pixel-space DiTs than in latent-space DiTs. By analyzing intermediate representations, we find that register tokens produce cleaner feature maps at high noise levels, which may contribute to their effectiveness in pixel-space generation. We further observe that recent pixel-space DiT architectures implicitly incorporate register-like mechanisms, which may partially account for their strong empirical performance. Motivated by these observations, we propose Register Guidance, a technique that amplifies the contribution of register tokens responsible for improving visual structure and coherence.

Symbolic regression (SR) aims to discover explicit mathematical expressions that explain observed data and is widely used in domains where interpretability is essential. Because interpretability requires expressions to reflect meaningful regularities, SR is sensitive to observations that deviate from the dominant relationship. Such irregular observations, or outliers, are common in real-world data and can hinder SR from identifying underlying regularities. Robust regression mitigates this by downweighting observations with large residuals. However, deciding which observations should be treated as outliers is often ambiguous and depends on user interpretation and domain knowledge, a perspective largely overlooked in existing SR studies. This motivates approaches that present multiple candidate expressions, allowing users to examine different residual patterns and choose expressions consistent with their expertise. We propose diversified residual symbolic regression (DRSR), which achieves high predictive accuracy while promoting diversity with respect to residual patterns based on the Quality-Diversity paradigm. DRSR collects multiple expressions that fit the data well but differ in how residuals are distributed, enabling post-search selection aligned with domain knowledge. On a synthetic mixture dataset, DRSR produces more diverse expressions than conventional SR while capturing multiple underlying relationships. On a real-world astronomical dataset, DRSR discovers multiple expressions consistent with known physical relationships.

LLM quantization has become essential for memory-efficient deployment. Recent work has shown that quantization schemes can pose critical security risks: an adversary may release a model that appears benign in full precision but exhibits malicious behavior once quantized by users. However, existing quantization-conditioned attacks have been limited to relatively simple quantization methods, where the attacker can estimate weight regions that remain invariant under the target quantization. Notably, prior attacks have consistently failed to compromise more popular and sophisticated schemes, limiting their practical impact. In this work, we introduce the first quantization-conditioned attack that consistently induces malicious behavior that can be triggered by a broad range of advanced quantization techniques, including AWQ, GPTQ, and GGUF I-quants. Our attack exploits a simple property shared by many modern quantization methods: large outliers can cause other weights to be rounded to zero. Consequently, by injecting outliers into specific weight blocks, an adversary can induce a targeted, predictable weight collapse in the model. This effect can be used to craft seemingly benign full-precision models that exhibit a wide range of malicious behaviors after quantization. Through extensive evaluation across three attack scenarios and LLMs, we show that our attack achieves high success rates against a broad range of quantization methods on which prior attacks fail. Our results demonstrate, for the first time, that the security risks of quantization are not restricted to simpler schemes but are broadly relevant across complex, widely-used quantization methods.

Network quantization has emerged as one of the most practical model compression techniques, which significantly reduces a model's memory and compute consumption by mapping floating-point numbers to low-bit representations. However, existing quantization methods typically suffer from the speed-accuracy tradeoff and limited generalization. To address these issues, recent compensation-based methods offer an efficient yet general solution by introducing additional lightweight linear layers into the quantized network. However, the accuracy of these methods suffers from their limited compensation capability and high sensitivity to outliers. In this paper, we propose Nonlinear Bipolar Compensation (NBC), a post-training quantization approach that introduces nonlinear compensation to reduce the effect of outliers. We further design Bipolar Logarithmic Transformation (BLT), which compresses outliers by mapping both the quantized input and the quantization error into a transformed space. A simple linear layer is then applied for compensation in the transformed space, preserving the efficiency of our method. Extensive experiments across various tasks, models, and quantization methods confirm the effectiveness, efficiency, robustness, and generality of our NBC approach.

We introduce XFP, a dynamic weight quantizer for LLM inference that inverts the conventional workflow: the operator specifies reconstruction quality floors on per-channel cosine similarity (one strict floor for attention and shared experts, one lazy floor for routed-expert MoE); XFP determines codebook size, outlier budget, and packing per layer automatically -- no Hessian, no calibration data, no manual bit-width selection. Each weight matrix is decomposed into a sparse fp16 outlier residual and a dense sub-byte index tensor into a per-group learned codebook. Two storage modes share one auto-select frontend and one fused decode kernel: V2 (per-channel Lloyd) and V2a (shared library of L=32 codebooks per layer). On Qwen3.5-122B-A10B under V2, XFP reaches 138 tok/s single-stream decode on workstation hardware (RTX PRO 6000 Blackwell, TP=2) at 94.49% GSM8K strict-match (3 seeds, n=3957), and is 49% faster than Marlin INT4 at TP=1. For models that do not fit in the target memory envelope, we present the H-Process: a quality-driven iteration over the two cosine thresholds that finds the operating point at which the model just fits while still producing sensible output. Three constraints define its search space: the operator-set thresholds, an OOM boundary at quantize-on-load, and a garbage boundary in generation (cosine similarity steers; benches verify). On Qwen3.5-397B-A17B (512 routed experts/layer), the H-Process fits the full expert population into 2x96 GB at ~3.4 effective bits and delivers 100.9 tok/s long-output decode at 66.72% GSM8K strict-match on the full 1319-problem set (single seed at submission; multi-seed evaluation in progress), exceeding INT4 with routed-expert pruning on memory, throughput, and accuracy simultaneously.

Topological clustering, and its main algorithm ToMATo, is a clustering method from Topological Data Analysis (TDA) which has been applied successfully in several applications during the last few years. This is due to its high versatility, as clusters are detected from the persistent components in the sublevel sets of any user-defined function (gene expression, pixel values, etc), and efficiency, as topological clustering enjoys robustness guarantees. However, ToMATo is also limited in several ways. First, a graph on the data points needs to be provided as a hyper-parameter of the method (whose fine-tuning is left to the user). Second, ToMATo is known to be very sensitive to outlier values in the function range. Finally, and most importantly, ToMATo can only handle one function at a time, whereas it is critical to use several functions in various applications. In this article, we introduce ToMAToMP: the first topological clustering method able to handle several functions at the same time with theoretical guarantees. More specifically, we leverage a recent tool from multi-parameter persistent homology, called MMA decomposition, to design our clustering algorithm, and prove that it enjoys robustness properties. As corollaries, we show that it can be used to make ToMATo independent of graph tuning, and robust to outliers. Finally, we provide a set of numerical experiments showcasing the efficiency and quality of the clusterings produced by ToMAToMP, by showing strong improvement over non-topological and topological baselines for various datasets.