DeCoFlow: Structural Decomposition of Normalizing Flows for Continual Anomaly Detection

In industrial environments, new product categories arrive sequentially, requiring continual anomaly detection without access to past data. Normalizing Flows (NFs) provide exact density estimation but suffer from catastrophic forgetting as parameter updates across tasks distort the density manifold. While parameter isolation can prevent interference, it must preserve the strict invertibility and Jacobian validity of NFs. To satisfy these requirements, we exploit the inherent property that affine coupling layers maintain transformation validity regardless of subnet parameterization. Based on this, we propose DeCoFlow, which decomposes subnets into a frozen universal base and task-specific low-rank adapters to isolate updates. We further introduce Task-Specific Alignment, Auxiliary Coupling Layers, and Tail-Aware Loss to compensate for frozen-base rigidity. DeCoFlow achieves state-of-the-art image-level AUROCs of 98.40% on MVTec-AD and 93.00% on VisA, while maintaining parameter-level zero forgetting (0.00% FM under correct routing) with only 2.27M parameters per task.

Cliff Tokens: Identifying Single-Token Failure Triggers in LLM Mathematical Reasoning

Large language models (LLMs) reach high accuracy in mathematical reasoning, but individual traces on the same problem diverge; some arrive at the correct answer while others fail. Prior work analyzes failure at the step, chunk, or sentence level, or at tokens where failure has already occurred. Neither identifies the precise token that triggers the shift toward failure. We introduce the cliff token, a token where the token-wise potential drops significantly under an adaptive threshold that scales with the local token-wise potential, based on a one-sided two-proportion z-test. Across seven models and three mathematical reasoning benchmarks (GSM1K, MATH500, AIME 2025), cliff tokens act as failure triggers; deleting the first cliff token and resampling recovers pass@64 to 1.0, while keeping it limits recovery to between 0.71 and 1.00. We further introduce a cliff taxonomy of deterministic, uncertain, and sampled-off cliffs, defined by greedy choice and token entropy. Each type has distinct probabilistic characteristics, and the taxonomy generalizes across model scales. Finally, we validate the taxonomy via single-token preference optimization at cliff positions (Cliff-DPO). Trained on GSM8K, Cliff-DPO improves accuracy across benchmarks by up to +6.6. Optimizing at uncertain and sampled-off cliffs improves reasoning, while deterministic cliffs do not.

Asking Is Not Enough: Protocol Sensitivity in LLM Confidence Calibration

LLM confidence calibration is often evaluated by comparing two signals: token-probability scores and verbalized confidence. These signals are sometimes treated as direct readouts of model uncertainty, but their comparison depends on measurement choices that are rarely made explicit. In the main analysis, we hold the verbalized-confidence elicitation fixed: a single prompt template, probability scale, and output format. We then vary the measurement axes that define the verbalized-vs-token comparison: which answer string receives the token-probability score, how that score is read from the answer tokens, and under which conditioning context it is measured. We evaluate this design on four QA benchmarks across three open 7--8B base/Instruct model families, with larger Qwen2.5 variants as same-family robustness checks. The resulting comparison is sensitive to these choices: conditioning context changes the sign or magnitude of the ECE gap across settings, token readout produces smaller but still sign-moving changes, and changing the ECE estimator has little effect. Under the default generated-answer, bare-context protocol, Instruct settings are close to parity rather than showing a large calibration gain for verbalized confidence. In a separate supplied-answer analysis, surface-plausible wrong answers receive nearly the same confidence as supplied gold answers, suggesting that verbalized confidence also reflects answer plausibility and provenance rather than correctness alone. We argue that both confidence signals should be treated as protocol-dependent behavioral measurements, and provide a reporting checklist covering elicitation provenance, scored answer, token-probability readout, and conditioning context.

Detecting Time Series Anomalies Like an Expert: A Multi-Agent LLM Framework with Specialized Analyzers

Recent studies have explored large language models for time-series anomaly detection, yet existing approaches often rely on a single general-purpose model to directly infer anomaly indices or intervals, limiting controllability, interpretability, and reliability for complex anomaly patterns. We propose SAGE (Specialized Analyzer Group for Expert-like Detection), a multi-agent framework for structured anomaly diagnosis in univariate time series. It decomposes anomaly analysis into four specialized Analyzers for point, structural, seasonal, and pattern anomalies. Each Analyzer applies family-specific numerical tools and diagnostic visualizations to generate evidence, while an evidence-grounded Detector consolidates the evidence into confidence-scored anomaly records with intervals and candidate types. A Supervisor then converts these structured records into analyst-facing diagnostic reports. SAGE further constructs synthetic in-context examples from normal-reference training segments, without using real anomalous segments or anomaly-type labels as in-context examples. Across three benchmarks, SAGE achieves the best average performance among strong ML/DL and language-model-based baselines. Ablation studies and human evaluation further show that the proposed framework improves detection reliability and the practical usefulness of diagnostic outputs.

Forecasting Anomaly Precursors via Uncertainty-Aware Time-Series Ensembles

Detecting anomalies in time-series data is critical in domains such as industrial operations, finance, and cybersecurity, where early identification of abnormal patterns is essential for ensuring system reliability and enabling preventive maintenance. However, most existing methods are reactive: they detect anomalies only after they occur and lack the capability to provide proactive early warning signals. In this paper, we propose FATE (Forecasting Anomalies with Time-series Ensembles), a novel unsupervised framework for detecting Precursors-of-Anomaly (PoA) by quantifying predictive uncertainty from a diverse ensemble of time-series forecasting models. Unlike prior approaches that rely on reconstruction errors or require ground-truth labels, FATE anticipates future values and leverages ensemble disagreement to signal early signs of potential anomalies without access to target values at inference time. To rigorously evaluate PoA detection, we introduce Precursor Time-series Aware Precision and Recall (PTaPR), a new metric that extends the traditional Time-series Aware Precision and Recall (TaPR) by jointly assessing segment-level accuracy, within-segment coverage, and temporal promptness of early predictions. This enables a more holistic assessment of early warning capabilities that existing metrics overlook. Experiments on five real-world benchmark datasets show that FATE achieves an average improvement of 19.9 percentage points in PTaPR AUC and 20.02 percentage points in early detection F1 score, outperforming baselines while requiring no anomaly labels. These results demonstrate the effectiveness and practicality of FATE for real-time unsupervised early warning in complex time-series environments.

COMET: Codebook-based Online-adaptive Multi-scale Embedding for Time-series Anomaly Detection

Time series anomaly detection is a critical task across various industrial domains. However, capturing temporal dependencies and multivariate correlations within patch-level representation learning remains underexplored, and reliance on single-scale patterns limits the detection of anomalies across different temporal ranges. Furthermore, focusing on normal data representations makes models vulnerable to distribution shifts at inference time. To address these limitations, we propose Codebook-based Online-adaptive Multi-scale Embedding for Time-series anomaly detection (COMET), which consists of three key components: (1) Multi-scale Patch Encoding captures temporal dependencies and inter-variable correlations across multiple patch scales. (2) Vector-Quantized Coreset learns representative normal patterns via codebook and detects anomalies with a dual-score combining quantization error and memory distance. (3) Online Codebook Adaptation generates pseudo-labels based on codebook entries and dynamically adapts the model at inference through contrastive learning. Experiments on five benchmark datasets demonstrate that COMET achieves the best performance in 36 out of 45 evaluation metrics, validating its effectiveness across diverse environments.

AlienLM: Alienization of Language for API-Boundary Privacy in Black-Box LLMs

Modern LLMs are increasingly accessed via black-box APIs, requiring users to transmit sensitive prompts, outputs, and fine-tuning data to external providers, creating a critical privacy risk at the API boundary. We introduce AlienLM, a deployable API-only privacy layer that protects text by translating it into an Alien Language via a vocabulary-scale bijection, enabling lossless recovery on the client side. Using only standard fine-tuning APIs, Alien Adaptation Training (AAT) adapts target models to operate directly on alienized inputs. Across four LLM backbones and seven benchmarks, AlienLM retains over 81\% of plaintext-oracle performance on average, substantially outperforming random-bijection and character-level baselines. Under adversaries with access to model weights, corpus statistics, and learning-based inverse translation, recovery attacks reconstruct fewer than 0.22\% of alienized tokens. Our results demonstrate a practical pathway for privacy-preserving LLM deployment under API-only access, substantially reducing plaintext exposure while maintaining task performance.

naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurement

Physics-Informed Neural Networks (PINNs) are effective methods for solving inverse problems and discovering governing equations from observational data. However, their performance degrades significantly under complex measurement noise and gross outliers. To address this issue, we propose the Noise-Adaptive Physics-Informed Neural Network (naPINN), which robustly recovers physical solutions from corrupted measurements without prior knowledge of the noise distribution. naPINN embeds an energy-based model into the training loop to learn the latent distribution of prediction residuals. Leveraging the learned energy landscape, a trainable reliability gate adaptively filters data points exhibiting high energy, while a rejection cost regularization prevents trivial solutions where valid data are discarded. We demonstrate the efficacy of naPINN on various benchmark partial differential equations corrupted by non-Gaussian noise and varying rates of outliers. The results show that naPINN significantly outperforms existing robust PINN baselines, successfully isolating outliers and accurately reconstructing the dynamics under severe data corruption.

Interaction as Interference: A Quantum-Inspired Aggregation Approach

Classical approaches often treat interaction as engineered product terms or as emergent patterns in flexible models, offering little control over how synergy or antagonism arises. We take a quantum-inspired view: following the Born rule (probability as squared amplitude), \emph{coherent} aggregation sums complex amplitudes before squaring, creating an interference cross-term, whereas an \emph{incoherent} proxy sums squared magnitudes and removes it. In a minimal linear-amplitude model, this cross-term equals the standard potential-outcome interaction contrast \(Δ_{\mathrm{INT}}\) in a \(2\times 2\) factorial design, giving relative phase a direct, mechanism-level control over synergy versus antagonism. We instantiate this idea in a lightweight \emph{Interference Kernel Classifier} (IKC) and introduce two diagnostics: \emph{Coherent Gain} (log-likelihood gain of coherent over the incoherent proxy) and \emph{Interference Information} (the induced Kullback-Leibler gap). A controlled phase sweep recovers the identity. On a high-interaction synthetic task (XOR), IKC outperforms strong baselines under paired, budget-matched comparisons; on real tabular data (\emph{Adult} and \emph{Bank Marketing}) it is competitive overall but typically trails the most capacity-rich baseline in paired differences. Holding learned parameters fixed, toggling aggregation from incoherent to coherent consistently improves negative log-likelihood, Brier score, and expected calibration error, with positive Coherent Gain on both datasets.

Quantum Entanglement as Super-Confounding: From Bell's Theorem to Robust Machine Learning

Bell's theorem reveals a profound conflict between quantum mechanics and local realism, a conflict we reinterpret through the modern lens of causal inference. We propose and computationally validate a framework where quantum entanglement acts as a "super-confounding" resource, generating correlations that violate the classical causal bounds set by Bell's inequalities. This work makes three key contributions: First, we establish a physical hierarchy of confounding (Quantum > Classical) and introduce Confounding Strength (CS) to quantify this effect. Second, we provide a circuit-based implementation of the quantum $\mathcal{DO}$-calculus to distinguish causality from spurious correlation. Finally, we apply this calculus to a quantum machine learning problem, where causal feature selection yields a statistically significant 11.3% average absolute improvement in model robustness. Our framework bridges quantum foundations and causal AI, offering a new, practical perspective on quantum correlations.