Rare Events

As agents are deployed with increased autonomy, even extremely rare events along their stochastic output trajectories can occur and prove catastrophic. Safe deployment therefore does not depend on whether these events can occur, but on how often they might. We study the problem of estimating the probability of rare events that arise from stochastic variation in the agent's own actions. Estimating this type of risk requires searching over the combinatorially vast space of trajectories. Naive Monte Carlo is computationally prohibitive in this regime, and constructing effective importance sampling (IS) proposals requires coordinated changes to a context-dependent chain of conditional distributions. We develop a new IS method that perturbs the original model's weights to construct the proposal. The proposal is itself a differentiably parameterized language model, enabling gradient-based search over weight space. We formulate an objective that combines a differentiable surrogate for event amplification and an adaptive regularization scheme that dynamically balances amplification against estimator stability. We evaluate our approach on $\sim$120M and $\sim$2.6B models across three event families spanning 300+ rare events as rare as $10^{-9}$, with reference probabilities computed with $<10\%$ relative standard error. In our most verifiable settings, we observe that our IS estimator achieves over $800\times$ compute-weighted efficiency gains over naive Monte Carlo for events with probabilities lower than $10^{-7}$. Our implementation is available at https://github.com/namkoong-lab/iterative-unalignment.

The brain needs an accurate internal model of the world to generate predictions and guide behavior. However, it must estimate the statistical structure of the environment from limited experience. This is particularly difficult for rare events, whose observed frequencies in a limited sample may substantially under- or overestimate their true frequencies. How the brain constructs an accurate internal model despite this sampling problem remains unclear. We address this problem using a Bayesian Confidence Propagation Neural Network (BCPNN) trained on event sequences from a Markov-chain random walk with controlled event frequencies. Treating the underlying Markov structure as the ground truth, we train the network on limited sample of event sequences and then allow it to generate autonomous replay based on the learned structure. We evaluate replay fidelity at the levels of both marginal event frequencies and conditional transition structure. We find that moderate neural noise, modeled as temporally correlated random fluctuations in unit activity during replay, is critical for faithful internal simulation. Without this variability, deterministic replay systematically under- or overrepresents rare events, whereas moderate noise restores both their marginal and conditional occurrence. Moderate noise also broadens the range of parameter values that produce accurate replay, making the model more robust to parameter variation. Together, these results support noise-assisted internal simulation as a potential mechanism for compensating for sampling errors arising from limited experience. Our model also provides a testable framework for investigating how altered neural variability may impair internal-model fidelity in disorders such as Parkinson's disease.

Text-to-speech that reads raw text has no lexicon: a rare word is read as guessed. Remedies train a reading-and-accent channel on recorded speech or edit words one at a time from exemplars. We do neither. The frozen backbone reads a sentence containing a common word it already says correctly, and its own output then serves as the teacher for the same sentence, with that word replaced by a tagged, accented reading; this training pair is the whole idea. On Sarashina2.2-TTS, screened raters at Fleiss' kappa = 0.85 hear the prescribed accent on 0.89 of unseen words against 0.57 for kana, which cannot express one; kana wins no pair; naturalness is not measurably hurt. Moved untuned to autoregressive, diffusion, and encoder-decoder backbones, it transfers reading, 0.25 to 0.47 above no edit on 319 words, and on CosyVoice 2 accent on two words in three, but not on Irodori; the paper locates why.

Cross-vehicle federated learning enables vehicles to collaboratively improve perception models while keeping locally collected driving data private. However, vehicle participation is transient, and a vehicle may depart before training converges while permanently taking its local data. When this departing vehicle holds most samples of a target class, the class becomes rare in the remaining FL network, and its recognition can silently degrade as the shared backbone continues to evolve. Recovering the class is difficult since the few remaining samples provide a noisy prototype estimate, while FL privacy constraints prevent centralized access to raw data or per-sample features. This paper presents MPT, a cross-vehicle FL framework that maintains rare-class recognition by reconstructing its prototype at every round from privacy-preserving class-level statistics. MPT combines a barycentric decomposition that tracks drift shared with remaining-class prototypes, a covariance-based residual prediction that estimates out-of-span drift, and an adaptive calibration that weighs the remaining rare-class samples according to their reliability. We evaluate MPT on three vehicle classification tasks and four backbones against representative calibration and drift-compensation baselines. MPT outperforms all baselines in rare class F1, reaching 0.516 on the nuImages dataset with only 1% of rare-class samples remaining, without raw data, per-sample features, or retraining.

Multimodal entity linking grounds entity mentions in text and images to knowledge-base entries. These systems degrade on rare entities, but prior work measures rarity primarily through popularity-based metrics such as pageviews. We broaden this view using knowledge-graph structural metrics that capture how well an entity is documented and connected. These metrics identify many rare entities that popularity metrics miss. Across the resulting rare-entity slices, state-of-the-art accuracy drops by 15.4-39.9%, showing that different rarity definitions expose different failure modes. To address these failures, we introduce a simple, training-free framework in which a reasoning-capable vision-language model iteratively searches and reasons over Wikipedia, gathering evidence dynamically. Controlled experiments show that reasoning and retrieval are complementary. Reasoning alone does not significantly improve accuracy on rare entities. Retrieval without reasoning improves rare-entity accuracy but can hurt overall accuracy. Their combination performs best. On MERLIN, a multilingual multimodal entity linking benchmark over five languages (Hindi, Indonesian, Japanese, Tamil, Vietnamese), our best system improves over the state of the art by 6.9% overall and by up to 23.3% on rare-entity slices. We release MERLIN-Rare, rare-entity test slices for targeted evaluation, with our framework.

Users of a deployed language model routinely encounter behaviours that testing almost never surfaces, since deployment puts the model through orders of magnitude more interactions than any evaluation can simulate. Automated auditors make testing cheap to scale and flexible enough to cover almost any specified behaviour, yet their lack of optimisation pressure makes them sample-inefficient. To address this shortcoming, we introduce BLOOM-WILT, a full auditing pipeline that elicits natural multi-turn instances of rare behaviours, without training cost or access beyond the target's next-token distribution. On the input side, WILT's auditor model revises its conversational strategy across rounds, learning from previous scored interactions. On the output side, WILT adaptively reweights the target's decoding using the model's own distribution conditioned on an elicitation prompt, so that behaviour-relevant generations are sampled ahead of others it finds equally probable when unprompted. We evaluate WILT across 4 target models and 8 behaviours, where it beats the baseline auditor in 30 of the 32 settings and overturns the previous model safety rankings. WILT raises average behaviour presence from 51% to 100% when eliciting self-harm encouragement from Qwen3.5-4B, beating every elicitation method we port into the same pipeline at matched compute, without pushing output probability below the baseline's.

This paper proposes methods to extract over 50 types of events from a Dutch historical corpus spanning the 17th and 18th centuries. The methods we propose aim to tackle a very challenging scenario in Machine Learning: extracting the long-tail of the long-tail. Historic data from before the 19th century is in itself a niche domain not covered in the pre-training of Large Language Models, and we aim to extract events only scarcely annotated in the training data available for this domain. We propose creating expert classifiers for subgroups of the events present in the training data. We make these groupings based on similar frequency in the training data or on semantic relatedness. Experts trained on underrepresented events are assigned higher priority when predicting to avoid being dominated by frequency biases. We refer to this new way of combining classifiers, specifically tailored to protect the long-tail, as ROBE: Reversed-Order-Biased-Experts. We also propose a controlled method to create domain-specific synthetic data.\ Our two implementations of ROBE outperform a simple fine-tuned encoder model with a .16 increase in precision and a .05 increase in recall respectively. The best model achieves a .11 increase in f1 for a group of long-tail classes in our niche data set.

AI-assisted facial phenotyping supports rare genetic disorder prioritization by retrieving visually similar diagnosed cases from facial image reference databases such as the GestaltMatcher Database (GMDB). Existing GestaltMatcher-based retrieval frameworks compare each test image with individual gallery images in a facial phenotype embedding space. However, this pointwise formulation does not fully exploit available evidence, because patients may have multiple images and disorders may be represented by multiple diagnosed gallery patients. We propose an inference-time multi-level evidence aggregation framework that improves facial phenotype retrieval without modifying the underlying GestaltMatcher-Arc encoder. The framework combines embedding-level patient aggregation of multiple images from the same individual, patient-weighted disorder centroids, and hybrid individual-centroid scoring to integrate test-patient observations, disorder-level gallery evidence, and local nearest-neighbor evidence. We evaluated the approach on GMDB v1.1.4 across disorders represented during training (GMDB-Freq), unseen disorders (GMDB-Rare), and multi-image patient subsets, using a unified gallery containing both GMDB-Freq and GMDB-Rare disorders. Multi-level evidence aggregation improved mean per-disorder top-$N$ retrieval accuracy across all evaluation subsets. Top-1 accuracy increased from 38.52% to 48.82% on GMDB-Freq and from 19.38% to 23.79% on GMDB-Rare. On multi-image subsets, top-1 accuracy increased from 46.12% to 60.94% on GMDB-Multi-Freq and from 18.54% to 26.71% on GMDB-Multi-Rare. These findings show that inference-time aggregation can improve next-generation facial phenotype retrieval without retraining the encoder, supporting a shift from isolated single-image matching toward multi-level aggregation of patient and disorder evidence for rare-disorder prioritization.

Recognizing new and rare words - named entities, acronyms, domain specific special words, and other items scarce in training data - remains a key challenge for automatic speech recognition (ASR). We compare two strategies for this: context biasing methods, where an ASR model is extended such that during inference a word list can be supplied, and speech large language models (LLMs) prompted with context directly. We evaluate two context biasing methods based on Whisper against three speech LLMs across read and non-read speech, reporting biased, unbiased, and overall word error rate (WER). The context biasing methods cut biased WER by up to 88% relative while leaving other words largely unaffected. Speech LLMs excel on read speech but generalize less well to non-read speech, and prove sensitive to distractor count and prompt word order. We characterize the resulting trade-offs to guide method selection.

Similarity search over sparse set-valued data is often dominated by frequent background attributes because classical measures such as Jaccard, cosine, and Hamming compare objects through atomic overlap. IDF (Inverse document frequency) weighting partially reduces this effect but remains atom-wise and cannot explicitly represent informative higher-order co-occurrences. We introduce RareSense, a rarity-aware similarity framework for sparse transactional anomaly data. RareSense mines minimal rare itemsets as intermediate structures, derives reliable rare association rules, maps objects into sparse rare-rule profiles, and compares them using weighted Jaccard similarity. Rule weights combine inverse support, confidence, lift, structural complexity, and stability, so that neighborhoods are determined by shared rare evidence rather than uniform feature overlap. We show that IDF-weighted Jaccard is a restricted singleton case of RareSense, and that the induced distance is a pseudometric on the original objects and a metric over equivalence classes defined by identical rule profiles. Experiments across four benchmark families spanning cybersecurity and general categorical domains show that RareSense attains the highest observed macro-average query-conditioned retrieval performance among the evaluated similarity measures. The statistical analysis indicates significant overall differences, with corrected paired comparisons favoring RareSense over the atomic baselines. The gains remain workload-dependent and are strongest when anomalies share repeatable rare higher-order structure. For global anomaly ranking, RareSense achieves the highest observed macro-average performance while remaining statistically comparable to several strong dedicated detectors.

The introduction of LAFOV PET scanners brings significant sensitivity gains but also a substantial increase in the background rate from accidental coincidences, phantom-scattered and detector-scattered photons. While machine learning methods have been applied to background reduction in PET imaging, they target specific background components in post-processing rather than event-by-event classification on the raw data. In this work, we formulate coincidence classification as a supervised multi-class problem and evaluate XGBoost, AdaBoost and Neural Network classifiers as pre-reconstruction filters, using Monte Carlo simulations of the Siemens Biograph Vision Quadra scanner with NEMA IEC and anthropomorphic XCAT phantoms. We investigate two feature sets: a 4-feature representation based on the Attenuation Factor, photon time difference, energy sum, and energy difference, and an extended 6-feature set that incorporates topology-based variables. A systematic robustness study via cross-phantom inference reveals that the 4-feature models generalise significantly better across different phantom geometries, with XGBoost suffering an accuracy loss of only 0.04 compared to 0.13 for the 6-feature variant. Our best models achieve accuracies of up to 0.74 and 0.69 for the NEMA IEC and XCAT phantoms, respectively, outperforming traditional geometry-based cuts. However, we show that this compact feature set not only provides limited suppression of in-phantom scattered coincidences, but it also can lead to non-trivial spatial patterns. With scattered coincidences being the dominant background component in clinical conditions, this suggests that while the method serves as an effective and geometry-agnostic replacement for traditional cut-based selection, meaningful further gains in image quality will require either larger input representations or dedicated treatment of the phantom-scattered component.

We study imbalanced crowdsourcing with a focus on class-dependent annotator accuracy, a setting that, to the best of our knowledge, remains relatively underexplored despite its importance in real-world inspection systems where the labels of greatest operational importance are also the rarest ones. In this setting, annotators may be reliable on both classes, unreliable on both classes, majority-class specialists, or minority-class specialists. Existing models only partially address this problem: they either capture class-dependent errors but ignore item difficulty, or they model item difficulty without capturing class-dependent errors. To fill this gap for imbalanced datasets in crowdsourcing, we introduce a generative aggregation model combining item difficulty with class-dependent annotator competence. The model allows both annotator abilities and item difficulties to vary across classes. We then revisit Condorcet's Jury Theorem in the class-imbalanced setting. We also show that majority voting asymptotically preserves the underlying class proportion. We evaluate our model on $33$ real-world crowdsourcing datasets, covering multiclass tasks such as images and text, as well as two large-scale regimes: large-scale annotation datasets, with many annotations per item, and large-scale item datasets, with a large number of annotated instances. Across these diverse settings, our model consistently achieves the highest minority recall while remaining competitive in balanced accuracy, making it particularly relevant when rare-label recovery is the primary objective.

Imbalanced regression problems arise when the target variable has an asymmetric distribution, resulting in underrepresented value ranges in the dataset. Traditional approaches for identifying rare instances rely on a relevance function that assigns higher importance to specific regions of the target distribution. However, the effectiveness of imbalance-aware learning methods depends strongly on how relevance is defined. In more complex scenarios, such as bimodal distributions, traditional relevance functions struggle to capture rarity, as they assign fixed relevance values based solely on target values, thereby compromising the distinction between truly rare and normal instances. To address these limitations, this study proposes an Instance Hardness-based relevance function (InHaR) for identifying rare instances in regression problems. Unlike traditional relevance functions, the proposed approach incorporates learning difficulty, allowing rarity to be inferred not only from the target distribution but also from the difficulty of instances for the learning algorithm. This property is particularly important in bimodal scenarios, where rarity cannot be accurately inferred from target values alone. Experimental results demonstrate that the InHaR correctly identifies rare regions under bimodal distributions and, when used to guide resampling strategies such as Random Oversampling (RO) and Gaussian Noise (GN), leads to significant improvements in predictive performance compared to traditional relevance-based approaches. The code, dataset, and further details about the proposed method are publicly available at https://github.com/VitorLeitao/instance-hardness-Imbalanced-regression.

Rare concept generation focuses on synthesizing customized images conditioned on text prompts that describe objects with unusual attributes. Previous works failed to align the generated images with rare concepts, resulting in incorrect attribute rendering or inconsistent composition of concepts. Such failures, as we observed, stem from the inherent common knowledge bias in the training stage of diffusion models, where objects are strongly associated with their common attributes, making it difficult to break these associations when generating rare concepts. To address such challenges, in this paper, we propose a novel Counterfactual Inference-based Diffusion approach, dubbed CI-Diff. CI-Diff blocks the interference of the model's inherent common knowledge bias and utilizes the Natural Direct Effect to capture the independent influence of the text prompt of rare concepts on image generation so that decoupling the unusual attributes from the rare concepts. To this end, we reformulate the classifier-free guidance mechanism to highlight the atypical attributes. To the best of our knowledge, we are the first to introduce causal inference into the rare concept generation task. Extensive experiments on the RareBench benchmark validate the superiority of CI-Diff over state-of-the-art diffusion models. Our code can be accessed from https://github.com/200204jzy/CI-Diff.

Safety-critical perception systems must reliably detect rare object classes within small label spaces, a setting that long-tailed detection methods, designed for hundreds of classes with dense annotation, fundamentally do not address. Open-vocabulary detectors offer a promising alternative, as they use natural language queries at inference time, making prompt quality a first-class lever for detection performance. We exploit this property to address class imbalance: rather than retraining models or collecting additional annotations, we ask whether iteratively refining the language prompts, fed to frozen detectors, can improve minority class detection. We introduce C-GAP Caption-Guided Augmentation and Prompting), a detector-agnostic, annotation-free framework that operates in two phases. First, we establish a composite caption baseline combining per-image scene descriptions with class-quantity context, which we show outperforms scene-description only or class-quantity-only prompts across multiple open-vocabulary architectures and benchmarks. Second, an LLM iteratively refines each image's caption individually, with trials triaged into accept, tentative, or regenerate buckets based on minority-class AP@0.5 against a dynamic threshold derived from the composite baseline. Refinement terminates early once sufficient AP@0.5 gain is achieved. No detector weights are updated at any stage. Our experiments shows that C-GAP improves minority-class average precision up to 53% over the baselines. On COCO, C-GAP improves minority-class AP@0.5 by ~81% relative over the composite baseline (17.69 -> 32.09). Experiments confirm that composite captions provide the critical foundation for effective refinement: using scene-description-only or class-quantity-only prompts as the refinement starting point yields diminishing returns, supporting both stages of C-GAP as necessary contributions.

Autonomous systems under partial observability act on beliefs, not raw sensor events. QANTIS treats the quantum processor as a calibrated belief-update service in that loop: it receives a prior and an observation model, estimates the rare-event evidence term, and returns an ordinary posterior to a classical planner. This paper asks whether that service can be reused across a sequential Tiger POMDP horizon on present IBM Heron hardware without corrupting the planner-facing posterior. We answer with a controlled hardware case study rather than an end-to-end autonomy or wall-clock speedup claim. The study compares no amplification, guarded Grover amplification, and all-step fixed-point amplification on the same trajectory, then checks whether the returned posterior would change the downstream action. All-step FPAA preserves the Tiger posterior across the reported 8-step and 12-step primary runs, and the 20-step and 32-step controls remain inside the same operating band. In every reported decision check, the hardware posterior and the exact Bayes posterior select the same immediate action. Boundary-aware BIQAE stabilizes amplitude estimation near zero and near one, while a rare-event sweep maps the logical sample-complexity envelope for one-in-a-million evidence. The result is an operating envelope for a hardware-calibrated belief-update primitive, not a standalone hardware-advantage claim.

Rare events govern the safety profile of modern AI systems, yet their probabilities are extremely difficult to estimate: direct Monte Carlo requires prohibitive sample budgets. Subset Simulation (SS) addresses this by decomposing a rare-event probability into moderate conditional probabilities over nested intermediate events. However, classical SS requires a handcrafted scalar performance function whose sublevel sets define those events, demanding detailed knowledge of the failure geometry and limiting transfer to new domains. We propose SCARCE (Scalable Cascade Analysis for Rare-event Characterisation via Embeddings), which replaces the performance function with learned latent representations and geometric rulers that score proximity to failure regions. Adaptive thresholding constructs nested intermediate events directly from data. We formalise SCARCE through a non-negative supermartingale, yielding a high-probability upper envelope that remains valid under early stopping. On MNIST misclassification, where dense Monte Carlo provides ground truth, SCARCE achieves approximately 400--500 times lower mean absolute error than grid-searched traditional SS while eliminating systematic over-counting. We then study PAIR-style LLM jailbreaks under a fleet-level threat model with adversarial fraction $η$. On Llama-Guard-3-8B hidden states, a PCA-based ruler attains 2.6% mean relative error for $η\geq 10^{-3}$ against finite-sample references whose average bootstrap relative half-width is 27.9%, and transfers to a GCG-style corpus with 2.93% relative error after recalibration. A directional criterion $\mathrm{KL}(p_{\mathrm{good}}\,\|\,p_{\mathrm{bad}})$ ranks rulers consistently with estimation error (Spearman $ρ=0.83$).

In-the-wild expression recognition persistently fails on a few rare emotions, and the standard explanation is class imbalance. Through a controlled multi-task study on two benchmarks, we show the failure is instead a property of affect geometry: the rare classes are degenerate on Russell's circumplex, and that degeneracy bounds what any loss or cost can achieve. Our instrument is a circumplex-cost optimal-transport term that prices expression confusions by their valence-arousal distance. The term improves the official score and expression macro-F1, but a control most studies omit shows the gain is not geometric: a uniform cost, equivalent to a generic confidence penalty, matches it on Aff-Wild2 (p=0.625) and significantly exceeds it on AffectNet (+0.057 over base, larger than the circumplex). What the geometry reshapes is the structure of the errors, making them affectively nearer the truth on Aff-Wild2 (p=0.031 against the uniform control), an effect that does not survive on AffectNet, where a visual confound at the far corner of the circumplex overwhelms it. The rare-class failure, by contrast, is stable across both datasets we examine: the degenerate pairs (anger-fear on Aff-Wild2, anger-contempt on AffectNet) resist frequency-based interventions, the transport term, and an action-unit-augmented cost built specifically to separate them. We conclude that progress on rare expressions requires representations that distinguish the classes, not supervision that reprices their confusions, and we provide the controls and metrics needed to tell the two apart.

Rare events in time series are critical to model but hard to learn due to data scarcity. Current generative models struggle with extreme values. We observe that rare events leave distinct topological fingerprints - transitions in Betti numbers from point-cloud embeddings - that are more stable and discriminative than statistical moments. We introduce PHINN, a flow-matching framework using dynamic Betti curves as conditioning signals and a persistence landscape loss for homology consistency. It scales to multivariate data, includes a natural-language interface to set Betti targets, supports cross-domain meta-learning and few-shot generation, and provides certified adversarial robustness. On financial, epidemiological, and multi-modal benchmarks, PHINN outperforms statistical and diffusion baselines in topological fidelity (beta-RMSE down 41-63%, transition accuracy up 84%) and matches jump-diffusion models in tail coverage while exceeding them in shape fidelity. All results have 95% confidence intervals.

Principal Component Analysis (PCA) preserves variance, not the information needed to detect rare catastrophic events. This paper proves the existence of a {\it Risk Shadow}: PCA can retain over 99.9999 percent of total variance while completely erasing all signal about rare, high-impact failures. When this happens, even the best possible classifier operating on the PCA representation reduces to a constant predictor. The root cause is a fundamental mismatch between variance maximization and tail risk awareness. To break the shadow, we introduce Expectile PCA (ExPCA) and Tail-Preserving PCA (TP-PCA), two methods that reweight the data covariance toward high-impact events. We prove theoretically that ExPCA strictly outperforms PCA in retaining rare-event information, and we validate our claims on synthetic data and a real-world credit card fraud detection benchmark. Our results call for a fundamental rethinking of variance-based dimensionality reduction in high-stakes decisions.

Contextual anomaly detection aims to identify abnormal behavior conditional on context variables, but practical deployments often face highly imbalanced context distributions where rare regimes can be critical information. Under such frequency bias, context-conditioned models can produce unstable decisions and excessive false alarms in rare contexts. We propose Rarity-Gated Feature-wise Linear Modulation (RGFiLM), a rarity-aware conditioning module that combines feature-wise modulation (i.e., context-conditioned scaling and shifting of hidden features) with a gate controlled by a data-driven rarity score. The rarity score is estimated from the empirical distribution of context variables and regulates how strongly context modulates intermediate representations: the gate becomes more decisive under rare contexts while remaining conservative under frequent contexts. We evaluate RGFiLM on maritime trajectory anomaly detection using AIS motion sequences with ERA5 environmental context in an environment-sensitive detour scenario. When instantiated in a sequential anomaly scoring pipeline, RGFiLM achieves the best mean F1--False Positive Rate (FPR) trade-off among the compared context-agnostic and context-conditioned methods. These results suggest that explicitly accounting for context rarity is an effective approach for reducing false alarms in context-sensitive anomaly detection.

Pedestrian Attribute Recognition (PAR) is critical for video surveillance, enabling forensic search and re-identification systems. Extreme class imbalance remains a fundamental obstacle when merging PETA and PA-100K into a 109,000-image composite corpus, where minority attributes have positive sample fractions below 1%. This causes standard BCE optimization to suppress rare traits, a phenomenon we term the majority negative class cheating trap. We present a systematic ablation of Multi-Label Focal Loss hyperparameters (alpha and gamma) on a ResNet-18 backbone. A calibrated configuration (alpha=0.50, gamma=2.0) achieves a Macro F1-score of 62.32%, matching BCE baseline while preserving superior hard-example mining and convergence dynamics. Our approach uses pure loss-function engineering with zero computational overhead for edge deployment. We identify the Sparsity Wall, a hard boundary where positive sample fractions below 0.1% make global loss reweighting ineffective, requiring instance-level intervention.

Single-Molecule Force Spectroscopy (SMFS) provides unprecedented insights into biomolecular mechanics, yet the high-throughput generation of force-extension trajectories creates a severe data curation bottleneck. Identifying rare molecular unbinding events within thousands of noise-dominated curves traditionally relies on tedious, non-scalable manual auditing. Here, we present a system-agnostic, interpretable deep learning framework tailored to overcome extreme class imbalance in automated SMFS triage. Utilizing 1D-to-2D rasterized geometric matrices, we deployed a modified ResNet18 architecture governed by an asymmetric Focal Loss objective function. We evaluated this framework on the complex mechanical unfolding pathways of the R. champanellensis cellulosome. Under hyper-imbalanced test conditions where the target interaction constituted only 1.34% of the dataset (13 true events out of 970 traces), the model achieved an overall accuracy of 0.9196 and a remarkable True Positive Rate (Recall) of 0.9231. By implementing an empirically calibrated dual-threshold triage system, the pipeline automatically discarded 880 unambiguous background noise traces , reducing the manual curation workload by over 90% while safely preserving high-value rare data. Finally, Gradient-weighted Class Activation Mapping (Grad-CAM) visually validated that the network's decisions are firmly anchored in the relevant geometric features of the force curves, specifically localizing on the structural unbinding regions, effectively mitigating 'black-box' skepticism. Built for free cloud-based execution, this open-source tool democratizes scalable, highly precise molecular discovery across the biophysics community.

Financial crashes, cascading failures in infrastructure, and critical errors in AI systems are frequently triggered by events that occur with extremely small probability. Efficiently discovering and sampling events with probability below a threshold is therefore of critical interest. Yet this task is highly non-trivial using existing classical or quantum methods. Being rare, such events require an immense sampling overhead to collect sufficient data samples. Moreover, because the rare events are not known in advance, they cannot be flagged for amplification using standard techniques. Here, we introduce a quantum algorithm for rare-event discovery and sampling without first learning which events are rare. The algorithm achieves the optimal quantum scaling with the rarity threshold. We further demonstrate that this can achieve a quadratic speedup for heavy-tailed systems whose tail has nonvanishing total mass, and translates into a robust polynomial speedup for stationary stochastic processes, with the exponent determined by its entropy-rate structure.

Path sampling methods generate ensembles of reactive trajectories connecting metastable states, but extracting mechanistic insight from these data remains nontrivial. We introduce Flux Matching, a framework that learns two complementary objects directly from reactive trajectory data: a current velocity $u(z)$, whose streamlines trace the dominant reaction pathways, and a scalar potential $h(z)$, obtained from a weighted Helmholtz-Hodge decomposition of the reactive current, that serves as a data-driven reaction coordinate. Both minimize quadratic functionals over the reactive path ensemble, analogous to the flow matching loss in generative modeling, and require no knowledge of the underlying dynamics or stationary distribution. Unlike committor-based methods, $u$ and $h$ remain well-defined under projection onto non-Markovian collective variables, and their level sets in turn provide adaptive interfaces for improved sampling with enhanced sampling methods. Flux Matching is validated through the generation of current velocity trajectories and rate constant calculations on molecular systems.

Active learning is now standard practice in labeling ecological data, enabling ecologists to quickly process large volumes of field data to understand and monitor natural environments. Current practices evaluate active learning inductively, estimating predictive performance on a held-out test set. We argue that this evaluation is misaligned with most ecological tasks, where the goal is to transductively label an entire pool of data as efficiently as possible. We demonstrate that ignoring the human-in-the-loop underestimates the importance of continuing to label, particularly for classes in the long tail which may be of disproportionate ecological importance (rare species, uncommon behaviors, etc.). Our analysis shows that, for this long tail, the transductive objective shifts importance from prediction to discovery: the true challenge becomes finding "needles in the haystack," examples of rare classes that are embedded within dense regions of abundant classes in the latent geometry, which we quantify with a novel metric of sampling difficulty. Finally, to translate these insights to practical ecological workflows, we propose a conservative hybrid stopping criterion inspired by ecological rarefaction curves, and show that combining predictive performance with discovery criteria reduces premature stopping on long-tailed pools, improving rare-class recovery when discovery, not classification, is the limiting factor.

Estimating the causal effect of time-varying treatments on survival outcomes in large observational studies is computationally demanding, particularly when outcomes are rare. While g-formula-based methods such as the iterative conditional expectation (ICE) estimator provide a principled framework for longitudinal causal inference, they become computationally expensive, especially when bootstrap-based variance estimation is required. In addition, outcome rarity at each time point induces severe class imbalance, leading to instability and convergence issues in logistic regression and related models. To address these challenges, we propose a principled subsampling and reweighting strategy for longitudinal survival data that can be applied to a range of existing causal effect estimators in this setting, including the ICE estimator. The proposed method substantially reduces computational burden while preserving consistency and improving estimation stability in rare-outcome settings. We evaluate the method through simulations and validate it using a large-scale EHR cohort study on social and behavioral determinants of health (SBDH) and suicide risk, demonstrating its effectiveness for modeling rare outcomes in longitudinal data.

We study linear contextual bandits under rare parameter updates: the learner may incorporate reward feedback into its parameter estimate only at a small number of update times, while still observing contexts online and selecting actions sequentially. This viewpoint clarifies a practical distinction that is often blurred in the literature: many "strictly batched" methods additionally restrict within-interval context adaptivity, meaning that the action rule inside an interval cannot depend on the sequence of realized contexts/actions in that interval (beyond the current round's context). For linear contextual bandits, we propose two practical algorithms with only $O(\log\log T)$ parameter updates. Our first algorithm BLCE-G attains minimax-optimal regret (up to polylogarithmic factors in $T$) simultaneously in both the small-$K$ and large-$K$ regimes under a static schedule. Our second algorithm BLCE removes the near G-optimal design step -- a dominant computational bottleneck in prior strictly batched static-grid methods -- yet preserves minimax-optimal regret and achieves the lowest known runtime complexity among optimal algorithms. We further extend these rare-update and computational principles to generalized linear contextual bandits. Overall, our results yield statistically optimal algorithms under $O(\log\log T)$ parameter updates that are also computationally efficient in practice.

Building on recent formalizations of root cause analysis for rare events (``outliers'') in structural equation models, we propose a formal definition of a causal pathway and discuss its testable implications. We identify conditions under which these implications depend only on a causal abstraction defined by the pathway of rare events, rather than on the full causal graph of the underlying system. Accordingly, we introduce an abstraction of causal structure to pathways of rare events that bridges simple verbal causal explanations and detailed causal modeling.

Generative models have a persistent limitation: their tendency to memorize training data can create legal liabilities and erode creative diversity. Understanding which samples are memorized in whole or in part, and under what conditions, therefore remains an important open problem. Here we answer the question "Are atypical or rare samples memorized first?" in the negative. We train diffusion models on strings generated according to the production rules of the Random Hierarchy Model (RHM), and find that samples composed of common substrings are preferentially memorized. This holds true even if the training data consists of entirely unique samples, indicating that deduplication at the data point level does not provide a meaningful privacy guarantee. Correspondingly we predict, then observe, delayed memorization for fat-tailed datasets (i.e., those with more atypical samples). This effect is amplified when fat-tails are introduced into high-level production rules. These together suggest that dataset diversity, particularly at higher levels of abstraction, plays an important role in staving off memorization. Finally, we identify an intermediate regime of partial memorization in which common substrings are learned first and subsequently overproduced during generation. If training is stopped in this regime, models will exhibit the reversion-to-the-mean blandness often derided as "slop".

We investigate how internal representations emerge across hierarchical processing systems by introducing a neuroscience-inspired framework for analyzing deep spiking neural networks (SNN) through the lens of functional connectivity. Drawing on concepts from systems neuroscience and information theory, we form the first-order functionally-connected (1FC) group of a neuron based on its statistically significant pairwise correlations with neurons from the previous layer of a trained SNN architecture. We then track its response properties during inference under various conditions. Our analysis shows that several principles of functional connectivity previously observed in biological cortex are preserved in spiking ResNet architectures. These 1FC ensembles display interesting properties: their aggregate cofiring reliably predicts downstream neuronal responses through a robust, ReLU-like input-output relationship, whose gain scales systematically with ensemble size. Reliable encoding of the presented class emerges only during high 1FC cofiring events, which themselves occur infrequently, indicating that informative representations are concentrated in rare but highly coordinated activity patterns. Under uniform random noise or adversarial perturbations, these response profiles are disrupted, particularly in early and intermediate layers. This enables a targeted high-resolution interrogation at specific nodes and pathways. We showed that the functional connectivity structure is shaped by learning and this structure breaks under weight permutation. These establish 1FC ensembles as a functionally meaningful substrate for input encoding and information transfer, with potential implications in designing targeted fine-grained diagnostics on the information flow.

Class imbalance is a fundamental challenge in medical image segmentation, where frequent classes typically dominate training at the expense of rare classes. Loss-based approaches mitigate imbalance by reweighting the per-pixel loss within the batch, while sampling strategies control which images enter the batch. Yet neither explicitly controls which classes appear within the batch, leaving rare-class exposure only partially rebalanced. In this work, we adopt episodic sampling from few-shot learning to promote class-balanced batch construction in a fully supervised setting. We decouple episodic sampling from its conventional metric-learning context and evaluate it in body composition segmentation in CT. We compare episodic sampling against random and weighted sampling on nine muscle and adipose tissues, derived from 210 scans of the public SAROS dataset. Training is performed under full- and low-data regimes, with additional comparisons under matched training iteration budgets. Under full-data training, all three strategies performed comparably (mean Dice 0.882 for episodic, 0.878 for random and weighted). Under low-data training, episodic sampling outperformed random and weighted (0.787 vs. 0.758 and 0.762), driven by a 12-fold difference in training iterations. Under matched training budgets, random and weighted overfit earlier, while episodic improved for approximately three times more iterations before plateauing. Our findings identify the training iteration budget as under-recognized confound in sampling strategies, motivating iteration-aware evaluation protocols for small datasets. Furthermore, the residual advantage of episodic sampling is consistent with an implicit regularization effect of class-balanced batches, offering a low-cost, model-agnostic strategy for class-imbalanced medical image segmentation. Code is available at https://github.com/iasonsky/episodic-sampling.

Cardiovascular disease remains the leading cause of death worldwide, and early detection of arrhythmias through continuous ECG monitoring on wearable devices can prevent life-threatening events. Federated Learning (FL) enables privacy-preserving collaborative training by keeping raw ECG data on device, yet standard FL incurs prohibitive communication overhead and standard deep learning models cannot fit on ultra-low-power microcontrollers. We propose Family-Grouped Hierarchical Federated Learning (Family-FL), a three-tier architecture that uses the family as a natural privacy boundary for intra-family aggregation before global synchronization. We further design a hardware-constrained Tiny CNN-LSTM architecture with only 669 parameters, INT8-quantized to occupy merely 4.65KB Flash and 2.95KB RAM, meeting the constraints of STC32G12K128-class microcontrollers. Experiments on the MIT-BIH Arrhythmia Database (mean of 5 independent runs with different seeds) demonstrate that Family-FL reduces communication volume by 76.7% compared to FedAvg while maintaining comparable accuracy. Family-FL-Tiny achieves 91.9 +/- 1.2% accuracy with macro-F1 of 0.483 +/- 0.031, reducing total communication to 0.31% of FedAvg. The model achieves reliable ventricular arrhythmia detection (per-class F1 = 0.80), the most clinically critical abnormality for home-based preliminary screening. These results demonstrate the technical feasibility of privacy-preserving federated learning on ultra-resource-constrained microcontrollers through simulation-based evaluation. We honestly discuss limitations: no hardware deployment, single-dataset validation (MIT-BIH, 47 subjects), reduced rare-class sensitivity, and absence of formal differential privacy guarantees.

Class imbalance is a persistent challenge in visual recognition, particularly in safety-critical domains where collecting positive examples is expensive and rare events are inherently underrepresented. We propose a lightweight synthetic data augmentation pipeline that fine-tunes a LoRA adapter on as few as 20-50 real images of a rare class and uses a pretrained diffusion model to generate synthetic samples for training. We systematically vary the synthetic-to-real ratio and evaluate the approach across two structurally different domains: chest X-ray pathology classification (NIH ChestX-ray14) and industrial surface crack detection (Magnetic Tile Defect dataset). All evaluations are performed on held-out sets of real images only. Across both domains, synthetic augmentation consistently improves rare-class recall and F1 compared to training with real data alone. Performance improves with moderate synthetic augmentation and shows diminishing returns as the synthetic ratio increases. These results suggest that LoRA-adapted diffusion models provide a simple and scalable mechanism for augmenting rare classes, enabling effective learning in data-scarce scenarios across heterogeneous visual domains.

Digital personas powered by Large Language Models (LLMs) are increasingly proposed as substitutes for human survey respondents, yet it remains unclear when they can reliably approximate human survey findings. We answer this question using the LISS panel, constructing personas from respondents' background variables and pre-2023 survey histories, then testing them against the same respondents' held-out post-cutoff answers. Across four persona architectures, three LLMs, and two prediction tasks, we assess performance at the question, respondent, distributional, equity, and clustering levels. Digital personas improve alignment with human response distributions, especially in domains tied to stable attributes and values, but remain limited for individual prediction and fail to recover multivariate respondent structure. Retrieval-augmented architectures provide the clearest gains, but performance depends more on human response structure than on model choice: personas perform best for low-variability questions and common respondent patterns, and worst for subjective, heterogeneous, or rare responses. Our results provide practical guidance on when digital personas could be appropriate for survey research and when human validation remains necessary.

Recent advances in uncertainty quantification for time series forecasting show that conformal prediction can provide reliable prediction intervals, yet standard conformal methods are often inefficient under temporal dependence, drift, and heterogeneous error behavior. Existing methods typically either update miscoverage rates over time or learn unconstrained calibration weights, without explicitly separating two central sources of nonstationarity: smoothly drifting error distributions and co-existing distinct error regimes. We introduce RareCP, a regime-aware retrieval method for adaptive conformal time series prediction. RareCP learns local calibration representations through a mixture of cosine-attention experts that each capture distinct error regimes, while a compact hypernetwork adapts the kernel parameters to track temporal drift. Given a new forecasting context, RareCP retrieves the top-k most relevant calibration examples, assigns similarity weights, and forms a weighted conformal quantile over their signed residuals, yielding asymmetric prediction intervals. The adaptive kernel is trained using a smooth interval score objective, with a parameter-space anchor to a lightweight teacher kernel to preserve stable local representations. On the GIFT-Eval benchmark, RareCP improves interval efficiency over recent conformal baselines and foundation model uncertainty estimates while maintaining empirical coverage. Ablations confirm that regime-specific experts, drift-adaptive kernels, sparse retrieval, and teacher anchoring each contribute to the final performance.

Contrastive Representation Learning (CRL) has achieved strong empirical success in multiple machine learning disciplines, yet its theoretical sample complexity remains poorly understood. Existing analyses usually assume that input tuples are identically and independently distributed, an assumption violated in most practical settings where contrastive tuples are constructed from a finite pool of labeled data, inducing dependencies among tuples. While one recent work analyzed this learning setting using U-Statistics to estimate the population risk, the techniques used therein require the risk of each class to concentrate uniformly, making excess risk bounds scale in the order of $ρ_{\min}^{-{1}/{2}}$ where $ρ_{\min}$ denotes the probability of the rarest class. Such a dependency can be overly pessimistic in the extreme multiclass settings where there are many tail classes which contribute minimally to the overall population risk. Our contributions are two-fold. Firstly, we improve upon the previous work and prove a bound with a sample complexity of the same order as the number of classes $R$, regardless of the distribution over classes. Furthermore, we formulate a different estimator that captures the concentration of the risk \textit{across classes}, enabling sharper bounds in extreme multi-class learning scenarios, especially where class distributions are long-tailed. Under mild assumptions on the class distributions, the resulting sample complexity is $\mathcal{O}(k)$ where $k$ is the number of samples per tuple.

Long-tailed class distributions are pervasive in multi-class medical datasets and pose significant challenges for deep learning models which typically underperform on tail classes with limited samples. This limitation is particularly problematic in medical applications, where rare classes often correspond to severe or high-risk diseases and therefore require high diagnostic accuracy. Existing solutions-including specialized architectures, rebalanced loss functions, and handcrafted data augmentation-offer only marginal improvements and struggle to scale due to their limited and largely deterministic variability. To address these challenges, we introduce a diffusion-model-driven synthetic data augmentation pipeline tailored for medical long-tailed classification. Our approach features a novel inpainting diffusion model combined with an Out-of-Distribution (OOD) post-selection mechanism to ensure diverse, realistic, and clinically meaningful synthetic samples. Evaluated on the ISIC2019 skin lesion classification dataset, one of the largest and most imbalanced medical imaging benchmarks, our method yields substantial improvements in overall performance, with particularly pronounced gains on tail classes with more than $28\%$ improvement on the class with the fewest samples. These results demonstrate the effectiveness of diffusion-based augmentation in mitigating long-tail imbalance and enhancing medical classification robustness.

Pretrial risk assessment tools are used on over one million U.S. defendants each year, yet their use for predicting rare violent re-offense faces a basic statistical barrier. We derive a universal precision bound -- the Likelihood Ratio Wall -- showing that when violent re-arrest rates are low (2-5%), achieving even a 50% hit rate among people labeled "high risk" (positive predictive value, or PPV) would require tools far more discriminative than current instruments appear to be. For rare outcomes, a tool can have respectable-looking performance metrics and still be wrong most of the time it flags someone as "high risk for violence." We show that post-hoc score recalibration cannot solve this problem because it does not improve the tool's underlying ability to separate true positives from false positives. We further prove a Surveillance Ceiling: when over-policing inflates recorded "risk factors" among those who would not re-offend, the maximum achievable precision is structurally lower for over-policed groups, even at equal offense rates. We translate these results into the Number Needed to Detain (how many people must be detained to prevent one violent offense), and propose that risk reports should communicate this uncertainty explicitly. Our findings suggest that for rare violent outcomes, debates about fairness metrics alone are incomplete: under current data regimes, the available features may not support high-confidence individualized detention decisions.

The most technologically consequential materials are often the rarest: they occupy narrow regions of chemical space, obey competing physical constraints, and appear only sparsely in existing databases. High-kappa dielectrics, high-Tc superconductors, and ferromagnetic insulators are to name a few. This scarcity fundamentally limits today's data-driven materials discovery, where machine-learning models excel at interpolation but struggle to generate genuinely new candidates. Here, we introduce DielecMIND, an artificial intelligence framework that reframes materials discovery as a reasoning-driven exploration instead of a database-screening problem. Using high-kappa dielectrics as a data-scarce and technologically stringent test case, DielecMIND combines large-language-model hypothesis generation for the first time with physics validated first-principles calculation to navigate chemical space beyond known compounds. Prior to our work, only 14 experimentally or computationally validated materials with kappa > 150 were known. Our framework discovers and validates 5 new such compounds, expanding this rare-materials class by a remarkable = 35% in a single study. Among them, we find that Ba2TiHfO6 exhibits a dielectric constant of 637, minimal loss at low optical frequencies, and stability up to 800 K. Beyond dielectrics, this work demonstrates a new paradigm for artificial-intelligence-guided discovery: one that generates a small number of physically grounded, experimentally plausible candidates yet measurably expands sparsely populated functional materials spaces. Thus, DielecMIND points toward a general strategy for discovering rare, high-impact functional materials where data scarcity has long constrained progress.

Detecting fraudulent credit card transactions remains a significant challenge, due to the extreme class imbalance in real-world data and the often subtle patterns that separate fraud from legitimate activity. Existing research commonly attempts to address this by generating synthetic samples for the minority class using approaches such as GANs, VAEs (Variational Autoencoders), or hybrid generative models. However, these techniques, particularly when applied only to minority-class data, tend to result in overconfident classifiers and poor latent cluster separation, ultimately limiting real-world detection performance. In this study, we propose the Causal Prototype Attention Classifier (CPAC), an interpretable architecture that promotes class-aware clustering and improved latent space structure through prototype-based attention mechanisms and we couple it with the encoder of a Variational Autoencoder-Generative Adversarial Network (VAE-GAN) in order to achieve improved latent cluster separation moving beyond post-hoc sample augmentation. We compared CPAC-augmented models to traditional oversamplers, such as SMOTE, as well as to state-of-the-art generative models, both with and without CPAC-based latent classifiers. Our results show that classifier-guided latent shaping with CPAC delivers superior performance, achieving an F1-score of 93.74% and recall of 92.85%, along with improved latent cluster separation. Further ablation studies and visualizations provide deeper insight into the benefits and limitations of classifier-driven representation learning for fraud detection. The codebase for this work can be found at the following link: https://github.com/claudiunderthehood/VAEGAN-CPAC.git.

Data imbalance persists as a pervasive challenge in regression tasks, introducing bias in model performance and undermining predictive reliability. This is particularly detrimental in applications aimed at predicting rare events that fall outside of the domain of the bulk of the training data. In this study, we review the current state-of-the-art regarding sampling-based methods and cost-sensitive learning. Additionally, we propose novel approaches to mitigate model bias. To better assess the importance of data, we introduce the density-distance and density-ratio relevance functions, which effectively integrate empirical frequency of data with domain-specific preferences, offering enhanced interpretability for end-users. Furthermore, we present advanced mitigation techniques (cSMOGN and crbSMOGN), which build upon and improve existing sampling methods. In a quantitative evaluation, we benchmark state-of-the-art methods on 10 synthetic and 42 real-world datasets, using neural networks, XGBoosting trees and Random Forest models. Our analysis shows that while most strategies improve performance on rare samples, they degrade it on frequent ones. The trade-off becomes larger the more the performance on rare samples is increased. However, to reduce this effect we demonstrate that constructing an ensemble of models -- one trained with imbalance mitigation and another without -- can be used. The key findings underscore the superior performance of our novel crbSMOGN sampling technique with the density-ratio relevance function for neural networks, outperforming state-of-the-art methods.

Many high-stakes screening tasks require predicting rare outcomes from unstructured text, where errors are costly and decisions must be auditable. We introduce Random Rule Forest (RRF), an interpretable ensemble that uses a large language model (LLM) not as an end-to-end predictor but as a generator of simple YES/NO questions. Each question acts as a weak learner, and their responses are combined by a plain unit-weight vote into an auditable ``green-flags'' scorecard: enough independent positive signals indicate a higher chance of success. We argue this deliberate simplicity is a robust default when positives are scarce and learned weights are hard to estimate. We evaluate RRF in two low-base-rate domains. On early-stage startup screening from founder profiles, RRF produces a transparent scorecard whose precision is several times the base rate (with light expert input raising it further) and, unlike direct prompting, its operating point can be controlled directly. On an established Phase~I clinical-trial benchmark, RRF outperforms published baselines on the threshold-independent metrics PR-AUC and ROC-AUC. Together these show that LLMs can serve as auditable feature generators for high-stakes text-based decisions, combining transparency with competitive predictive performance.

Imbalanced labels can cause frequent samples to dominate AI-based quantitative remote sensing, degrading rare-event retrieval. In rain-rate retrieval based on satellite infrared brightness temperatures, this imbalance leads to systematic underestimation of rare high-intensity rainfall. In this study, Hurdle-Retrieval Model Imbalanced Learning (RMIL) is proposed. Following a divide-and-conquer strategy, Hurdle-RMIL separates zero inflation from the long-tailed distribution of positive rain. A hurdle model handles zero inflation, whereas RMIL exploits invariance under fixed observation conditions of the rainfall-to-satellite forward process to derive a Bayes-based transformation linking conditional distributions under naturally long-tailed and hypothetical balanced rainfall. This transformation enables the balanced-distribution model to be learned from natural samples without constructing a balanced dataset. Comparisons with conventional learning, classification-regression modeling, cost-sensitive learning, and generative learning using test data from multiple regions in China show that Hurdle-RMIL mitigates systematic underestimation and improves detection of rare high-intensity and extreme rainfall without markedly degrading lower-threshold accuracy. At 0.1-10 mm per hour, its root mean square error remains close to those of the best baselines, and it yields the highest equitable threat score (ETS) at most evaluated thresholds, with its advantage becoming more pronounced at high thresholds. At 30 mm per hour, its ETS is 0.051 versus 0.015 for the best baseline, and its mean error is -25.41 mm per hour versus -28.98 mm per hour. Case studies further show improved representations of rainfall intensity and spatial extent, demonstrating that Hurdle-RMIL effectively addresses rainfall-distribution imbalance and improves the retrieval of rare high-intensity rainfall.