Decision Thresholds

We study an optimal intervention problem for linear threshold models. This is a popular class of dynamical network systems whereby a number of agents, identified with the nodes of a graph, strategically change their binary action (0 or 1) according to a threshold rule. Specifically, an agent adopts action 1 if and only if the fraction of its neighbors in the interaction graph that do so is greater than or equal to a prescribed threshold. Assuming that a planner can modify the agents' thresholds at a cost equal to the aggregate threshold increase, we study the minimum intervention cost needed to ensure global convergence to the all-1 configuration. Our main contribution is the introduction of a new graph-theoretic quantity, called oriented path number, that is the minimum number of disjoint paths needed to cover the graph that can be oriented to form a directed acyclic graph. When thresholds are all equal to 1/2, the optimal cost is shown to coincide with the oriented path number, whereas, in the general case, it turns out to be the main ingredient of a bound on the optimal intervention cost.

Long-text image--text congruence scoring is increasingly important for vision-language systems that must evaluate whether detailed textual descriptions match visual content. However, raw similarity scores from dual-encoder models are difficult to interpret as calibrated congruence measures, especially under the modality gap between image and text embeddings. This paper proposes Congruency Score (CS), a lightweight calibration layer that maps image--text similarity evidence into a bounded score. Using DOCCI and Urban1k, we evaluate four frozen vision-language backbones and show that observed reductions in post-projection centroid distance do not uniformly improve image--text retrieval performance. Human-grounded evaluations on DOCCI further reveal a trade-off: direct post-hoc calibration preserves high association with human judgments, whereas selected projection-based configurations can reduce threshold-relevant slope and intercept distortions at the cost of retrieval performance and association strength. These results establish long-text image--text congruence scoring as a calibrated score-estimation problem, where retrieval performance, human association, and threshold calibration must be evaluated as distinct objectives. CS provides a lightweight way to expose and operationalize this separation.

Using food package images to monitor sodium and salt content against South Africa's R214 sodium limits is challenging when screening decisions require product identity, nutrition facts panel evidence, reporting basis, and category-specific thresholds. This study presents a conservative image-based workflow that combines region detection, optical character recognition (OCR), product identity and sodium evidence extraction, R214 category assignment, deterministic threshold comparison, and independent vision language model comparison. The evaluation used 442 packaged food products and 3 929 full package images from a real-world South African food packaging dataset. A YOLO26s small detector generated 4 195 region crops, and strict post-processing produced one sodium evidence row per product. The integrated workflow produced 290 OUTSIDE R214 SCOPE, 139 REVIEW, seven SCREEN-PASS, and six SCREEN-FAIL outcomes. The independent Qwen2.5-VL 7B vision language model workflow produced 387 OUTSIDE R214 SCOPE, 31 REVIEW, twenty SCREEN-PASS, and four SCREEN-FAIL outcomes. The workflows agreed on exact R214 category assignment for 415 of 442 products (93.9%) and on whether the assigned category was within R214 scope for 416 of 442 products (94.1%). Final screening outcome agreement was 307 out of 442 products, or 69.5%. Manual verification on 60 products showed lower strict outcome agreement than regulated status agreement, while all manual INSUFFICIENT DATA cases were kept out of SCREEN-PASS and SCREEN-FAIL by both automated workflows. The findings show that conservative image-based screening can organise package evidence, identify clear cases, and assign uncertain cases to REVIEW rather than forcing SCREEN-PASS or SCREEN-FAIL decisions.

Prequential adaptation of frozen tabular foundation models under temporal drift, with each label revealed only after prediction, helps some deployments and harms others, yet current practice does not predict which. We study the sources and limits of these gains. A diagnostic anatomy attributes gains to four recurring mechanisms under a streaming protocol that removes three optimistic biases and quantifies a fourth. Within an agnostic total-variation drift class, the target conditional is only partially identified: its identified-set diameter, the \emph{wall}, is irreducible from unlabeled data uniformly in sample size. A second, orthogonal $L^2$ projection wall quantifies what the frozen representation cannot express. Two canonical mechanism priors collapse the first wall. Under stated nuisance-rate conditions, the wall can be estimated from labeled historical windows at a $\sqrt N$ rate above the margin threshold $\gamma^\star=d_0/(2\alpha_s)$. At $\gamma=0$, the conditional lower-bound program depends on an open affinity estimate; the positive-margin lower branch also remains open. Semi-synthetic data illustrate the finite-sample mechanism with calibrated exponents. Stream-level proxies on eight industrial streams fall on the difficult side under a stated roughness bound, while the equality case $\gamma=\gamma^\star$ remains unresolved.

Objective Prediction models are commonly trained using objectives such as Bernoulli negative log-likelihood (NLL), although downstream clinical decisions may depend on specific risk thresholds. We introduce Smooth Net Benefit ($\sigma$NB), a differentiable approximation of Net Benefit designed to align model training with threshold-specific clinical utility. Materials and Methods We evaluated $\sigma$NB as a training objective for logistic regression, generalized additive models (GAMs), and XGBoost with three Hessian implementations. Experiments used the Framingham cardiovascular risk dataset and 44 TabZilla datasets comprising 72 dataset-threshold combinations. Results $\sigma$NB training did not consistently improve Net Benefit in Framingham. Across the TabZilla benchmark, mean standardized Net Benefit for logistic regression increased from 0.5669 with NLL to 0.5765 with $\sigma$NB (mean difference 0.0096, 95% CI -0.0001 to 0.0193). For GAMs, mean standardized Net Benefit decreased from 0.5921 to 0.5625 (mean difference -0.0296, 95% CI -0.0721 to 0.0129). For XGBoost, NLL achieved 0.6745 compared with 0.6723--0.6735 across $\sigma$NB implementations. In logistic regression, $\sigma$NB gains were positively associated with the performance advantage of XGBoost over NLL-trained logistic regression. Discussion The effect of $\sigma$NB was context dependent, with modest gains concentrated in logistic regression and little benefit for more flexible model classes. This suggests that decision-focused optimization may be most useful when limited model flexibility leaves greater scope for improvement. Conclusion Our results do not support $\sigma$NB as a general replacement for NLL training, but support further investigation of decision-focused objectives in settings where conventional likelihood-based training may not adequately capture decision-relevant structure.

Pseudo-labeling is a strong paradigm for semi-supervised medical image segmentation, yet its effectiveness is highly sensitive to confidence thresholding. In abdominal multi-organ segmentation, a fixed global threshold is particularly suboptimal because organ classes differ substantially in size, appearance, and learning difficulty. In this work, we propose ThreshGuide, a class-aware threshold adaptation framework that uses labeled data to guide pseudo-label selection on unlabeled data. Built upon a standard teacher-student architecture, the teacher model evaluates labeled samples during training to estimate class-aware threshold targets by maximizing an error-aware F\b{eta} criterion that balances precision and coverage. These targets are then smoothed with an exponential moving average (EMA) and used to filter unlabeled voxels in a class-dependent manner. Experiments on FLARE2022 and AMOS2022 show that ThreshGuide performs competitively overall, yielding clear improvements specifically on hard-to-learn organs.

Automated prediction of Enzyme Commission (EC) numbers plays a central role in functional annotation and computational drug discovery. However, standard multi-label machine learning pipelines frequently rely on default decision thresholds (t=0.50), assuming balanced prior distributions across target heads. In this study, we present a systematic empirical diagnostic of uncalibrated fixed decision boundaries operating under severe class imbalance across N = 14,096 annotated compounds categorized into six primary EC classes (EC1-EC6). Our results highlight a pronounced Accuracy Paradox: while the multi-label system achieves a deceivingly high mean accuracy of 77.16%, the macro F1-score (0.3976) and macro recall (0.3872) reveal severe predictive breakdown. Majority target classes suffer from hyper-sensitivity and over-prediction, whereas minority classes exhibit sharp recall decay, culminating in a total decision boundary collapse for EC6 (Recall = 0.00%) despite underlying discriminative power (ROC-AUC = 0.5857). Feature correlation analysis further reveals high linear redundancy among topological indices relative to fingerprint density metrics. Ultimately, this diagnostic study demonstrates that standard point predictions mask critical errors in bioinformatics workflows. We establish target-specific threshold optimization and post-hoc conformal calibration as essential, open-source post-processing safeguards for reliable applied machine learning and deep learning architectures.

The paper describes a replication experiment to assess "the distribution of editing procedures across micro and macro units as an indicator of the strain of text production". We investigate various pause thresholds to isolate Micro and Macro units and conclude that process-based units might be more suitable entity.

Restricted eigenvalue (RE) bounds govern stable recovery by norm-regularized estimators. For isotropic sub-Gaussian measurements, the benchmark sample size is $1+w(A)^2$, where $w(A)$ is the Gaussian width of the normalized descent cone. The COLT 2015 open-problem note (Banerjee et al., 2015) asked whether the same law follows for heavy-tailed designs from a uniform small-ball condition alone. We give an explicit and systematic negative answer to the general question as formulated there: the proposed law fails in its full dimension-free, arbitrary-set form, and the missing obstruction is simultaneous threshold occupancy. A constant-width polyhedral descent cone with fixed small-ball constants has zero empirical RE on every sample path up to half the ambient dimension. More generally, every finite range space admits exact threshold encoding in an arbitrarily narrow spherical cap and a lift to a full polyhedral descent-cone section. For every fixed threshold VC dimension $d$, as $β\downarrow0$, the sharp worst-case sample complexity is $Θ(β^{-1}[d\log(1/β)+\log(1/δ)])$. The separation persists under exact isotropy and all finite moments: on the same constant-width cone, Gaussian measurements succeed with $O(1+\log(1/δ))$ samples, whereas an isotropic heavy-tailed design fails pathwise for $n\lesssim\sqrt{p/\log p}$. Gaussian smoothing yields an everywhere-positive $C^\infty$ density while retaining arbitrarily poor RE. Under isotropy, a distribution-free fallback governed by affine dimension times squared enclosing radius is sharp on this family.

Large language models exhibit a modular internal organization that mirrors well-studied functional networks of the human brain, but how this organization forms during training is unknown: prior work has characterized finished models, not the formation process. We track formation step by step: we train a Pythia-410M model from scratch (two trajectories, bf16 and fp32) and run attribution patching at every step, alongside probes for gradient norms, effective updates, weight norms, and first-order loss decomposition across 14 tasks in four cognitive domains. Three findings. First, the modular map is pre-carved: before any learning, the dominant task pair already overlaps at ~3.6x the attribution substrate (a task-independent baseline), and its layer-0 concentration is an architecture-level constant on this model family. Second, the partition locks in through two sharp jumps whose amplitudes do not track the learning-rate schedule (the second reaching 20.4 sigma quiet-window / 6.2 sigma global), accompanied by gradient-level relative deprivation--winners receive 2.25->2.73x the loser's gradient supply, 9.5-11.5 standard deviations below a random control--that does not propagate to updates or weights. Third, deviation from the substrate appears only in the domain being learned, consistent with the hypothesis that modularity tracks learning. We close by separating the feature-level account we can defend from the mechanistic questions we cannot, and we pre-register the scale-threshold hypothesis behind our ongoing 2.8B experiments.

TRACE (Math & Lienhart, arXiv:2602.01135) reads causal graphs over event types out of a pretrained autoregressive sequence model by thresholding a per-position conditional-mutual-information estimate at a fixed tau. We independently replicate its headline synthetic result: with tau selected on a validation split, mean per-sequence F1 against exact interventional truth reaches 0.90-0.91 at vocabulary size 1000 (paper: 0.91) and 0.86-0.91 from 100 to 2000. First, the optimal threshold is pinned to the truth margin, not to any constant: at every size the errors at tau* straddle the delta = 0.05 margin defining ground truth (missed true edges lie just above it, accepted false ones just below), and the blind optimum lands near delta/2 times the estimator's calibration, confirmed out of sample at 5000. Second, at a single global threshold TRACE mostly recovers a direct, adjacent-influence graph: lag-1 true edges are recalled at 0.97-0.99, while true edges at lag 2 or more read orders of magnitude lower---the reading-scale price of randomizing mediating positions, which an exact test of direct causal effect requires when the truth is unknown. A per-lag threshold family recovers a third to a half of lag-2 truth; on lag-uniform data one validated threshold recalls every lag at 0.40-0.87, 8-26 pp below an atomic-intervention control at lags 3-6. Third, the default lag decay of the paper's synthetic benchmark concentrates about 85% of interventional truth at lag 1 and pushes the rest below the estimator's noise floor, so headline F1 there certifies lag-1 recovery only and conflates the benchmark's skew with the algorithm's own limit; a flatter decay separates the two. Fourth, F1 saturates from N = 2 particles at the selected threshold---a property of the threshold's margin over the noise floor, not of the estimator, which converges as N^(-1/2). We distill five practitioner rules.

We study finite-sample linear regression in the presence of varied and unknown label noise, focusing on the heteroskedastic and adaptive linear regression models. Heteroskedastic linear regression models settings where the labels are of varying quality. We receive $n$ pairs $(X_i,Y_i)$ with labels $Y_i=X_i^\topβ+\varepsilon_i$, where $\varepsilon_i\sim N(0,σ_i^2)$ and the variances are unknown to the estimator. One natural measurement of the difficulty of this problem is the number of samples $m$ for which $σ_i^2\le1$ (larger $m$ is easier). We obtain a polynomial-time estimator with rate $\tilde{O}((nd^3/m^4)^{1/6})$ when $m\gg d^{3/4}n^{1/4}$, as well as nearly-matching lower bounds. For $d=O(1)$, our estimator achieves error $o(1)$ when $m\gg n^{1/4}$, whereas $L_1$ regression and other traditional approaches require $m\gg n^{1/2}$. In adaptive linear regression, the errors are drawn i.i.d. from an unknown distribution $p$, and our goal is to design a generic estimator that performs nearly as well as the best custom estimator that knows $p$. We introduce a (computationally inefficient) adaptive estimator that, so long as $p$ is a mixture of $k$ symmetric log-concave densities, achieves error comparable with the optimal estimator that knows $p$ and has $\tildeΘ(n/k)$ samples. For $k=1$, we show that $L_q$ regression (with data-dependent $q$) gives a polynomial-time estimator. Finally, to study the computational limits of both problems, we introduce the planted linear regression problem, where $X_i\sim N(0,I_d)$, $m$ unknown samples are noiseless, and the rest have error $\varepsilon_i\sim N(0,1)$. We conjecture that recovering $β$ up to error $\ll\sqrt{d/n}$ (or exactly) may have an information-computation gap between $m=d+1$ and $m\sim d^{3/4}n^{1/4}$, as is suggested by our near-matching polynomial-time estimator and statistical query (SQ) lower bound.

We study a Restart POMDP (Partially Observable Markov Decision Process) on a general Borel state space, where the controller either lets the hidden state evolve unobserved or restarts the system and observes the new state. Exploiting a sufficient-statistic representation consisting of the last observed state and the elapsed time since restart, we reduce the problem to a fully observed MDP. Under a natural one-step cost deterioration condition, we prove that optimal policies have a threshold structure in the elapsed time for both the discounted and total undiscounted cost criteria. When the state space is partially ordered and the kernel is stochastically monotone, we further show that the optimal threshold is nonincreasing in the state. For the average cost criterion, under additional assumptions of geometric ergodicity and domination of the transient gain, we establish analogous threshold results via the vanishing discount approach, after showing the uniform boundedness of the optimal thresholds and relative value functions.

Systems often need to combine two numerical assessments of the same yes/no question. The appropriate formula depends on what the numbers represent and on how the sources are related. Averaging is correct when one of several alternative interpretations applies; multiplying odds is correct when probability reports are based on conditionally independent evidence and a common prior; and probabilities of alternative successful derivations require their dependence or shared evidence to be taken into account. We state the assumptions behind several common combination rules and derive the corresponding combined probabilities. Two groups of Monte Carlo experiments address different questions. First, controlled generating mechanisms verify that the derived rule recovers the correct probability in the situations for which its assumptions hold. Second, the same mechanisms measure the consequences of using a mismatched rule, using logarithmic score and threshold decisions with different costs. Distinct pooling rules can produce the same binary decision at threshold 1/2 while assigning substantially different probabilities, so binary accuracy alone can conceal important differences. We also give probabilistic interpretations of conflicting-evidence rules and show that, for overlapping derivations, retaining the identities of shared uncertain premises permits direct calculation of the probability that at least one derivation is available. Pairwise combination of proof probabilities loses information when there are three or more derivations.

Machine learning models achieve strong predictive accuracy for 90-day outcome prediction in acute ischaemic stroke, yet clinical adoption is limited by the misalignment of model explanations with clinicians' reasoning. Motivated by a clinician user study calling for clinical guideline-aligned cut-offs, we ask whether continuous predictors can be replaced by clinically informed categorical encodings without sacrificing performance. On a multi-centre European registry stratified into three treatment cohorts, we compare standard and fully categorised gradient-boosted models, the latter using stroke guideline-aligned, treatment-specific thresholds. The fully categorised models are statistically indistinguishable from their continuous counterparts in two of the treatment cohorts, with a significant drop in predictive accuracy in one cohort. Global feature importance rankings remain consistent, suggesting that discretising continuous predictors into guideline-based categories preserves the core hierarchy of prognostic factors across all treatment groups. Guideline-based categorisation is thus a viable design choice for stroke-outcome models.

Causal perception occurs when agents with competing Structural Causal Models (SCMs) of the same system infer different probability distributions, including the hypothetical distributions implied by each agent's SCM under the same set of interventions. It shapes how agents reason about the system and how they perceive its fairness. Causal perception is a promising probabilistic framework, but it has remained purely theoretical. This work provides the first implementation of the causal perception framework of Álvarez and Ruggieri (2025). We operationalize structural (agents disagree on the causal graph) and parametrical (agents agree on the causal graph but disagree on its weights) causal perception. We design algorithms for computing interventional and counterfactual distributions and propose suitable distance measures to quantify the disagreement. Using the German Credit dataset, we illustrate how causal perception affects accuracy and fairness in a multi-expert decision setting. We show that the perception verdict is sensitive to the choice of distance metric and threshold. We also show that causal perception changes fairness assessments and threshold-based decisions. Bias proves situated with respect to the agent's SCM, demonstrating that competing worldviews in fairness problems cannot be ignored.

Decoders of anesthetic state from cortical activity fail across drug classes, most notoriously ketamine, but reported accuracy cannot say whether the neural representation or only the decision threshold has failed; we separate the two in a controlled preparation with ground-truth labels. We decoded awake versus anesthetized from mouse electrocorticography (the 250-Hz-bandlimited local field potential, sampled at 1875 Hz) under leave-one-anesthetic-out evaluation across five mechanistically distinct anesthetics (isoflurane, dexmedetomidine, ketamine, propofol, and midazolam), comparing a spatially blind band-power decoder, covariance/Riemannian representations, and Riemannian domain adaptation, with all statistics at the session level and mouse-level cluster bootstrapping for the ketamine fold. The representation transfers: band-power ranks awake versus anesthetized at a session AUROC of at least 0.96 on every held-out drug, ketamine included (0.980, cluster confidence interval 0.821 to 1.000). The failure is confined to the threshold: across three representations the ketamine ranking is near-invariant while its balanced accuracy swings from chance to high, and a permutation test is significant for ranking (p = 0.0025) but not for fixed-threshold accuracy (p = 0.3795). Riemannian domain adaptation is net-negative. A causal, label-free threshold anchored to the subject's own pre-induction baseline fixes ketamine (balanced accuracy 0.50 to 0.85) and dominates domain adaptation. Because the ketamine test sessions come from three mice that also contribute training drugs, this is within-subject cross-drug transfer; we do not claim population-level transfer across subjects. In cross-drug state decoding the actionable failure is calibration, not representation.

On-policy distillation (OPD) provides dense teacher supervision along student-generated trajectories, but its online rollout process incurs substantial computational cost, particularly when a few long responses delay batch completion. Existing acceleration methods typically control rollout length using fixed budgets or absolute teacher--student agreement thresholds, which may not reflect learning progress across different models and training stages. We propose Adaptive FastOPD, a progress-aware strategy that expands the rollout horizon only when learning near the current boundary region has plateaued and the current horizon is sufficiently utilized. The former is determined from four teacher--student signals measured relative to their values upon entering each horizon, making expansion responsive to stage-specific progress rather than a predefined step interval or an absolute threshold on the raw agreement signals, while the latter prevents a small number of long responses from triggering increases in rollout cost. Across two teacher--student pairs, Adaptive FastOPD achieves the highest average performance while reducing training time by 49.1--71.2% relative to OPD 15K, and remains robust across a range of hyperparameter settings.

High-stakes decision systems in credit scoring, fraud detection, healthcare, and industrial safety require reliable uncertainty quantification under severe class imbalance and asymmetric error costs. Standard marginal conformal prediction (CP) provides valid overall coverage guarantees; however, we show that it severely under-covers rare, costly minority classes, with minority-class coverage dropping to as low as 0.5% on certain datasets. To characterize and address this limitation, we conduct a comprehensive benchmark comparing marginal CP, class-conditional (Mondrian) CP, and cost-controlled abstention mechanisms across 15 real-world imbalanced tabular datasets, 7 classification models, 3 probability calibration techniques, and 10 random seeds, resulting in 3,150 experimental runs. Our results show that Mondrian CP restores valid minority-class coverage, achieving an average minority-coverage improvement of 61.7 percentage points over marginal CP (p < 1e-80). Furthermore, combining Mondrian CP with cost-controlled abstention significantly reduces expected decision cost compared with standard decision boundaries, confidence-based rejectors, and risk-controlled rejectors under realistic human review budgets. We further quantify dataset-specific break-even thresholds at which deferring ambiguous instances to human experts becomes cost-effective. These findings provide practical guidance for deploying distribution-free, cost-aware uncertainty quantification in high-stakes decision support systems.

Reports on how sparsification, compression, and lottery tickets change model behavior have been mixed in the prior literature, with beneficial effects observed in some studies and adverse effects in others. Moreover, prior work has not considered actual deployment conditions, where decision logic is already fixed for the incumbent. To assess these mixed findings from a practical standpoint, we study the production-replacement question at the deployment level, namely whether an accuracy-matched lottery ticket or another sparse challenger can replace an incumbent dense model without reconfiguring downstream decision logic. We therefore audit a broad, protocol-specific panel of deployment-relevant behaviors spanning calibration, OOD response, class-level reliability, representations, and downstream policy decisions, and summarize clean-accuracy-excluded deviations with a behavioral-compatibility distance. Across extensive experiments, sparse candidates repeatedly recover dense-reference accuracy yet remain behaviorally different; in several study-band-matched settings, LTs also show lower corruption accuracy. In small-gap settings with fixed-threshold policy diagnostics, lottery-ticket replacement changes 7% to 10% of accept--review decisions. This churn creates precisely the burden that drop-in replacement is meant to avoid: reconfiguring and revalidating downstream decision logic. These findings establish the limits of clean-accuracy certification: Establishing compatibility with a fixed incumbent is distinct from attributing churn uniquely to sparsity or treating every measured deviation as harmful. Our theory explains the routing result: Even exact pointwise top-1 agreement cannot bound fixed-threshold decision changes, and small confidence shifts near the operating boundary can generate first-order routing churn.

In picture-based agricultural insurance for smallholder farmers, missed damage detections carry substantially higher cost than false alarms: a farmer who sustained real losses receives no payout, while unnecessary expert review is operationally costly but reversible. Standard multi-class classifiers optimize global accuracy but provide no mechanism to operationalize or control this asymmetric cost structure at inference time. We propose CascadeCropNet, a two-stage cascade architecture calibrated to satisfy a target recall constraint (Rec-Damaged >= 0.95) through threshold selection. A lightweight Sentinel model performs binary health triage; samples exceeding a calibrated damage probability threshold tau are escalated to a specialist Expert model for fine-grained diagnosis. This design provides explicit, deployment-time control over the safety-efficiency trade-off without retraining. Evaluated on the Eyes on the Ground dataset (23,804 images from Kenyan smallholder maize farms), the cascade achieves Rec-Damaged = 0.974 at tau = 0.5, reducing missed damage cases by up to 54% relative to a flat baseline. Under evaluation alignment, the representational gap reduces to +0.008 F1-macro, confirming the contribution is architectural rather than representational. Under input degradation, the system prioritizes escalation over confident misclassification, reflecting error containment through architectural isolation rather than intrinsic model robustness. These results demonstrate that cascade architectures can operationalize safety-oriented decision constraints through calibrated routing in settings where reliability matters more than aggregate accuracy. These properties depend on threshold calibration and deployment conditions and do not constitute guarantees under arbitrary distribution shift.

Security and privacy are primordial requirements for Federated Learning (FL), especially in fields such as healthcare and genomics where sensitive information has to be analyzed. Our FL framework is designed to address these challenges while proposing a modular, flexible and micro-service architecture. More precisely, it integrates an efficient gRPC communication layer and a Finite State Machine to ensure robust component synchronization and threat detection, while relying on a fault-tolerant secure aggregation protocol using a Threshold variant of the CKKS homomorphic cryptosystem. This allows blind model aggregation by an orchestration server, requiring a minimum of $t$-out-of-$N$ active clients for decryption while minimizing communication overhead thanks to both cryptographic and network protocols. We ensure IND-CPA-D security through noise flooding and mitigate the recent key-recovery attack on synchronized decryptors by renewing the collective key material at every round. We demonstrate the framework's effectiveness through diverse use cases, ranging from standard image recognition (EMNIST) to complex genomic classification including breast cancer subtyping on TCGA, evaluating system performance across different threshold values and model scales.

The recently deployed Entry/Exit System (EES) introduces large-scale biometric verification into European border control, requiring face recognition systems to operate at extremely low false match rates (FMR). While regulatory frameworks define performance targets at the EES Central System level, they do not specify how verification thresholds should be calibrated in practice at the Member State level. In operational settings, obtaining representative real-world data for calibration is often constrained by legal, logistical, and privacy limitations. In this work, we investigate the use of synthetic face data for threshold calibration in document-to-live verification scenarios relevant to border control systems. We analyze the alignment of genuine and impostor score distributions between synthetic and real datasets and evaluate the transferability of calibrated thresholds across domains, with a focus on low-FMR operating points. Our results show that synthetic data can approximate calibration behavior in controlled settings, but fails to reliably generalize to unconstrained conditions due to mismatches in score distribution tails. These discrepancies lead to significant degradation in recognition performance and increased vulnerability to morph-based attacks. We further demonstrate that calibration outcomes are highly dataset-dependent, even across synthetic datasets. Overall, our findings highlight that while synthetic data is useful for system development and preliminary calibration, our results indicate that reliable threshold selection in high-security deployments typically requires validation and adjustment using representative real-world data.

Active RAG systems decide when to retrieve external knowledge during generation, making them a budget-sensitive case of agentic RAG and self-adaptive retrieval. Yet evaluations often leave the operating point underspecified: two systems may both claim a 50% evidence-usage budget while realizing different held-out usage rates, so higher accuracy can reflect a looser budget rather than a better retrieval policy. We study budget-aware evaluation for Active RAG by recasting active retrieval as utility estimation, where retrieval is valuable only through its marginal correctness change over a no-retrieval answer. This view separates three questions that single-point evaluations conflate: whether trigger scores rank useful retrieval decisions, whether thresholds calibrated on past data meet future budgets, and how trigger-side computation changes deployment cost. We operationalize these questions with exact top-k utility frontiers, deployable threshold frontiers, conservative budget frontiers, harm audits, and cost decompositions. Across knowledge-intensive multi-hop QA datasets and open instruction models, retrieval harm is non-negligible, router rankings change across datasets and budgets, nominal thresholds can miss target usage, and simple uncertainty or retrieval-score baselines often rival learned utility routers. Budget-aware Active RAG evaluations should therefore report frontiers, realized usage, threshold-transfer error, harm rates, and cost decompositions alongside accuracy.

We study whether strictly positive marginal values restore the compatibility of envy-freeness up to one good (EF1) and Pareto optimality (PO) for indivisible goods. For two agents, we identify the exact threshold in the number of goods. Every instance with at most seven goods and strictly increasing valuations admits an allocation that is both EF1 and PO, without any submodularity assumption. In contrast, we construct an eight-good instance with normalized, integer-valued, strictly increasing, submodular valuations in which every EF1 allocation is strictly Pareto dominated. Thus, eight goods are necessary and sufficient for a two-agent counterexample. Finally, we strengthen the three-agent NP-hardness result of Chandramouleeswaran and Nimbhorkar (2026): deciding whether an EF1 and PO allocation exists remains NP-hard for normalized, integer-valued, monotone submodular valuations even when zero marginals are confined to eight fixed agent-good pairs, all involving a single agent.

For two decades, the standard remedy for class-imbalanced learning has been to fabricate synthetic minority examples, and the standard evidence of their validity has been a check that cannot fail: synthetic points are scored against the very data that generated them. We de-bias the check. Validity becomes a population quantity -- the probability that a synthetic point truly belongs to the minority class -- with a consistent estimator that scores synthetic points against withheld real data. Where held-out ground truth is available, the classical test underestimates true invalidity in 96-99% of method-by-imbalance-ratio cells, while the de-biased estimator tracks it closely. We prove validity is a property of the data, not the method: class overlap sets an invalidity floor no faithful generator escapes, making oversampling redundant where classes separate and invalid where they overlap. Across 91 methods, three classifiers, and datasets spanning medicine and finance -- including a generator engineered to pass the classical check -- none clears both bars: gains over the best trivial baseline are noise-thin (median below 0.01 F1, a decision threshold's reach), and most damage calibration. We release the audit as a pip-installable test and flip the burden of proof: synthetic minority data must now demonstrate, on the data at hand, both validity and information gain.

We characterize per-bit-position fault sensitivity in ML inference across 16 workloads -- spanning transformer-based models and attention-free CNNs -- and across three floating-point formats. Our central empirical finding is a sharp bit-sensitivity transition: flipping any of the least-significant fraction bits up to a data-type-specific threshold, Xsafe, degrades task metrics by less than 1% under deterministic single-bit stress tests. Sensitivity rises through the upper fraction bits and spikes at the exponent-mantissa boundary, where a single-bit flip causes catastrophic collapse. Because low-order bits are largely inconsequential while high-order and exponent bits are critical, uniform SECDED protection -- which guards every bit equally at 12.5% storage overhead -- is unnecessarily conservative. We derive per-data-type Xsafe floors (FP16: 6, BF16: 4, FP32: 15) and workload-aware tiers that widen the unprotected region for resilient model classes, raising ECC savings to 37.5-62.5% without retraining. Text-conditioned diffusion models dictate the conservative floor; vision encoders, NLU models, and resilient LLMs tolerate wider bypass regions. These floors and tiers drive an Unequal Error Protection (UEP) codec with per-cacheline data-type tags and a dual-partition SRAM architecture for ML accelerators. Validation across 870+ fault-injection runs confirms selective protection holds under contiguous 2- and 3-bit upsets. The codec reduces ECC area by 27.8% relative to uniform SECDED; dual-voltage operation of the non-critical partition lowers gross BF16 read energy by about 17%, with a roughly 4% dual-partition macro-area overhead.

Procuring supervised fine-tuning (SFT) data forces a buyer to decide, before any downstream training, whether a candidate corpus is worth acquiring. We present \sys{}, a statistics-first gating architecture that treats procurement as a cost-aware routing problem over three intrinsic quality axes -- diversity, utility, and redundancy. Cheap blind measurements are summarised into per-axis estimates with confidence intervals; a gate accepts a decision only when intervals are tight, sample sizes are adequate, and the axes agree, otherwise it escalates the case to an adjudicative debate between a buy-advocate and a reject-advocate judge, resolved by a presiding verdict. On a controlled benchmark of 12 datasets ($2{\times}3{\times}2$ grid over the three axes) with 5 seeds, the gate reaches 0.90 accuracy and 0.83 $F_1$ at $0.017 per unit, sitting between an always-verify baseline (0.75) and an oracle upper bound (0.98) while spending less than always-escalate ($0.020). We further report honest negative diagnostics of the debate path: a con-side win rate of 0.80 ($p\approx3{\times}10^{-6}$) and a 52% position-flip rate under advocate swapping expose negativity and positional biases that a naive LLM-judge would hide. We frame the injected-knob evaluation explicitly as a controlled synthetic benchmark for measurement fidelity and routing calibration, and delimit external validity as future work.

Conformal prediction certifies that a classifier's prediction sets cover the truth, and that certificate is marginal. Many recognition benchmarks build distribution shift into evaluation, placing disjoint conditions in the training and test splits. Under that shift the certificate stays reassuring while per class coverage fails silently: on a real cross subject skeleton benchmark marginal coverage holds near ninety percent while the worst class is covered about seventy percent and ten of sixty classes fall below eighty percent. This class specific undercoverage stays hidden behind a single reassuring marginal number. Once the shift acts jointly on covariates and labels, the target class conditional score law is unidentified, so no label free method is at once per class valid and efficient uniformly over target laws consistent with the observed source joint distribution and target covariate marginal. The per class labels needed to recover every class threshold to a given tolerance grow as the inverse square of that tolerance and the logarithm of the class count, with matching bounds for classwise threshold procedures. Pseudo labels do not shortcut it: the best prediction powered estimator gains at most a small constant factor where coverage collapses. Across three real shifts and an image corruption benchmark, source label calibration recovers much of the gap while marginal coverage holds, and stops once it breaks.

A randomized algorithm may terminate almost surely even though exceptional random tapes make it run forever. This paper studies the survival tail, the Kolmogorov complexity of one such tape, and the Hausdorff dimension of all of them. For each $s>0$ at which the powered repair matrices commute, the main theorem bounds $\sum_wP[w]^s$ over surviving prefixes $w$, uniformly over deterministic nonanticipating selectors. The case $s=1$ controls termination; the full family gives weak-source and dimension bounds. The source powers contain information absent even from the ordinary repair kernel and the complete stopping-time law. Under one common finite tape source, two overlapping disagreement-repair rules on a four-vertex path have the same ordinary kernels and the same stopping-time law for every selector, yet their nontermination dimensions can be arbitrarily close to zero and one. At one common source-power level, the same dominated tape source makes one rule run forever but gives the other an exponential stopping tail. The separation is caused by action labels that produce the same state transition and are therefore invisible at power one. For bounded-dependence $k$-SAT, conditional block min-entropy above the trace-growth threshold gives exponential termination, and the effective dimension of an individual infinite run is bounded by the trace growth induced by the clauses repaired infinitely often. Tree formulas asymptotically attain the maximum-degree dimension and global source bounds, while clique formulas attain the graph-specific one-step threshold in the stated regime. An exact backward likelihood identity complements these setwise results with tail and coding bounds for each run.

Frontier AI companies have published capability thresholds that differ substantially, making it difficult for third parties to verify whether a threshold has been crossed or to compare requirements across companies. Moreover, without common minimum thresholds, risk mitigation may be inconsistent, creating a potential race to the bottom in safety standards. We develop a methodology for deriving harmonized thresholds across three risk domains. For misuse risks (cyber and biological), we take expected harm as the key primitive and use an explicit risk-modeling approach that accounts for risk channels and model release conditions. For automated AI R&D, we base our proposed threshold on the observed rate of AI progress rather than expected harm. Our analysis expands upon prior work and highlights existing empirical gaps and limitations.

Moderation systems increasingly rely on external toxicity tools, but those tools are unreliable under code-mixing, transliteration, slang, and language mismatch. We study the \emph{conditional reliability} of toxicity priors in Indian multilingual and code-mixed short text: English toxicity, Indic abuse, and rule-based severity cues can be useful evidence, but only in some linguistic and abuse-severity contexts. We propose ToxGate, a trust-fusion head that conditions each auxiliary signal on the encoder representation before adding it to the prediction state. Across three short-text abuse datasets, four transformer encoders, and five seeds per setting, ToxGate improves over matched plain encoders in 10 of 12 in-domain settings and 7 of 8 transfer settings. The largest and most interpretable gains occur in high-risk moderation slices, including explicit slurs, violent threats, and cross-dataset transfer. The broader lesson is that moderation systems should treat external toxicity tools and priors as conditional evidence rather than fixed features or ground truth, in focused ablations, source-specific gating gives the strongest results in transfer, severe-abuse slices, and high-risk triage.

LEED v4.1 BD+C certification remains a document-intensive process that requires reviewers to read hundreds of pages of project evidence and apply credit-specific threshold logic by hand. This paper investigates whether small, locally deployed language models can perform meaningful screening of LEED documentation and how deterministic symbolic components should share that work. A neuro-symbolic pipeline is introduced that aligns project PDFs to LEED credit sections, retrieves evidence with credit-aware keyword signatures, verifies compliance with a locally hosted 4-billion-parameter language model, and applies a LEED-specific numeric checker to quantitative thresholds. Experiments on four university buildings (484 PDFs, 153 credit-level decisions) show that a 4-billion-parameter model (gemma3:4b) is the strongest text-only core verifier, achieving 67.3% accuracy and outperforming a larger 8-billion-parameter model (llama3.1:8b) in this task. The deterministic numeric checker corrects arithmetic errors on key quantitative credits, moving EA-p2 from 50% to 100% accuracy and improving several other credits when required values are reliably extracted. At the same time, the full neuro-symbolic configuration achieves 61.6% overall accuracy, trailing the best text-only baseline due to extraction failures and conservative behavior on qualitative categories. Systematic ablations show that adding low-resolution drawing images (150-300 dpi) consistently reduces accuracy, and that prompt effectiveness depends on the building's ground-truth PASS rate: rubric prompts perform best on documentation-rich projects, while chain-of-thought prompts perform best on documentation-lean projects. Within the specific scope of LEED v4.1 BD+C compliance verification over raw project documentation, this pipeline and its baselines provide an initial reproducible reference point for both accuracy and failure modes.

As frontier language models advance, policymakers and model developers need methods for assessing whether model access materially increases a non-expert actor's ability to plan high-consequence Chemical, Biological, Radiological, or Nuclear (CBRN) misuse relative to public tools alone. Existing CBRN evaluations differ in non-expert definitions, threat scope, baselines, scoring rubrics, and decision rules, making results difficult to compare across studies. We introduce a Threshold Exceedance Criteria (TEC) framework that decomposes an uplift study into independently executable components: determining non-expert participant eligibility, defining the CBRN threat scope for the study, and statistically estimating material uplift. We then operationalize the TEC framework in a large-scale empirical study using a design that determines two forms of uplift: generative (where a model assists plan creation from scratch) and revisionist (where a model assists refinement of an existing plan). The study produced attack plans across the CBRN domains, which we evaluated through subject-matter-expert review to estimate generative and revisionist uplift. Applying the framework, our empirical study revealed domain heterogeneity: under this controlled pre-release evaluation, model-assisted plans sometimes received expert-equivalent instructional ratings, but confirmed material uplift was limited to the radiological domain. These findings informed mitigation and deployment-governance decisions rather than characterizing deployed model behavior. We conclude with methodological lessons for future CBRN uplift evaluations, emphasizing prespecified criteria, explicit baselines, separation of generative and revisionist estimates, and careful distinction between preliminary screening signals and confirmed risk determinations.

We study the population gradient flow of an infinitely wide two-layer neural network learning a misspecified single-index model in high dimension. The two layers are optimized jointly, with a perturbative parameter tuning the relative training speed between the first and second layer. This setting was considered by Berthier, Montanari and Zhou in \cite{berthier2024learning}, who conjectured a hierarchical learning scenario with explicit timescales as the second layer is trained faster than the first. In this paper, we prove that the constant and linear components of the hidden link function are indeed recovered within the predicted timescales, at sharp explicit thresholds. We then analyze the onset of learning of the quadratic component and show that the components learned at earlier stages continue to influence the dynamics in an essential way. Our proof is based on quantitative approximation results for singularly perturbed flows evolving near a manifold defined by integral constraints. At a phenomenological level, we also show that the empirical measure of the weights displays singular behaviour when reaching the quadratic component of the hidden link, with a small fraction of neurons growing significantly while the remaining ones rearrange to preserve the components already learned.

Few-shot spheroid segmentation must adapt to new cell lines, microscopes, and illumination conditions from only a small set of annotated images. While foundation few-shot segmenters can be accurate, their large opaque backbones make it difficult to understand which visual cues drive success or failure. We study this question with HyperBank, a differentiable bank of classical image-processing operators combining Frangi vesselness, a Sauvola threshold pyramid, structure-tensor responses, gradient magnitude, and Laplacian-of-Gaussian filters. HyperBank is fitted on the annotated support images and evaluated on disjoint held-out images across three independently acquired spheroid datasets. We treat it not as a general replacement for foundation models, but as a compact, interpretable few-shot microscopy pipeline and an analytic-prior probe of which classical cues carry the few-shot signal. The results show that, adapted on the same few annotated support images, a compact bank of analytic priors is competitive with, and on small-cluster, contrast-driven data can outperform, much larger foundation models, while those models remain stronger on externally sourced, texture-dominated spheroids. Leave-one-family-out ablations indicate that the useful few-shot signal is distributed across operator families and strengthened by support-set-tuned morphology.

A model should refuse two different things: answers it would get wrong, and questions it should not answer at all, such as unanswerable ones or ones resting on a false premise. The usual recipe thresholds a single confidence score, which cannot tell these apart. Across five instruction-tuned models from three families (2B to 14B), we find they are separate axes. Ordinary answer-confidence tracks whether an answer is right but is nearly blind to whether the question is answerable; a linear probe on hidden states does the reverse. The blind spot does not shrink with scale. It is worst on naturally occurring false-premise questions (CREPE). There, answer-confidence, P(IK), P(True), and even asking the model outright whether a premise is false all stay near chance, while a hidden-state probe reaches 0.69 to 0.77 AUROC: the model represents a problem it will not report. This turns out to be fixable. Instructing a model to check premises backfires, because it then disputes sound and false premises alike (57% false challenges), unable to tell them apart; routing the same instruction with the probe roughly triples challenge precision. We turn the two axes into a calibrated policy that answers only when an answerability score and a correctness score each clear a separately certifies behave differently: the unanswerable-answer rate is controllable at every scale, while the wrong-answer rate is capped by model accuracy, so the guarantee tightens as threshold policy certifies both budgets at 0.75 coverage of correct answers, against 0.31 for a single threshold; at 14B it is the only policy that certifies at all.

In chest X-ray (CXR) classification, acceptable ranking performance can still leave rare-positive patients below threshold, especially within subgroups. We study this pre-deployment fairness problem as an audit question: after a long-tailed multi-label CXR model is converted from scores into decisions, who is missed? Across VinDr-CXR and MIMIC-CXR/CXR-LT, we use a diagnostic ladder to separate class-level long-tail losses, subgroup-aware weighting, group robustness, and threshold selection. On VinDr-CXR, group-tail weighting followed by tail-aware thresholding reduces tail FNR from 0.665 to 0.269, sex worst-group FNR from 0.705 to 0.157, and age worst-group FNR from 0.822 to 0.133, while macro-mAP increases from 0.611 to 0.635. On MIMIC-CXR/CXR-LT, the same score-to-threshold comparison reduces tail FNR from 0.866 to 0.741 and lowers worst-group FNR across sex, age, race, and insurance; residual missed-positive rates nevertheless remain high. Paired bootstrap contrasts on VinDr support the thresholded FNR reductions, and GroupDRO reference runs indicate that aggregate group robustness alone does not remove rare subgroup misses in this setting. The study supports a narrow audit claim: rare-label fairness in CXR depends jointly on the finding, subgroup, and operating threshold, not on label frequency or ranking metrics alone.

Activation functions are considered an essential primitive for neural nonlinearity, i.e., they enable neural networks to serve as universal approximators. In this paper, we show that this nonlinearity can also be achieved by input-conditioned threshold gating through branches as a universal primitive. We demonstrate that standard activations -- whether piecewise-linear (ReLU, PReLU, Hardtanh) or smooth (SiLU, Sigmoid, Tanh, GELU) -- are in fact instances of a single Threshold Gating (TG) primitive. For softmax, we show that it admits an exact TG conversion via its equivalent per-element Sigmoid form. We then validate these equivalences by converting pretrained networks across CNNs, transformer-based models, and recurrent architectures, preserving model performance without requiring retraining. Threshold Gating also enables training from scratch that goes beyond replacing existing activations, enabling gains in model compression, performance, and shorter training. We also propose a 'Minimal Branch Theorem' which relates the minimum number of required branches in our primitive to the trainability of general deep neural networks. In terms of hardware implementation, TG maps to a unified implementation in the case of analog in-memory systems, addressing the bottleneck of analog-to-digital and digital-to-analog converters (ADC/DAC) that is known to significantly impact power consumption and on-chip area.

Can a platform tell, before deployment, whether an open-weight checkpoint has had its refusal mechanism stripped? Runtime guards cannot: they score generations, not the artifact. We combine two cheap internal signals, a reference-anchored activation refusal-gap and a weight-recovery energy of the base-to-candidate weight difference, into a threshold-free checkpoint audit. The two are negatively correlated and label-complementary: the gap supplies refusal-specificity and the weight energy supplies recall. On a 273-checkpoint registry spanning Qwen, DeepSeek-distilled Qwen, Llama, and Gemma, their z-sum separates 57 public abliterations from 37 benign fine-tunes, merges, and instruction-tunes at AUROC 0.95, significantly above either signal alone (0.84, 0.90), and a Youden-calibrated threshold transfers to held-out families at balanced accuracy 0.89 (FPR 0.11), missing only 4 of 57. We then map two failures, in order of severity: a spoofed reference evades both axes with no training (ΔW=0, \r{ho}=1 by construction), and a white-box owner trains a checkpoint past the threshold while it stays guard-unsafe and coherent. The audit is effective triage, not tamper-proofing: it presumes an attested reference, and its claims are bounded by the registry we evaluate it on.

Multimodal CT-MRI registration is central to image-guided radiotherapy, surgical navigation, and diagnostic workflows, but most pipelines report only aggregate quality metrics without per-case reliability signals. We propose a reliability-aware framework that converts registration quality into Green/Yellow/Red risk categories using data-learned thresholds. CT images were registered to T1-weighted MRI using rigid and affine transformations on 90 paired slices from 18 patients across brain, abdominal, and neck anatomies. Reliability was assessed using Delta NMI, Delta SSIM, Dice overlap, registration stability, and inverse consistency error, combined into a single score R. Thresholds learned from training patients were applied unchanged to held-out test patients. Affine registration outperformed rigid registration on NMI and SSIM, yielding 44% Green classifications versus 33% for rigid. Reliability-filtered registrations improved the average alignment profile compared with unfiltered methods. Per-anatomy analysis showed substantial variation, with stronger reliability for abdominal registrations than brain registrations. Weight sensitivity analysis identified Dice overlap as the dominant reliability component. The proposed framework provides an interpretable quality-control layer for multimodal registration, while risk thresholds reflect statistical rather than clinical validation.

Two-sided marketplaces connect distinct user groups whose interests often conflict -- improving outcomes on one side could degrade the other side's experience. To address this challenge, we deploy an integrated framework for personalizing free-value thresholds -- a policy governing the scope of complimentary services for job listings -- across a two-sided job marketplace connecting millions of employers and job seekers. Our personalized policy delivers statistically significant and economically sizable lift in the target metric while respecting engagement guardrail constraints. Direct application of standard uplift methods proves insufficient here for two reasons. First, cross-side externalities demand multi-objective optimization: maximizing employer-side metrics risks harming job seeker engagement, with effects varying substantially across job segments. Second, marketplace interference necessitates cluster-level randomization, limiting us to few discrete treatment levels -- effectively a form of positivity violation that rules out methods designed for continuous treatments. We contribute an integrated framework with three components. Our ensemble-based hybrid ranking models target and guardrail metrics separately, cutting guardrail risk by over 10% for equivalent target gains compared to single-objective approaches. A treatment effect extrapolation method extends our estimates from limited experimental variation to untested policy levels, relying on monotonicity assumptions that we validate empirically. Finally, we present production deployment, where post-launch data confirms both extrapolation accuracy and guardrail compliance. Our deployed system demonstrates that principled methodology can enable meaningful personalization even when experiments are severely constrained and different objectives compete -- common conditions that characterize many real-world marketplaces.

This paper describes our submission to SemEval-2026 Task 9 on detecting multilingual, multicultural, and multievent online polarization. We address all three subtasks: binary polarization detection, polarization type classification, and manifestation identification for English and Swahili. Our approach leverages transformer-based models (RoBERTa-base for English, AfroXLMR-base for Swahili) with class-weighted loss functions to address severe label imbalance and per-label threshold tuning to optimize multi-label classification. On the test set, we achieve F1 macro scores of 0.7901 (English) and 0.7910 (Swahili) for Subtask 1, 0.4615 (English) and 0.4808 (Swahili) for Subtask 2 and 0.4791 (English) and 0.5830 (Swahili) for Subtask 3, which give competitive performance on the leaderboard, demonstrating the effectiveness of our methods for handling imbalanced multi-label polarization detection. Our error analysis reveals that models struggle with dehumanization detection and lack of empathy.

Reasoning models spend test-time compute unevenly across instances, and a growing family of early-exit rules -- confidence thresholds, entropy monitors, answer-stability checks, and learned stoppers -- promises to reclaim the waste. These rules, however, are evaluated under heterogeneous protocols that leave the deployment question unanswered: at a fixed tolerance for losing correct answers, which policy saves more compute, and does the saving survive probe overhead? We answer this question with a controlled study across 18 task-model settings spanning GSM8K, MATH-500, MMLU-Pro, AIME-90, and GPQA on Qwen3 and DeepSeek-R1-distilled models, using LearnStop, a hidden-state-free logistic stopper over prefix-observable features, as the learned policy instrument. Under matched lost-correct risk at $α$ = 0.15, with the scalar competitor selected on calibration data from confidence, entropy, confidence-leap, and run-stability exits, the answer forms three regimes. Learned stopping wins on all four primary Qwen3 free-form math settings (+3.2 to +21.2 pp additional total-token saving); calibrated scalar exits win on multiple-choice MMLU-Pro; and small hard benchmarks (AIME-90, GPQA) admit no certifiable aggressive policy at all. A trajectory decomposition predicts the regime: learning pays where answers oscillate and correctness evidence is spread across complementary signals, while a single confidence threshold suffices where most instances are already solved at the first checkpoint. Cost accounting sharpens the picture further -- the same policy that saves 32% of tokens under KV-cache forking costs 121% extra under black-box repeated prefilling. Together, these results replace the single-method race with a decision procedure for choosing a stopping rule from the trajectory structure and serving regime of the target workload.

The specification number $σ_n(f)$ of a Boolean threshold function $f$ on $n$ variables is the least number of points whose $f$-values determine $f$ uniquely among all threshold functions. Its essential points form the unique minimum such set. We develop Zuev's geometric interpretation: the threshold functions are the chambers of a central hyperplane arrangement in the $(n+1)$-dimensional space of weights and thresholds, and the essential points of a function correspond exactly to the facets of its chamber, so the specification number is the chamber's facet number. The lower bound $σ_n(f)\ge n+1$ becomes the fact that a pointed full-dimensional cone has at least $n+1$ facets, with equality for simplicial chambers. The average specification number $\overlineσ_n$ becomes an average facet count. We evaluate this average exactly via the resonance arrangement and bound it through a theorem of Fukuda, Tamura, and Tokuyama, obtaining $\overlineσ_n\le 2n$; hence $\overlineσ_n=Θ(n)$. This settles a question of Gutekunst, Mészáros, and Petersen. The method also extends to polynomial threshold functions. The same geometry links threshold functions with a threshold zonotope, whose vertices are modified Chow vectors. Its one-skeleton is the one-inclusion graph, and a vertex's degree is the specification number of that function. Finally, we treat the operations of Lozin et al. on functions of minimum specification number. Adding a variable and extending on a variable both take the product of a chamber closure with a half-line, preserving simpliciality. For the symmetric-variables extension we give an exact thresholdness criterion and show that minimum specification number is preserved whenever the extension is a threshold function. We also resolve a question they pose concerning a fourth operation.

In recent work it has been shown that colluding AI agents can use steganographic methods to exchange malicious information. Whether a transformer can implement steganographic methods depends on what cryptographic functions it can implement, since a transformer that can implement a cryptographic function within its layers has source-free randomness access. Despite existing circuit-complexity results, no prior work maps specific cryptographic constructions to transformer architectures. As Merrill et al. have shown that saturated transformers can be seen as threshold circuits, we first generate threshold circuits for three different cryptographic constructions (Keccak functions, Merkle--Damgard constructions and Merkle Trees) and then map these circuits to different transformer architectures. We derive verified scaling laws for the width and depth of the circuits which implement each cryptographic construction and propose two different mappings: no-attention mapping, tokens-as-gates mapping. Beyond its security implications, this work contributes to by establishing a methodology for deriving structural guarantees on transformer computational capacity. Specifically, we derive constructive upper bounds on what a transformer of a given depth and width could plausibly compute, providing a principled foundation for capability evaluations of transformer-based AI systems.

Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions. Such cost functions can have a multitude of local optima and yet, gradient-based optimization appears to converge to near-global optima. Within a simple supervised learning setting, we develop a precise picture of which parts of the empirical risk landscape are accessible by polynomial-time algorithms. We are given i.i.d. pairs $\{(\boldsymbol{x}_i,y_i):\; 1 \le i\le n\}$ with $\boldsymbol{x}_i\in \mathbb{R}^d$ standard Gaussian feature vectors, and $y_i\in\mathbb{R}$ response variables that depend on $\boldsymbol{x}_i$ through their projections on an unknown $k$-dimensional subspace. We use empirical risk minimization to learn a model that depends on an $m$-dimensional projection of the data (e.g., an $m$-neurons neural network). We propose an incremental approximate message passing (IAMP) algorithm and precisely characterize the training error it achieves, as well as the relation between test and training error, in the high dimensional asymptotics $n,d\to\infty$, with $n/d\toα\in (0, +\infty)$. Based on earlier work in related models, we expect that the performance achieved by our algorithm is optimal among polynomial-time algorithms.

Variational Monte Carlo (VMC) is a central algorithm in electronic structure theory and has gained renewed importance through modern neural-network ansätze such as FermiNet. At its core, VMC seeks ground states by minimizing the Rayleigh quotient by stochastic optimization. In this work, we show that the resulting stochastic optimization problem is intrinsically governed by the nodal geometry of the underlying wave function. More precisely, we establish that properties of the nodal set determine the integrability of the local energy and gradient estimators that drive VMC. For broad and practically relevant ansatz classes, including Slater-Jastrow wave functions with variable-exponent Slater-type orbitals, we prove that these estimators are generically heavy-tailed and fail to admit higher moments. At the same time, for general analytic ansätze, we prove weak moment bounds for the relevant estimators and identify precise low-moment regimes, showing how generic and degenerate nodal structures lead to different integrability thresholds. Building on this analysis, we introduce a new robust variant of VMC $\unicode{x2013}$ coined PS-Clip-VMC $\unicode{x2013}$ which is based on clipping both the local energy and the gradient random variable. We prove that PS-Clip-VMC converges both in expectation and with high probability in the weak moment regime of VMC. Preliminary experiments for training FermiNet on Atoms with up to 18 electrons suggest that PS-Clip-VMC is significantly more robust than standard methods.

Respiratory acoustic foundation models (FMs) are benchmarked exclusively on smartphone recordings, yet clinical deployment increasingly targets body-coupled (BC) wearables whose sensors attenuate high-frequency content through tissue and bone, leaving FM reliability uncharacterised. We introduce BCoughBench, evaluating five FMs (OPERA-CT/CE/GT, HeAR, M2D+Resp) on nine classification tasks (AUROC, sensitivity at 95% specificity, Expected Calibration Error) and three age regression tasks (MAE vs. a mean-predictor baseline) across five EBEN-simulated BC sensor conditions on five labeled cough datasets. Mean AUROC declines from 0.785 (smartphone) to 0.689-0.723, degrading most under temple vibration pickup ($Δ$ = -0.096) and least under the soft in-ear ($Δ$ = -0.062). No FM meets the clinical sensitivity threshold (Se@Sp95 $\geq$ 0.20) on most disease tasks under any BC sensor. Sex classification on the CIDRZ cohort collapses (AUROC 0.954 to 0.596-0.628, $Δ$ = -0.341) while COVID detection is nearly unaffected ($Δ$ = -0.004). Age regression is robust, improving under the forehead accelerometer on CoughVID (MAE 9.61 to 8.97 yr); HeAR leads on regression and demographic tasks, M2D+Resp on disease and characteristic tasks. BCoughBench provides a reproducible framework for FM evaluation under wearable conditions.

The minimum variance distortionless response (MVDR) beamformer is widely used for multichannel speech enhancement due to strong noise suppression while preserving target signals. In practice, its performance is sensitive to microphone self-noise and array mismatches. Existing approaches typically rely on fixed, manually tuned WNG thresholds or diagonal loading, leading to suboptimal performance under unknown or time-varying acoustic conditions. This paper proposes a data-driven MVDR framework that adaptively estimates the WNG constraint using a deep neural network. The network jointly predicts a time-frequency noise mask for covariance estimation and a frequency-dependent WNG threshold, enabling dynamic robustness-directivity control. A differentiable robust MVDR layer is integrated into the framework, allowing end-to-end optimization. Experiments demonstrate consistent improvements in speech quality and intelligibility over conventional fixed-WNG MVDR methods.

This paper studies the expressive power of ASPIC$^+$ argumentation frameworks with uncertain preference profiles by comparing them with several abstract formalisms with uncertain defeats. Most of our results are negative (and some of them are theoretically unexpected). We also conjecture a positive, non-trivial threshold for the expressivity of uncertain preferences, and prove some essential preliminary steps toward the confirmation of this conjecture.

Speech deepfake countermeasures (CMs) are compared almost exclusively by equal error rate (EER), a metric computed at an oracle threshold chosen on the labeled test set. Deployed CMs enjoy no such oracle: a threshold must be fixed in advance and applied to unlabeled target data. We audit this gap with a frozen state-of-the-art SSL-AASIST detector trained on ASVspoof 2019 LA. While its in-domain EER is 0.21%, transferring its LA-calibrated threshold to the In-the-Wild corpus yields a half total error rate (HTER) of 39.5%, with 78.7% of bona fide speech rejected, even though the In-the-Wild EER (11.2%) appears moderate. We then test whether popular unlabeled test-time corrections close this gap, and first prove a simple proposition: any strictly increasing score transform, including z-norm, temperature/shift calibration, and embedding mean alignment under a frozen linear head, cannot change EER. An audit of seven corrections on In-the-Wild and ASVspoof 2021 DF confirms the proposition empirically and exposes two further failure modes: AS-norm with an unlabeled target cohort collapses (EER 11.2% to 60.2%), and pseudo-label calibration that reduces HTER by 38% relative on In-the-Wild degenerates to 50% HTER on DF21, whose spoof prior is 96%. No audited correction reduces EER by more than 1% relative. We recommend reporting HTER at a transferred threshold alongside EER.

Singular learning theory characterises the complexity of a deep network through the geometry of its loss singularities. The local learning coefficient (LLC), the standard estimator of Watanabe's real log canonical threshold (RLCT, $λ$), reads this geometry as an integrated Bayesian scalar through SGLD, which needs per-task calibration and $10^4$-$10^6$ forward-backward passes per checkpoint. We introduce Dead-Direction Signatures (DDS), a family of cheap closed-form spectral readings of singular structure: each reads a network's activation matrix or per-sample-gradient Fisher-Gram at a chosen layer, replacing the SGLD posterior chain with spectral linear algebra. The readings rest on a dead-direction framework that predicts a structural correlation between activation- and Fisher-side spectra at any singular minimum, and a rank-multiplicative volume identity that single-eigenvalue monitors cannot produce: the active-volume $\log\det^{+}(G)$ slope counts the dead directions, tracking the rank-deficit $r$ across $r \in \{1,2,3,4\}$ (slope ratios $2.0, 3.1, 4.0$ at $r{=}2,3,4$ against the predicted $2,3,4$), where the smallest eigenvalue is rank-blind. On reduced-rank regression with closed-form $λ$, calibrated LLC recovers $λ$ at $99\%$ mean and the DDS observables rank-track it at the framework-predicted sign; on a non-linear modular-addition transformer DDS separates $d_{\mathrm{model}}$ across eighteen orders of magnitude where calibrated LLC at the protocol budget is rank-flat. Complementary to LLC's integrated posterior reading, DDS gives a directional, layer-local handle on a network's dead directions, read in closed form from its activation and gradient spectra.

Large language model (LLM) systems increasingly use uncertainty signals to allocate limited computation across verification, test-time scaling, tool execution, and other selective-compute decisions. Such policies rely on a \emph{global signal comparability assumption}: equal scores should carry comparable decision value across inputs. Using budgeted verification as a controlled diagnostic setting, we identify a failure mode of this assumption: uncertainty quality is heteroskedastic across cost strata, with some regions exhibiting near-random discriminability despite concentrating many errors. Under an explicit local model, we characterize the resulting distortion of global allocation and show that its upper bound scales with cross-stratum signal-quality dispersion. We separate weak signals, optimization instability, and structural heterogeneity through a controlled intervention hierarchy: Threshold, MP-Adapt, MP-Strat, and a deliberately simple cost-stratified thresholding intervention (CST). Across MBPP and MATH using Qwen3-8B, LLaMA3-8B, and GPT-4o-mini, global online adaptation yields inconsistent gains over static thresholding; MP-Strat partially recovers performance, while CST improves hit rate by up to 17 percentage points in strongly heterogeneous settings without gradient updates. These results identify structural heterogeneity, rather than optimizer weakness alone, as the primary bottleneck in the observed settings. More broadly, misaligned feedback structure cannot always be repaired by stronger optimization.

We ask a structural question: given unreliable elementary problem-solvers, what organizations of them solve hard problems reliably, and what are the limits? We develop a $decomposition~algebra$: elementary solvers are morphisms in a stochastic category, and four combinators (sequential composition, parallel ensembling, verification gating, and recursive reduction) generate the space of compound solvers. We equip this algebra with two homomorphisms, a $reliability$ valuation into the ordered monoid $([0,1],\le)$ and a $cost$ valuation into a commutative semiring, and we derive the composition laws that govern how reliability flows through structure. Our central results are (i) a $verification~odds~law$ (the result that names this report), showing that a verification gate multiplies the odds of correctness by the verifier's likelihood ratio $Λ$, so that $k$ conditionally independent gates yield geometric amplification; (ii) a $reliability~amplification~theorem$, giving target reliability $1-δ$ at $O(\log 1/δ)$ verification depth whenever $Λ>1$; and (iii) a $threshold~dichotomy$: above the critical parameters reliability can be driven arbitrarily close to one at logarithmic cost, while at or below them no amplification is possible. We then show that $self-organization$ is the least fixed point of a monotone improvement operator on the complete lattice of strategies, and that this fixed point equalizes marginal log-odds gain per unit cost. Finally, we prove matching limits: an information ceiling bounds per-gate amplification by a divergence quantity; shared error causes create a strictly positive voting floor, so diversity is $necessary$ for unbounded amplification. Reliability, in short, is neither free nor magical: it is bought with independent information, arranged by composition, and bounded by the verifier.

This study presents a statistical and machine learning framework for characterizing a hydrogen-based multi-energy system (H-MES) using one year of high-resolution operational data. Statistical analysis revealed a binary operation driven by renewable surplus, with solar irradiance explaining 45.7% of rank-based variance in hydrogen production, a large effect by conventional standards. Only high-irradiance periods triggered meaningful electrolyzer engagement, while electricity demand exerted a weaker inverse suppression effect ($ε^2 = 0.126$). Multiple regression confirmed electrolyzer power as the dominant linear predictor, with a synergistic solar-wind interaction. Notably, Random Forest analysis ranked wind output first in predictive importance despite its weak bivariate correlation (r = 0.167), revealing non-linear dynamics invisible to parametric methods. A sequence model exploited strong 24-hour autocorrelation (r = 0.845) for operational forecasting, while a reinforcement learning agent optimized hydrogen revenue dispatch. The core contribution is demonstrating that statistical and machine learning approaches are complementary for H-MES modeling and control.

The integration of artificial intelligence into human decision-making environments has introduced a previously undertheorized cost: the gradual surrender of human autonomy in exchange for access to information and computational assistance. Building on the Human Identity and Autonomy Gap (HIAG) framework, this paper advances a theoretical model of autonomy surrender as a measurable, cumulative process driven by cognitive bandwidth depletion. The model proposes three interacting mechanisms: the silent cost of AI assistance, in which autonomy is transferred incrementally and without awareness; the surrender threshold, beyond which reclaiming autonomous function becomes cognitively and psychologically difficult; and the recovery mechanism, which establishes the design obligation and the ethical responsibility accompanying deliberate human re-assumption of control. The paper argues that human re-entry into the decision loop is not a passive option but an active cognitive event requiring intentional bandwidth restoration. The design of AI systems must incorporate structured re-entry pathways, here termed recovery mechanisms, that preserve human agency while appropriately distributing responsibility. The model further predicts a terminal state, here termed preference inversion, in which functional dependence on AI assistance is experienced not as a deficit but as a preference, transforming the restoration of autonomy from a design problem into a cultural and political one. Implications are drawn for AI system design, governance frameworks, and human factors research.

Machine learning is increasingly used in critical domains, where both predictions and their associated confidence levels influence important decisions. To enhance transparency in such scenarios, it is important to understand why a model is confident or uncertain about its predictions. Recent logic-based approaches provide abductive explanations, minimal subsets of features sufficient to preserve the predicted class, with correctness guarantees. However, these methods focus solely on classification behavior and may produce explanations that cover instances with low predictive confidence. In this work, we introduce the concept of Minimum Confidence Threshold (MCT), which quantifies the weakest confidence guarantee provided by an abductive explanation. Building upon this concept, we propose confidence-aware abductive explanations, which preserve not only the predicted class but also a user-specified confidence guarantee. We formulate MCT computation as an optimization problem and introduce an algorithm for generating minimal explanations that satisfy a desired confidence threshold. We evaluate the proposed framework on boosted trees for binary classification, although the approach is applicable to other machine learning models that provide confidence scores. Experimental results show that traditional abductive explanations often provide substantially weaker confidence guarantees than the confidence associated with the explained instance itself. In contrast, confidence-aware explanations consistently improve the minimum confidence guaranteed by an explanation while requiring only a modest increase in explanation length. These properties make the proposed approach particularly suitable for applications where both predictive correctness and confidence are essential for trustworthy decision making.

We establish the first sharp thresholds for low-degree polynomial tests in planted-vs-planted settings, where the goal is to determine with vanishing error which of two structured planted mechanisms generated the observed data. We prove matching low-degree upper and lower bounds for counting communities in the planted submatrix and planted dense subgraph models. The resulting testing threshold coincides, down to the sharp constant, with the known low-degree recovery threshold. In contrast, the task of weak testing, where the goal is to outperform random guessing, does not have a sharp threshold but rather a smooth transition, which we identify. To prove our results, we develop a framework for planted-vs-planted testing that builds on a latent-variable expansion originating in low-degree recovery and employs new methods to identify and prune non-signal contributions.

Hard constraints are usually treated as terminal vetoes: once a candidate violates a requirement, the learned rule rejects it and any repair is handled outside the decision semantics. This misses a common deployed regime in which the system already knows a finite menu of modifications, such as adding a ticket option, changing a configuration, or requesting an available service upgrade. Existing constraint-learning, soft-relaxation, and recourse methods address nearby problems, but they do not learn whether an option should be repaired before being vetoed. We introduce Repair-Augmented Constraint Learning (RACL), a contextual decision framework that lifts known repair operators into the classifier semantics. A candidate is accepted when an affordable repair makes it feasible and preferred enough; otherwise the system returns a structured rejection credit and, when applicable, a repair plan. This repair-before-veto view strictly generalizes no-repair HASSLE-style semantics, reveals an irreducible false-veto gap for terminal-veto rules, separates binary-label non-identifiability from decision-rule learnability, and gives capacity and calibration bounds for the observed-feasibility shared-weight setting. Across controlled and DB1B-derived benchmarks, RACL recovers the intended credit and repair structure. On the hardest raw-data-derived tier, validation-selected RACL reduces false vetoes to 10/4039 (FVR 0.0025), versus about 1064/4039 for the strongest repair-search black-box baseline, while making the FVR/EDR trade-off explicit.