Daily Papers

Serial verification gates are a core reliability primitive in LLM harnesses: a candidate answer is returned only if k verifier calls all accept it. Under conditionally independent gates, the recent Odds Law (arXiv:2606.15712) shows that posterior log-odds grow linearly in k, so failure decays exponentially, and states that "a tight theory of partially correlated verifier cascades remains open." This note gives a minimal such theory. Modeling the per-instance false-accept rate on the generator's own errors as a latent variable αsim G (de Finetti), the exact cascade posterior is ell_k = ell_0 - ln m_k, with m_k the k-th moment of G. Then: (i) ell_k is concave in k for every non-degenerate G -- the Odds Law is its tangent at the first gate and an upper bound; (ii) for Beta(a,b) latents, failure decays polynomially, 1-r_k asymp k^{-b}, with correlation parameter ρ_v = 1/(a+b+1); (iii) a blind-spot atom of mass 1-π at α=1 caps the evidence extractable from any number of gates at -ln(1-π) nats, so reliability saturates below 1; (iv) letting the true-accept rate also vary (βsim H) yields a trichotomy -- gates eventually always help, plateau, or actively harm -- decided by the upper-tail exponents of G and H, with closed-form crossover k^dagger. The mechanism is survivorship: errors surviving gates are the high-α ones. The theory is measurable: R repeated verdicts per instance identify the first R moments of G, so two verdicts identify ρ_v; beta-binomial likelihood and NPMLE recover the reliability curve and the ill-posed ceiling. In synthetic tests, independence-based extrapolation underestimates failure by 20x at k=5 and ~3000x at k=10; the correlated fit at R=8 tracks held-out depths. The practical lever is decorrelation -- changing model family, modality, or evidence source -- not adding gates.

Self-Distillation Fine-Tuning (SDFT) enables a language model to act as its own teacher: by conditioning on a demonstration, the model produces an implicit reward via pointwise mutual information, which guides on-policy learning without external supervision. However, SDFT operates at training time: it requires gradient updates and access to expert demonstrations, making it inapplicable at inference. We propose test-time self-distillation, a decoding-time method that extracts a steering signal from the self-distillation framework without any parameter updates, reward models, or training data. Our key insight is that counterfactual contexts, i.e. fixed textual templates that hypothetically prime the model for excellent versus poor reasoning, can substitute for the demonstration. The log-odds ratio of a candidate answer under these two counterfactual conditions defines a new reward signal. We derive the optimal KL-regularized policy under this reward, which takes the form of a Gibbs reweighting of the base distribution. Crucially, this reweighting is global: it cannot be decomposed into independent per-token operations without ignoring future trajectory quality. We therefore approximate the target distribution via beam search. Experiments on mathematical reasoning (MATH500), code generation (HumanEval), and graduate-level science QA (GPQA) across multiple model scales show that test-time self-distillation improves over standard sampling, low temperature, beam search and power sampling baselines on average, demonstrating that the self-distillation principle can be operationalized at inference time.

On-policy distillation (OPD) transfers teacher knowledge on student-generated trajectories, but efficient sampled objectives reduce the teacher distribution to scalar credit on individual tokens. Such credit indicates whether a token should gain or lose probability, yet leaves the corresponding redistribution unspecified. We recast OPD as teacher-guided probability transport and propose RouteOPD (Routed On-Policy Distillation), which decomposes local teacher--student disagreement into student-excess sources and teacher-deficit destinations and couples them into explicit transport pairs. RouteOPD optimizes pairwise log-odds toward jointly realizable targets obtained from a bounded teacher potential, while adapting the transport budget to the concentration of teacher demand. This formulation directs updates toward teacher-preferred destinations and controls their magnitude within a single transport operator. Experiments across four teacher--student settings and four mathematical-reasoning benchmarks demonstrate that RouteOPD consistently outperforms sampled reverse-KL OPD, with improvements accompanied by higher routing fidelity and lower background leakage. These results demonstrate the effectiveness of explicitly modeling probability transport in on-policy distillation.

Decision APIs that return a probability for each option are routinely used as if those probabilities were properties of the options themselves. That reading is valid only if the model satisfies independence of irrelevant alternatives (IIA): adding an option that is neither the right answer nor its strongest rival should leave the odds between those two unchanged. We test this in a pre-registered study of jev-1.13.0, a hosted decision model, using 299,463 calls on intent classification (BANKING77, CLINC150) and topic classification (AG News). Every added option moves the log-odds between the gold label and the strongest wrong label: the root-mean-square systematic shift is 0.20-0.52 nats, 1.2 to 3 times the run-to-run variation, even when the added option takes at most 0.1% of the probability mass. The shifts are directional. An option similar to the wrong answer draws probability from it (+0.10 nats toward the gold label). A paraphrase of the wrong answer produces an intermediate pattern: the gold label's probability is almost conserved, but the paraphrase receives only about a third of the wrong answer's share rather than the half that strict substitution implies. The distortion grows steadily with the logarithm of the number of options, reaching about 1 nat at 255 options, and off-domain padding pushes the odds against the gold label. In contrast, questions packed into one call do not interact (bias < 0.001). Scoring each option with an independent yes/no question removes the option-set dependence but picks the right answer 8.7 points less often. Jev sits between two local baselines, an option-independent scorer and a prompt readout. Its probabilities are best read as relative to the option list they were computed over.

Traditional weight of evidence assigns a credit characteristic a value based on its association with default across a population. Credit analysis also requires an assessment of that characteristic in the context of an individual applicant's record. We study conditional weight of evidence for this purpose. It measures the change in default log odds from observing a characteristic after the remaining credit information is known. Its sign identifies whether the characteristic adds adverse or favorable information for that applicant, and its magnitude measures the strength of that information. The same characteristic value can therefore receive different assessments for applicants with different payment histories or other credit attributes. We develop estimators using gradient-boosted trees and evaluate their accuracy in a bureau-style simulation. Regressions of the full model's predicted probabilities recover conditional evidence more accurately than separate models fitted to default outcomes, provided the full model is accurate. They also recover a deliberately constructed file-age effect whose direction varies with utilization and is often missed by marginal weight of evidence. Local class-frequency estimates improve on marginal weight of evidence but remain inaccurate for some weak effects. An application to FICO HELOC data illustrates estimation when the population evidence is unknown. Conditional weight of evidence provides an applicant-specific interpretation of the information in a credit characteristic; its population summary, a conditional information value, splits the joint information in the record across blocks when averaged over orderings. Neither is an adverse action reason, which explains the fitted score difference between the applicant and chosen passing records.

Mechanistic interpretability (MI) requires full access to model internals, yet the APIs for most widely deployed language models at best expose log-probabilities over output tokens. This creates a surrogate problem: when do measurements made on open models allow us to make claims about a closed model? We evaluate surrogate fidelity at the prediction, attribution, and representation levels. For binary classification tasks, log-odds provide an API-compatible scalar readout of the model's representation space, and leave-one-out attributions provide insight into model behavior. Across eleven models spanning four families (Llama, Qwen, GPT, and Gemini), we find that prediction fidelity substantially overstates attribution fidelity: models that agree on what the answer is often disagree on why. We document an access-validity inversion: white-box signals like attention patterns and perturbation magnitudes are highly stable across models but only weakly predictive of causal attributions, which black-box input ablations capture by design. Mechanistic insight does not automatically transfer to closed targets, and prediction-level agreement is insufficient to warrant such transfer. Code and results are available at https://github.com/facebookresearch/surrogate.

LLM-based agents are increasingly used to simulate deliberative interactions such as negotiation, conflict resolution, and multi-turn opinion exchange. Yet generated transcripts often do not reveal why an agent's stance changes: movement may reflect evidence uptake, anchoring, role drift, echoing, or changed prompt and retrieval context. We introduce the Belief Engine (BE), an auditable belief-update layer that treats "belief" as an evidential state over a proposition and exposes it as scalar stance. BE extracts arguments into structured memory and updates stance with a log-odds rule controlled by evidence uptake u and prior anchoring a. Across multiple base LLMs, parameter sweeps show that these controls reliably shape stance dynamics while preserving an evidence-level update trail. On DEBATE, a human deliberation dataset with pre/post opinions, BE best reconstructs participants whose final stance follows extracted evidence; stable and evidence-opposed cases instead point to anchoring or factors outside the extracted evidence stream. BE provides configurable infrastructure for studying evidence-grounded deliberation, where openness, commitment, convergence, and disagreement can be tied to explicit update assumptions rather than hidden prompt effects.

Reinforcement learning (RL) with verifiable rewards constructs trajectory-level advantage estimates, yet it often fails to credit the few pivotal decisions that determine outcomes in long-horizon, multi-turn agentic tasks. Recent work introduces privileged self-distillation for credit assignment, providing denser supervision, but it remains unclear how such local signals should represent sequential credit. We propose AgentOPSD, a critic-free, recursive method for turn-level credit assignment in agentic reinforcement learning. AgentOPSD aggregates token-level teacher-student log-probability gaps into turn-level evidence and recursively updates a Bayesian belief state in log-odds space. This yields a principled reweighting scheme that converts sparse outcome supervision into turn-level credit signals and identifies pivotal turns through the marginal belief revision between consecutive states. The method is fully compatible with standard policy optimization and requires neither an additional critic nor extra rollouts. We evaluate AgentOPSD on ALFWorld, WebShop, and Search-QA using Qwen2.5 models at two scales (3B and 7B). AgentOPSD outperforms GRPO and strong self-distillation baselines, achieving 89.1% success on ALFWorld with Qwen2.5-7B. Ablation studies attribute the gains to turn-level aggregation and history-dependent recursive belief updates.

Protein Language Models (PLMs) have emerged as performant and scalable tools for predicting the functional impact and clinical significance of protein-coding variants, but they still lag experimental accuracy. Here, we present a novel fine-tuning approach to improve the performance of PLMs with experimental maps of variant effects from Deep Mutational Scanning (DMS) assays using a Normalised Log-odds Ratio (NLR) head. We find consistent improvements in a held-out protein test set, and on independent DMS and clinical variant annotation benchmarks from ProteinGym and ClinVar. These findings demonstrate that DMS is a promising source of sequence diversity and supervised training data for improving the performance of PLMs for variant effect prediction.

Large language model unlearning is consistently fragile under relearn attacks. On TOFU, fine-tuning on twenty forget examples substantially recovers held-out forget-set ROUGE for every method we evaluate, and we trace this fragility to optimization geometry. The per-token answer margin of fourteen post-hoc methods spanning gradient, preference, and distillation families converges into a narrow band above the retain reference in 41 of 42 method--size cells, a regularity we call the margin cliff. We prove that this cliff follows whenever the retain coupling holds the diagnostic log-odds of forget content above a floor, a condition that token-saturating losses induce at stationarity and that we verify directly on 34 of 42 cells. Margin Calibration (MC) is a plug-in polish adding a non-saturating margin hinge anchored at the reference's per-token margin plus a KL probe on a disjoint instruction corpus, restoring forget-side pressure where the native loss saturates. Under a stated gradient-dominance condition, whose on-trajectory gradient signature we measure by instrumenting the polish, its stationary set lies on the cliff-crossing side, yielding an attack-budget upper bound on the relearn margin lift. Across TOFU (three Llama-3 sizes, three forget tiers), MUSE-News on Llama-2-7B-hf, and a Phi-3.5 panel, a single frozen configuration wins all 14 head-to-head forget aggregates and all populated relearn cells (panel-mean post-attack ROUGE-L 0.41 to 0.18) and lowers raw membership AUC on 13/14, with reduced retain-side utility as the main cost. A deployment variant matches these gains without a retain-trained reference.

Proximal Policy Optimization (PPO) is widely used in reinforcement learning with verifiable rewards for language-model reasoning. While value evolution along trajectory characterizes relative token-level credit, yet standard critics often fail to track it under sparse terminal rewards. To model this evolution, we analyze the relation between successive prefix values and show that they admit a Bayesian decomposition with additive updates in log-odds space. We use this additive structure to construct Tracking-Value PPO (\method), a cumulative value parameterization that sums position-wise scalar outputs into value logits. These outputs are learned through terminal-outcome supervision on the reconstructed values. \method improves aggregate mathematical reasoning scores over PPO by 7.0 and 8.4 points on Qwen3-4B-Base and Qwen3-8B-Base, respectively, while improving out-of-distribution generalization. Gains extend to Qwen3-4B, Qwen2.5-Math-1.5B, Qwen3.5-9B and to countdown, and scientific coding tasks. Further analysis shows more accurate tracking of value evolution and more reliable advantage estimates. Our code is publicly available in https://github.com/LINs-lab/TPPO.

In embodied AI, safety risk can be latent: a benign instruction and a safe scene become hazardous only when composed. Prior work has advanced embodied safety by varying visual contexts or evaluating execution-time dynamics, but the complementary axis of fixing the scene and varying only the instruction remains underexplored. We introduce GuardianBench, an instruction-contrastive benchmark grounded in international safety standards that isolates this latent contextual risk through 3,024 instruction-scene examples organized as same-scene Safe/Unsafe contrastive pairs across various hazard categories. Benchmarking state-of-the-art vision-language models (VLMs) reveals instruction-insensitive verdicts: models disproportionately approve both instructions under a given scene; across the primary models, average pair accuracy is only 24.1%. Our systematic rationale audit localizes the dominant failure: models fail to bind the instruction-relevant cues that differentiate safe from unsafe compositions. As a post-training case study, Verdict Log-Odds Supervision (VLOS), a lightweight verdict-level objective, substantially improves performance on open-weight backbones. Together, our latent contextual risk task formulation, standards-grounded contrastive benchmark construction, pair-level and rationale-level failure diagnosis, and benchmark-enabled verdict calibration establish GuardianBench as a controlled evaluation suite for exposing and improving safety reasoning over instruction-scene compositions under latent contextual risk.

Language model agents are post-trained and deployed through a harness, the prompts, tools, and control logic that present a task to the model and execute its outputs. Harnesses are often revised and judged by how an already trained model performs under them, which assumes that what the model learned under one harness carries over to the next. We ask what a policy learns from its harness and what survives when the harness changes. Under KL-regularized control, we show that the log odds of an optimal policy recover how strongly its harness favors each action over the others, so a trained policy carries the preferences of its harness. Deployed return then equals the ceiling of the harness, the best return it offers, minus the mismatch of the policy, the return lost to its own suboptimal decisions. Training changes only the mismatch, while changing the harness moves both terms. Comparing harnesses with a fixed model therefore mixes what each harness offers with how well that model uses it. In MiniWoB++, post-training makes a model's preferences specific to its training harness. Reversing the order of the observation fields leaves every optimal decision unchanged yet lowers a trained model's success from 85.0% to 19.2%. Conversely, every new harness that a fixed-model comparison rejects but that raises the ceiling outperforms the original agent after further training under it, and ceiling and mismatch measured beforehand predict these gains. For coding-agent harnesses on Terminal-Bench Lite, ceiling minus mismatch estimated with a stronger model as a stand-in for the optimum reproduces the accuracy ranking, while either term alone does not. Code is available at https://github.com/2020-qqtcg/HRP.

We study training-inference mismatch in reinforcement learning with verifiable rewards (RLVR) for large language models, where rollouts are sampled by an inference engine while gradients are computed by a training engine, and the two engines assign different probabilities to the same tokens. To account for this discrepancy in policy updates, we introduce calibrated importance sampling (CIS). CIS is motivated by an empirically supported logit-displacement characterization that expresses the mismatch as an additive displacement varepsilon_t in log-odds, determined by the per-logit perturbation before the softmax, whose distribution is approximately invariant to token confidence. This characterization motivates a confidence-aware truncation: large positive displacements are truncated at a single constant threshold, which maps back to an importance-ratio cap that tightens as token confidence increases. Theoretically, we show that CIS replaces the unbounded second moment that governs the error of exact importance sampling with a term bounded by a constant, at the cost of a bias controlled by the truncated excess. In evaluation across three mixture-of-experts models and five mathematical reasoning benchmarks, CIS achieves the highest five-benchmark average on all three models among the evaluated baselines. Diagnostic analyses show that CIS places less truncation bias on low-confidence tokens than truncated importance sampling, while upward clipping of small importance weights reduces held-out accuracy.

PRefLexOR (Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning) combines preference optimization with concepts from Reinforcement Learning to enable models to self-teach through iterative reasoning improvements. We propose a recursive learning approach that engages the model in multi-step reasoning, revisiting, and refining intermediate steps before producing a final output in training and inference phases. Through multiple training stages, the model first learns to align its reasoning with accurate decision paths by optimizing the log odds between preferred and non-preferred responses. During this process, PRefLexOR builds a dynamic knowledge graph by generating questions from random text chunks and retrieval-augmentation to contextualize relevant details from the entire training corpus. In the second stage, preference optimization enhances model performance by using rejection sampling to fine-tune reasoning quality by continually producing in-situ training data while masking the reasoning steps. Recursive optimization within a thinking token framework introduces iterative feedback loops, where the model refines reasoning, achieving deeper coherence, consistency, and adaptability. Implemented in small language models with only 3 billion parameters, we should that even tiny models can iteratively teach themselves to reason with greater depth and reflectivity. Our implementation is straightforward and can be incorporated into any existing pretrained LLM. We focus our examples on applications in biological materials science and demonstrate the method in a variety of case studies that range from in-domain to cross-domain applications. Using reasoning strategies that include thinking and reflection modalities we build a multi-agent recursive self-improving inference approach to successively improve responses via repeated sampling in inference time.

The shift from monolithic LLMs to distributed multi-agent architectures demands new frameworks for verifying and securing autonomous coordination. Unlike traditional multi-agent systems focused on cooperative state alignment, modern LLM patterns: multi-agent debate, constitutional oversight, helper-critic loops-rely on adversarial critique for error correction and reasoning refinement. Since LLMs are dynamical systems whose latent states are imperfectly observable from verbalized outputs, securing these networks requires understanding both macroscopic topology and microscopic agent observability. This paper establishes a rigorous graph-theoretic framework for analyzing consensus in signed, directed interaction networks, bridging graph theory and LLM reasoning by formally mapping Transformer cross-entropy log-odds to the signed Laplacian. We characterize agreement stability through structural balance theory, showing how unbalanced critique cycles produce logical frustration and persistent reasoning oscillations, and prove that unobservable latent states from hidden system prompts act as topological Trojan horses that destabilize cooperative consensus. To resolve unobservable deadlocks, we restrict interaction topologies to chordal graphs and apply matrix decomposition with Gram-Schmidt orthogonalization, proving that rank-one spectral edge perturbations deterministically break expertise symmetry by shifting eigenvalues into the stable left-half plane. Core contributions include consensus theorems, polynomial-time Perfect Elimination Ordering verification algorithms, and large-scale empirical validation on clustered ensembles of LLaMA-3, Mistral, and Gemma agents.

Predicting the fitness impact of mutations is central to protein engineering but constrained by limited assays relative to the size of sequence space. Protein language models (pLMs) trained with masked language modeling (MLM) exhibit strong zero-shot fitness prediction; we provide a unifying view by interpreting natural evolution as implicit reward maximization and MLM as inverse reinforcement learning (IRL), in which extant sequences act as expert demonstrations and pLM log-odds serve as fitness estimates. Building on this perspective, we introduce EvoIF, a lightweight model that integrates two complementary sources of evolutionary signal: (i) within-family profiles from retrieved homologs and (ii) cross-family structural-evolutionary constraints distilled from inverse folding logits. EvoIF fuses sequence-structure representations with these profiles via a compact transition block, yielding calibrated probabilities for log-odds scoring. On ProteinGym (217 mutational assays; >2.5M mutants), EvoIF and its MSA-enabled variant achieve state-of-the-art or competitive performance while using only 0.15% of the training data and fewer parameters than recent large models. Ablations confirm that within-family and cross-family profiles are complementary, improving robustness across function types, MSA depths, taxa, and mutation depths. The codes will be made publicly available.

Methods for controlling large language models (LLMs), including local weight fine-tuning, LoRA-based adaptation, and activation-based interventions, are often studied in isolation, obscuring their connections and making comparison difficult. In this work, we present a unified view that frames these interventions as dynamic weight updates induced by a control signal, placing them within a single conceptual framework. Building on this view, we propose a unified preference-utility analysis that separates control effects into preference, defined as the tendency toward a target concept, and utility, defined as coherent and task-valid generation, and measures both on a shared log-odds scale using polarity-paired contrastive examples. Across methods, we observe a consistent trade-off between preference and utility: stronger control increases preference while predictably reducing utility. We further explain this behavior through an activation manifold perspective, in which control shifts representations along target-concept directions to enhance preference, while utility declines primarily when interventions push representations off the model's valid-generation manifold. Finally, we introduce a new steering approach SPLIT guided by this analysis that improves preference while better preserving utility. Code is available at https://github.com/zjunlp/EasyEdit/blob/main/examples/SPLIT.md.

A language model reads long text in one quadratic forward pass, stops at the context window, and loses accuracy with length before reaching it. We ask whether the read can be factorized when deciding over a finite set: which document is relevant, which option is supported, which passage is the evidence. Periscope, a training-free inference method, arranges the N chunks of a text on a K{times}K grid with K{=}lceilNrceil and asks a frozen model the same question about K local spans of consecutive chunks and K strided spans that sample the whole text, reading the log-odds of every answer at one token. Each answer takes its best local and strided score, and scoring every chunk by its two spans gives an evidence map at no further cost, whose peak is the chunk behind the answer. Every probe is about sc tokens for a text of s tokens and chunk size c, so a window of W tokens reaches W^{2}/c tokens at s^{1.5} cost. The map replaces the long read. On LongBench v2, reading only the K chunks the map ranks highest, 9k tokens, matches the same model's best window read across windows from 32k to 1M tokens, and on InfiniteBench, where the median context is 150k tokens, it leads the best window read by 5 points. The same map ranks BRIGHT's long-document corpora with the best NDCG@10 of six methods. Each call caches only one probe, so a 27B model reads 4.5M-token contexts on one 80GB GPU, where a single pass would need 296GB of cache. A long read then needs a GPU that holds the model, not one that holds the text.

The probabilistic reading of the cumulative accuracy profile (CAP) has a long industry lineage. Falkenstein, Boral and Carty (2000) state, in discrete form, that the default rate at a score percentile equals the portfolio average rate times the local slope of the power curve; van der Burgt (2008, 2019) formalizes this as the continuous identity p(Dmid x) = p_D, dy/dx and imports the continuous form as a working fact; Tasche (2009) analyzes the resulting calibration method; Voloshyn and Voloshyn (2023) substitute Bayes' theorem, f(xmid D)=p(Dmid x) f(x)/p_D, into the area integral and write the Gini as a functional of the calibration curve. The slope itself is already in the lineage (van der Burgt's dy/dx is the ratio of the two cumulative differentials), but it enters as a cited working fact, never as Bayes' theorem. We make that identification explicit and draw out its consequences. First, the CAP slope is Bayes' theorem in cumulative coordinates: the standardized PD it recovers is the posterior probability rescaled by the prior. The weight of the paper then falls on two results this reading unlocks. The odds form places the weight of evidence (the log of the likelihood ratio, i.e. the Bayes factor) and the information value inside one geometry (the weight of evidence at a point is the log of the ratio of the "bad" and "good" CAP slopes). The accuracy ratio, Somers' D_{xy}, and the Gini (2A-1)/(1-p_D) are revealed as one number computed three ways. Run in comparison mode (realized outcomes against model claims), the same identity recovers the reliability diagram in cumulative coordinates, with the sign of the gap between the empirical and model-implied Gini coefficients as a calibration diagnostic. A worked five-band example carries every identity in discrete form, and a kernel-density example extends them to the continuous case.

There is a candidate electromagnetic counterpart to the binary black hole merger GW190521, identified as ZTF19abanrhr within AGN J124942.3 + 344929. Additionally, GW190514 is proposed as a plausible precursor merger to GW190521 within a hierarchical merger scenario. In this study, we investigate the potential association between GW190514 and GW190521 as a hierarchical triple merger associated with ZTF19abanrhr, taking into account of sky position, distance, and mass of the sources using a Bayesian criterion. Our analysis reveals that the association is favored over a random coincidence, with a log Bayes factor of 16.8, corresponding to an odds ratio of sim199:1, assuming an astrophysical prior odds of 10^{-5}. Notably, when accounting for the primary masses of the two gravitational wave events as potential products of mergers in the AGN formation channel, the Bayes factor increases significantly, further enhancing the preference for this association by a factor of sim10^2, corresponding to a log Bayes factor of 21.5 and an odds ratio of sim2times10^4:1. Our results suggest strong evidence for the first hierarchical triple merger associated with an electromagnetic counterpart in the AGN formation channel. This work is crucial for understanding the formation mechanisms of massive black holes, the role of AGNs in hierarchical mergers, and the implications of multi-messenger astronomy.

The fairness of machine learning-based decisions has become an increasingly important focus in the design of supervised machine learning methods. Most fairness approaches optimize a specified trade-off between performance measure(s) (e.g., accuracy, log loss, or AUC) and fairness metric(s) (e.g., demographic parity, equalized odds). This begs the question: are the right performance-fairness trade-offs being specified? We instead re-cast fair machine learning as an imitation learning task by introducing superhuman fairness, which seeks to simultaneously outperform human decisions on multiple predictive performance and fairness measures. We demonstrate the benefits of this approach given suboptimal decisions.

This study evaluates deep neural networks for forecasting probability distributions of financial returns. 1D convolutional neural networks (CNN) and Long Short-Term Memory (LSTM) architectures are used to forecast parameters of three probability distributions: Normal, Student's t, and skewed Student's t. Using custom negative log-likelihood loss functions, distribution parameters are optimized directly. The models are tested on six major equity indices (S\&P 500, BOVESPA, DAX, WIG, Nikkei 225, and KOSPI) using probabilistic evaluation metrics including Log Predictive Score (LPS), Continuous Ranked Probability Score (CRPS), and Probability Integral Transform (PIT). Results show that deep learning models provide accurate distributional forecasts and perform competitively with classical GARCH models for Value-at-Risk estimation. The LSTM with skewed Student's t distribution performs best across multiple evaluation criteria, capturing both heavy tails and asymmetry in financial returns. This work shows that deep neural networks are viable alternatives to traditional econometric models for financial risk assessment and portfolio management.

Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by maximizing the logarithm of the likelihood function under the observed data. In this work, we examine this approach and identify potential hazards associated with the use of log-likelihood in conjunction with gradient-based optimizers. First, we present a synthetic example illustrating how this approach can lead to very poor but stable parameter estimates. Second, we identify the culprit to be the log-likelihood loss, along with certain conditions that exacerbate the issue. Third, we present an alternative formulation, termed β-NLL, in which each data point's contribution to the loss is weighted by the β-exponentiated variance estimate. We show that using an appropriate β largely mitigates the issue in our illustrative example. Fourth, we evaluate this approach on a range of domains and tasks and show that it achieves considerable improvements and performs more robustly concerning hyperparameters, both in predictive RMSE and log-likelihood criteria.

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

We study the problem of determining whether a piece of text has been authored by a human or by a large language model (LLM). Existing state of the art logits-based detectors make use of statistics derived from the log-probability of the observed text evaluated using the distribution function of a given source LLM. However, relying solely on log probabilities can be sub-optimal. In response, we introduce AdaDetectGPT -- a novel classifier that adaptively learns a witness function from training data to enhance the performance of logits-based detectors. We provide statistical guarantees on its true positive rate, false positive rate, true negative rate and false negative rate. Extensive numerical studies show AdaDetectGPT nearly uniformly improves the state-of-the-art method in various combination of datasets and LLMs, and the improvement can reach up to 58%. A python implementation of our method is available at https://github.com/Mamba413/AdaDetectGPT.

Log data have facilitated various tasks of software development and maintenance, such as testing, debugging and diagnosing. Due to the unstructured nature of logs, log parsing is typically required to transform log messages into structured data for automated log analysis. Given the abundance of log parsers that employ various techniques, evaluating these tools to comprehend their characteristics and performance becomes imperative. Loghub serves as a commonly used dataset for benchmarking log parsers, but it suffers from limited scale and representativeness, posing significant challenges for studies to comprehensively evaluate existing log parsers or develop new methods. This limitation is particularly pronounced when assessing these log parsers for production use. To address these limitations, we provide a new collection of annotated log datasets, denoted Loghub-2.0, which can better reflect the characteristics of log data in real-world software systems. Loghub-2.0 comprises 14 datasets with an average of 3.6 million log lines in each dataset. Based on Loghub-2.0, we conduct a thorough re-evaluation of 15 state-of-the-art log parsers in a more rigorous and practical setting. Particularly, we introduce a new evaluation metric to mitigate the sensitivity of existing metrics to imbalanced data distributions. We are also the first to investigate the granular performance of log parsers on logs that represent rare system events, offering in-depth details for software diagnosis. Accurately parsing such logs is essential, yet it remains a challenge. We believe this work could shed light on the evaluation and design of log parsers in practical settings, thereby facilitating their deployment in production systems.

System log anomaly detection is critical for maintaining the reliability of large-scale software systems, yet traditional methods struggle with the heterogeneous and evolving nature of modern log data. Recent advances in Large Language Models (LLMs) offer promising new approaches to log understanding, but a systematic comparison of LLM-based methods against established techniques remains lacking. In this paper, we present a comprehensive benchmark study evaluating both LLM-based and traditional approaches for log anomaly detection across four widely-used public datasets: HDFS, BGL, Thunderbird, and Spirit. We evaluate three categories of methods: (1) classical log parsers (Drain, Spell, AEL) combined with machine learning classifiers, (2) fine-tuned transformer models (BERT, RoBERTa), and (3) prompt-based LLM approaches (GPT-3.5, GPT-4, LLaMA-3) in zero-shot and few-shot settings. Our experiments reveal that while fine-tuned transformers achieve the highest F1-scores (0.96-0.99), prompt-based LLMs demonstrate remarkablezero-shot capabilities (F1: 0.82-0.91) without requiring any labeled training data -- a significant advantage for real-world deployment where labeled anomalies are scarce. We further analyze the cost-accuracy trade-offs, latency characteristics, and failure modes of each approach. Our findings provide actionable guidelines for practitioners choosing log anomaly detection methods based on their specific constraints regarding accuracy, latency, cost, and label availability. All code and experimental configurations are publicly available to facilitate reproducibility.

Software and System logs record runtime information about processes executing within a system. These logs have become the most critical and ubiquitous forms of observability data that help developers understand system behavior, monitor system health and resolve issues. However, the volume of logs generated can be humongous (of the order of petabytes per day) especially for complex distributed systems, such as cloud, search engine, social media, etc. This has propelled a lot of research on developing AI-based log based analytics and intelligence solutions that can process huge volume of raw logs and generate insights. In order to enable users to perform multiple types of AI-based log analysis tasks in a uniform manner, we introduce LogAI (https://github.com/salesforce/logai), a one-stop open source library for log analytics and intelligence. LogAI supports tasks such as log summarization, log clustering and log anomaly detection. It adopts the OpenTelemetry data model, to enable compatibility with different log management platforms. LogAI provides a unified model interface and provides popular time-series, statistical learning and deep learning models. Alongside this, LogAI also provides an out-of-the-box GUI for users to conduct interactive analysis. With LogAI, we can also easily benchmark popular deep learning algorithms for log anomaly detection without putting in redundant effort to process the logs. We have opensourced LogAI to cater to a wide range of applications benefiting both academic research and industrial prototyping.

Recent research across mathematical problem solving, proof assistant programming and multimodal jailbreaking documents a striking finding: when (multimodal) language model tackle a suite of tasks with multiple attempts per task -- succeeding if any attempt is correct -- then the negative log of the average success rate scales a power law in the number of attempts. In this work, we identify an apparent puzzle: a simple mathematical calculation predicts that on each problem, the failure rate should fall exponentially with the number of attempts. We confirm this prediction empirically, raising a question: from where does aggregate polynomial scaling emerge? We then answer this question by demonstrating per-problem exponential scaling can be made consistent with aggregate polynomial scaling if the distribution of single-attempt success probabilities is heavy tailed such that a small fraction of tasks with extremely low success probabilities collectively warp the aggregate success trend into a power law - even as each problem scales exponentially on its own. We further demonstrate that this distributional perspective explains previously observed deviations from power law scaling, and provides a simple method for forecasting the power law exponent with an order of magnitude lower relative error, or equivalently, {sim}2-4 orders of magnitude less inference compute. Overall, our work contributes to a better understanding of how neural language model performance improves with scaling inference compute and the development of scaling-predictable evaluations of (multimodal) language models.

Candidate-scoring decision models return a probability distribution over a presented set of answers. Public documentation of one such system, Jev, and of an open counterpart, JevAny, describes three training ingredients that determine what these probabilities estimate: soft targets from larger models, a frozen pretrained backbone and temperature calibration. We analyze each ingredient in Gaussian surrogates where the finite-sample risk can be computed exactly. A student trained on teacher targets inherits the teacher's bias, which more student data does not remove and agreement with the teacher does not reveal. A fixed representation lowers the risk only below an explicit sample-size threshold. In a probit model the exact recalibration map is a temperature scaling, which removes all excess risk only when the teacher's coefficient has the correct direction and otherwise leaves a residual that calibration diagnostics do not detect. Under Luce's choice axiom, candidate scores are coherent across refinements of an event if and only if they aggregate by log-sum-exp. On 231,521 credit card complaints from the Consumer Financial Protection Bureau, where the decision is whether a complaint ends in monetary relief, a student trained on a logistic teacher's probabilities ends at the teacher's decision cost while a student trained on outcomes goes 8% below it, a 30B model read zero-shot remains worse than the teacher after recalibration, and that model departs from the coherence condition by 17.5 decibans. Pretrained representations reduce the labeled data required and calibration corrects the scale of the probabilities, but neither corrects a biased teacher, so the probabilities have to be checked against realized outcomes.

We obtain almost sure bounds for the weighted sum sum_{n leq t} f(n){n}, where f(n) is a Steinhaus random multiplicative function. Specifically, we obtain the bounds predicted by exponentiating the law of the iterated logarithm, giving sharp upper and lower bounds.

To schedule LLM inference, the shortest job first (SJF) principle is favorable by prioritizing requests with short output lengths to avoid head-of-line (HOL) blocking. Existing methods usually predict a single output length for each request to facilitate scheduling. We argue that such a point estimate does not match the stochastic decoding process of LLM inference, where output length is uncertain by nature and determined by when the end-of-sequence (EOS) token is sampled. Hence, the output length of each request should be fitted with a distribution rather than a single value. With an in-depth analysis of empirical data and the stochastic decoding process, we observe that output length follows a heavy-tailed distribution and can be fitted with the log-t distribution. On this basis, we propose a simple metric called Tail Inflated Expectation (TIE) to replace the output length in SJF scheduling, which adjusts the expectation of a log-t distribution with its tail probabilities to account for the risk that a request generates long outputs. To evaluate our TIE scheduler, we compare it with three strong baselines, and the results show that TIE reduces the per-token latency by 2.31times for online inference and improves throughput by 1.42times for offline data generation.

Log analysis is crucial for ensuring the orderly and stable operation of information systems, particularly in the field of Artificial Intelligence for IT Operations (AIOps). Large Language Models (LLMs) have demonstrated significant potential in natural language processing tasks. In the AIOps domain, they excel in tasks such as anomaly detection, root cause analysis of faults, operations and maintenance script generation, and alert information summarization. However, the performance of current LLMs in log analysis tasks remains inadequately validated. To address this gap, we introduce LogEval, a comprehensive benchmark suite designed to evaluate the capabilities of LLMs in various log analysis tasks for the first time. This benchmark covers tasks such as log parsing, log anomaly detection, log fault diagnosis, and log summarization. LogEval evaluates each task using 4,000 publicly available log data entries and employs 15 different prompts for each task to ensure a thorough and fair assessment. By rigorously evaluating leading LLMs, we demonstrate the impact of various LLM technologies on log analysis performance, focusing on aspects such as self-consistency and few-shot contextual learning. We also discuss findings related to model quantification, Chinese-English question-answering evaluation, and prompt engineering. These findings provide insights into the strengths and weaknesses of LLMs in multilingual environments and the effectiveness of different prompt strategies. Various evaluation methods are employed for different tasks to accurately measure the performance of LLMs in log analysis, ensuring a comprehensive assessment. The insights gained from LogEvals evaluation reveal the strengths and limitations of LLMs in log analysis tasks, providing valuable guidance for researchers and practitioners.

Prompt sensitivity, which refers to how strongly the output of a large language model (LLM) depends on the exact wording of its input prompt, raises concerns among users about the LLM's stability and reliability. In this work, we consider LLMs as multivariate functions and perform a first-order Taylor expansion, thereby analyzing the relationship between meaning-preserving prompts, their gradients, and the log probabilities of the model's next token. We derive an upper bound on the difference between log probabilities using the Cauchy-Schwarz inequality. We show that LLMs do not internally cluster similar inputs like smaller neural networks do, but instead disperse them. This dispersing behavior leads to an excessively high upper bound on the difference of log probabilities between two meaning-preserving prompts, making it difficult to effectively reduce to 0. In our analysis, we also show which types of meaning-preserving prompt variants are more likely to introduce prompt sensitivity risks in LLMs. In addition, we demonstrate that the upper bound is strongly correlated with an existing prompt sensitivity metric, PromptSensiScore. Moreover, by analyzing the logit variance, we find that prompt templates typically exert a greater influence on logits than the questions themselves. Overall, our results provide a general interpretation for why current LLMs can be highly sensitive to prompts with the same meaning, offering crucial evidence for understanding the prompt sensitivity of LLMs. Code for experiments is available at https://github.com/ku-nlp/Understanding_the_Prompt_Sensitivity.

Sports betting's recent federal legalisation in the USA coincides with the golden age of machine learning. If bettors can leverage data to reliably predict the probability of an outcome, they can recognise when the bookmaker's odds are in their favour. As sports betting is a multi-billion dollar industry in the USA alone, identifying such opportunities could be extremely lucrative. Many researchers have applied machine learning to the sports outcome prediction problem, generally using accuracy to evaluate the performance of predictive models. We hypothesise that for the sports betting problem, model calibration is more important than accuracy. To test this hypothesis, we train models on NBA data over several seasons and run betting experiments on a single season, using published odds. We show that using calibration, rather than accuracy, as the basis for model selection leads to greater returns, on average (return on investment of +34.69% versus -35.17%) and in the best case (+36.93% versus +5.56%). These findings suggest that for sports betting (or any probabilistic decision-making problem), calibration is a more important metric than accuracy. Sports bettors who wish to increase profits should therefore select their predictive model based on calibration, rather than accuracy.

We apply empirical Bayes (EB) to mine data on 136,000 long-short strategies constructed from accounting ratios, past returns, and ticker symbols. This ``high-throughput asset pricing'' matches the out-of-sample performance of top journals while eliminating look-ahead bias. Naively mining for the largest Sharpe ratios leads to similar performance, consistent with our theoretical results, though EB uniquely provides unbiased predictions with transparent intuition. Predictability is concentrated in accounting strategies, small stocks, and pre-2004 periods, consistent with limited attention theories. Multiple testing methods popular in finance fail to identify most out-of-sample performers. High-throughput methods provide a rigorous, unbiased framework for understanding asset prices.

We consider adversarial multi-armed bandit problems where the learner is allowed to observe losses of a number of arms beside the arm that it actually chose. We study the case where all non-chosen arms reveal their loss with a fixed but unknown probability r, independently of each other and the action of the learner. We propose two algorithms that work for different ranges of r. We show that after T rounds in a bandit problem with N arms, the expected regret of our first algorithm is O((T /r) log N ) whenever rge(log T)/(2N), while our second algorithm achieves a regret of O((T/r) log (N+T)) for smaller values of r. We also give a quick estimation procedure that decides the range of~r. All our bounds are within logarithmic factors of the best achievable performance of any algorithm that is even allowed to know~r.

Information systems generate a large volume of event log data during business operations, much of which consists of low-value and redundant information. When performance predictions are made directly from these logs, the accuracy of the predictions can be compromised. Researchers have explored methods to simplify and compress these data while preserving their valuable components. Most existing approaches focus on reducing the dimensionality of the data by eliminating redundant and irrelevant features. However, there has been limited investigation into the efficiency of execution both before and after event log simplification. In this paper, we present a prediction point selection algorithm designed to avoid the simplification of all points that function similarly. We select sequences or self-loop structures to form a simplifiable segment, and we optimize the deviation between the actual simplifiable value and the original data prediction value to prevent over-simplification. Experiments indicate that the simplified event log retains its predictive performance and, in some cases, enhances its predictive accuracy compared to the original event log.

Large reasoning models have recently demonstrated strong performance on complex tasks that require long chain-of-thought reasoning, through supervised fine-tuning on large-scale and high-quality datasets. To construct such datasets, existing pipelines generate long reasoning data from more capable Large Language Models (LLMs) and apply manually heuristic or naturalness-based selection methods to filter high-quality samples. Despite the proven effectiveness of naturalness-based data selection, which ranks data by the average log probability assigned by LLMs, our analysis shows that, when applied to LLM reasoning datasets, it systematically prefers samples with longer reasoning steps (i.e., more tokens per step) rather than higher-quality ones, a phenomenon we term step length confounding. Through quantitative analysis, we attribute this phenomenon to low-probability first tokens in reasoning steps; longer steps dilute their influence, thereby inflating the average log probabilities. To address this issue, we propose two variant methods: ASLEC-DROP, which drops first-token probabilities when computing average log probability, and ASLEC-CASL, which applies a causal debiasing regression to remove the first tokens' confounding effect. Experiments across four LLMs and five evaluation benchmarks demonstrate the effectiveness of our approach in mitigating the step length confounding problem.

Logs are imperative in the development and maintenance process of many software systems. They record detailed runtime information that allows developers and support engineers to monitor their systems and dissect anomalous behaviors and errors. The increasing scale and complexity of modern software systems, however, make the volume of logs explodes. In many cases, the traditional way of manual log inspection becomes impractical. Many recent studies, as well as industrial tools, resort to powerful text search and machine learning-based analytics solutions. Due to the unstructured nature of logs, a first crucial step is to parse log messages into structured data for subsequent analysis. In recent years, automated log parsing has been widely studied in both academia and industry, producing a series of log parsers by different techniques. To better understand the characteristics of these log parsers, in this paper, we present a comprehensive evaluation study on automated log parsing and further release the tools and benchmarks for easy reuse. More specifically, we evaluate 13 log parsers on a total of 16 log datasets spanning distributed systems, supercomputers, operating systems, mobile systems, server applications, and standalone software. We report the benchmarking results in terms of accuracy, robustness, and efficiency, which are of practical importance when deploying automated log parsing in production. We also share the success stories and lessons learned in an industrial application at Huawei. We believe that our work could serve as the basis and provide valuable guidance to future research and deployment of automated log parsing.

Detecting the anomalies of web applications, important infrastructures for running modern companies and governments, is crucial for providing reliable web services. Many modern web applications operate on web APIs (e.g., RESTful, SOAP, and WebSockets), their exposure invites intended attacks or unintended illegal visits, causing abnormal system behaviors. However, such anomalies can share very similar logs with normal logs, missing crucial information (which could be in database) for log discrimination. Further, log instances can be also noisy, which can further mislead the state-of-the-art log learning solutions to learn spurious correlation, resulting superficial models and rules for anomaly detection. In this work, we propose MINES which infers explainable API invariants for anomaly detection from the schema level instead of detailed raw log instances, which can (1) significantly discriminate noise in logs to identify precise normalities and (2) detect abnormal behaviors beyond the instrumented logs. Technically, MINES (1) converts API signatures into table schema to enhance the original database shema; and (2) infers the potential database constraints on the enhanced database schema to capture the potential relationships between APIs and database tables. MINES uses LLM for extracting potential relationship based on two given table structures; and use normal log instances to reject and accept LLM-generated invariants. Finally, MINES translates the inferred constraints into invariants to generate Python code for verifying the runtime logs. We extensively evaluate MINES on web-tamper attacks on the benchmarks of TrainTicket, NiceFish, Gitea, Mastodon, and NextCloud against baselines such as LogRobust, LogFormer, and WebNorm. The results show that MINES achieves high recall for the anomalies while introducing almost zero false positives, indicating a new state-of-the-art.

This paper investigates the problem of generalized linear bandits with heavy-tailed rewards, whose (1+epsilon)-th moment is bounded for some epsilonin (0,1]. Although there exist methods for generalized linear bandits, most of them focus on bounded or sub-Gaussian rewards and are not well-suited for many real-world scenarios, such as financial markets and web-advertising. To address this issue, we propose two novel algorithms based on truncation and mean of medians. These algorithms achieve an almost optimal regret bound of O(dT^{1{1+epsilon}}), where d is the dimension of contextual information and T is the time horizon. Our truncation-based algorithm supports online learning, distinguishing it from existing truncation-based approaches. Additionally, our mean-of-medians-based algorithm requires only O(log T) rewards and one estimator per epoch, making it more practical. Moreover, our algorithms improve the regret bounds by a logarithmic factor compared to existing algorithms when epsilon=1. Numerical experimental results confirm the merits of our algorithms.

We revisit the noisy binary search model of Karp and Kleinberg, in which we have n coins with unknown probabilities p_i that we can flip. The coins are sorted by increasing p_i, and we would like to find where the probability crosses (to within varepsilon) of a target value tau. This generalized the fixed-noise model of Burnashev and Zigangirov , in which p_i = 1{2} pm varepsilon, to a setting where coins near the target may be indistinguishable from it. Karp and Kleinberg showed that Theta(1{varepsilon^2} log n) samples are necessary and sufficient for this task. We produce a practical algorithm by solving two theoretical challenges: high-probability behavior and sharp constants. We give an algorithm that succeeds with probability 1-delta from \[ 1{C_{\tau, \varepsilon}} \cdot \left(\lg n + O(\log^{2/3} n \log^{1/3} 1{\delta} + \log 1{\delta})\right) \] samples, where C_{tau, varepsilon} is the optimal such constant achievable. For delta > n^{-o(1)} this is within 1 + o(1) of optimal, and for delta ll 1 it is the first bound within constant factors of optimal.

We evaluate language models' capability to generate novel research ideas through the lens of compression. We aim to lower-bound the potentially tiny probability that a language model generates the essence of a future research idea without any hints. Rather than estimate this probability through expensive repeated sampling, our Priced Guidance framework measures the compression cost: how many additional bits of information are needed to guide the model to recover the target idea. We prove that if the model can recover the target idea with at most K bits of guidance in expectation, then it can generate the idea without any guidance with probability at least 2^{-K}. In our framework, the language model, called the generator, can pose a sequence of multiple-choice questions and specify a probability distribution over possible answers. A guide, which is a language model with access to the target idea, selects answers. If a selected answer has prior probability p, the generator pays -log_2 p bits. The generator aims to produce an idea that matches the essence of the target idea with minimal cumulative cost. This cumulative cost equals, up to an additive constant, the number of bits of information sent by the guide. Using this methodology, we evaluate five generator LLMs (Opus 5, Fable 5.1, GPT-6 Astra, GPT-5.6 Sol, and GLM 5.3) on the core ideas in 87 recent high-quality deep learning papers and we use LLM as judge to determine whether the generated idea matches the target in terms of the central research object and defining mechanism. Fable 5.1 achieves the lowest median compression cost at 69.9 bits, substantially lower than gzip's median of 5,712 bits for losslessly compressing the summary of the target idea. A uniform ensemble of Fable 5.1, Opus 5, and Astra further reduces the median compression cost to 55.8 bits and improves the generation probability lower bound by 18,000 times.

Online conformal prediction can fail when predictions shape actions and actions determine which outcomes enter calibration. Standard adaptive methods may retain marginal coverage while systematically miscovering the counterfactual outcomes of rarely selected actions. This paper formalizes the failure through counterfactual coverage and introduces Propensity-Weighted Online Conformal Prediction, an inverse-propensity-weighted recursion that debiases calibration. A doubly robust variant further reduces nuisance bias to the product of outcome-model and propensity errors. Under positivity, the resulting coverage rate matches an information-theoretic lower bound up to logarithmic factors. Experiments on synthetic decision tasks, open bandit data, and financial rebalancing show that PW-OCP and DR-OCP improve counterfactual coverage and downstream regret without sacrificing prediction-set sharpness.

Log anomaly detection, which is critical for identifying system failures and preempting security breaches, detects irregular patterns within large volumes of log data, and impacts domains such as service reliability, performance optimization, and database log analysis. Modern log anomaly detection methods rely on training deep learning models on clean, anomaly-free log sequences. However, obtaining such clean log data requires costly and tedious human labeling, and existing automatic cleaning methods fail to fully integrate the specific characteristics and actual semantics of logs in their purification process. In this paper, we propose a cost-aware, rule-enhanced purification framework, LogPurge, that automatically selects a sufficient subset of normal log sequences from contamination log sequences to train a anomaly detection model. Our approach involves a two-stage filtering algorithm: In the first stage, we use a large language model (LLM) to remove clustered anomalous patterns and enhance system rules to improve LLM's understanding of system logs; in the second stage, we utilize a divide-and-conquer strategy that decomposes the remaining contaminated regions into smaller subproblems, allowing each to be effectively purified through the first stage procedure. Our experiments, conducted on two public datasets and one industrial dataset, show that our method significantly removes an average of 98.74% of anomalies while retaining 82.39% of normal samples. Compared to the latest unsupervised log sample selection algorithms, our method achieves F-1 score improvements of 35.7% and 84.11% on the public datasets, and an impressive 149.72% F-1 improvement on the private dataset, demonstrating the effectiveness of our approach.

We study causal logistic bandits with counterfactual fairness constraints. The causal structure is given through known factual and counterfactual feature maps that share an unknown logistic reward parameter, but the learner observes only factual rewards. Consequently, the directions determining counterfactual feasibility need not be identifiable from the available feedback. The closest prior analyses either omit a coverage condition or impose a comparatively strong one, and do not establish matching lower bounds. We first show that some coverage condition is necessary: without a coverage-type restriction, factually indistinguishable environments with different optimal fair actions force Ω(T) expected joint loss. Under a weaker full-rank condition on the factual covariance pooled across actions, we identify a target-specific information scale V_star that measures the difficulty of estimating rewards and counterfactual effects from factual feedback. We construct worst-case families satisfying this condition on which every policy incurs expected joint loss Ωleft(left[V_starmin{log K,d}right]^{1/3}T^{2/3}right). We also give an explore--then--exploit procedure tuned using V_star and an adaptive algorithm that does not require its value. Both algorithms achieve max{R_T,V_T}=Oleft(left[V_starmin{log K,d}right]^{1/3}T^{2/3}+κd/σ_0^2right), where R_T is regret relative to the best fair action and V_T denotes the cumulative stage-wise positive violations. Thus the upper and lower bounds match in their leading dependence on T, V_star, and min{log K,d}, up to logarithmic factors.

Large Language Models (LLMs) are increasingly employed in real-world applications, driving the need to evaluate the trustworthiness of their generated text. To this end, reliable uncertainty estimation is essential. Since current LLMs generate text autoregressively through a stochastic process, the same prompt can lead to varying outputs. Consequently, leading uncertainty estimation methods generate and analyze multiple output sequences to determine the LLM's uncertainty. However, generating output sequences is computationally expensive, making these methods impractical at scale. In this work, we inspect the theoretical foundations of the leading methods and explore new directions to enhance their computational efficiency. Building on the framework of proper scoring rules, we find that the negative log-likelihood of the most likely output sequence constitutes a theoretically grounded uncertainty measure. To approximate this alternative measure, we propose G-NLL, which has the advantage of being obtained using only a single output sequence generated by greedy decoding. This makes uncertainty estimation more efficient and straightforward, while preserving theoretical rigor. Empirical results demonstrate that G-NLL achieves state-of-the-art performance across various LLMs and tasks. Our work lays the foundation for efficient and reliable uncertainty estimation in natural language generation, challenging the necessity of more computationally involved methods currently leading the field.

Large language models are increasingly used as decision aids whose probability judgments shape downstream choices. Whether those judgments carry a systematic directional tilt has been hard to detect: calibration metrics aggregate unsigned errors, and naturalistic uncertainty offers no ground-truth probability. When an LLM rates a startup's success at 70% but its failure at 15%, the missing 15 points expose a distortion no aggregate score flags. We introduce OptimismBench, which detects directional bias with inverted pairs: each scenario elicits both P(success) and P(failure), and asymmetry between the two framings yields a signed bias score without ground truth. Across 16 models from 8 providers, fourteen are optimistic; pessimism appears only in Anthropic's frontier tier. Eleven matched base-versus-chat pairs across four families show post-training sets the sign of the bias, with opposite shifts in different families. The pattern survives prompt, temperature, perspective, and self-debiasing ablations. A seventeen-model six-language comparison further shows model identity dominates language, with inter-model variance at 4.7x inter-language variance. We release 3,870 items across 10 languages for per-model directional-bias auditing. When alignment makes a model more helpful, it also tilts its probabilities; downstream pipelines inherit the tilt by default.

We consider a number of graph kernels and proximity measures including commute time kernel, regularized Laplacian kernel, heat kernel, exponential diffusion kernel (also called "communicability"), etc., and the corresponding distances as applied to clustering nodes in random graphs and several well-known datasets. The model of generating random graphs involves edge probabilities for the pairs of nodes that belong to the same class or different predefined classes of nodes. It turns out that in most cases, logarithmic measures (i.e., measures resulting after taking logarithm of the proximities) perform better while distinguishing underlying classes than the "plain" measures. A comparison in terms of reject curves of inter-class and intra-class distances confirms this conclusion. A similar conclusion can be made for several well-known datasets. A possible origin of this effect is that most kernels have a multiplicative nature, while the nature of distances used in cluster algorithms is an additive one (cf. the triangle inequality). The logarithmic transformation is a tool to transform the first nature to the second one. Moreover, some distances corresponding to the logarithmic measures possess a meaningful cutpoint additivity property. In our experiments, the leader is usually the logarithmic Communicability measure. However, we indicate some more complicated cases in which other measures, typically, Communicability and plain Walk, can be the winners.

Logs generated by large-scale software systems provide crucial information for engineers to understand the system status and diagnose problems of the systems. Log parsing, which converts raw log messages into structured data, is the first step to enabling automated log analytics. Existing log parsers extract the common part as log templates using statistical features. However, these log parsers often fail to identify the correct templates and parameters because: 1) they often overlook the semantic meaning of log messages, and 2) they require domain-specific knowledge for different log datasets. To address the limitations of existing methods, in this paper, we propose LogPPT to capture the patterns of templates using prompt-based few-shot learning. LogPPT utilises a novel prompt tuning method to recognise keywords and parameters based on a few labelled log data. In addition, an adaptive random sampling algorithm is designed to select a small yet diverse training set. We have conducted extensive experiments on 16 public log datasets. The experimental results show that LogPPT is effective and efficient for log parsing.

We propose an approach to estimate the number of samples required for a model to reach a target performance. We find that the power law, the de facto principle to estimate model performance, leads to large error when using a small dataset (e.g., 5 samples per class) for extrapolation. This is because the log-performance error against the log-dataset size follows a nonlinear progression in the few-shot regime followed by a linear progression in the high-shot regime. We introduce a novel piecewise power law (PPL) that handles the two data regimes differently. To estimate the parameters of the PPL, we introduce a random forest regressor trained via meta learning that generalizes across classification/detection tasks, ResNet/ViT based architectures, and random/pre-trained initializations. The PPL improves the performance estimation on average by 37% across 16 classification and 33% across 10 detection datasets, compared to the power law. We further extend the PPL to provide a confidence bound and use it to limit the prediction horizon that reduces over-estimation of data by 76% on classification and 91% on detection datasets.

Climbing grades are used to classify a climbing route based on its perceived difficulty, and have come to play a central role in the sport of rock climbing. Recently, the first statistically rigorous method for estimating climbing grades from whole-history ascent data was described, based on the dynamic Bradley-Terry model for games between players of time-varying ability. In this paper, we implement inference under the whole-history rating model using Markov chain Monte Carlo and apply the method to a curated data set made up of climbers who climb regularly. We use these data to get an estimate of the model's fundamental scale parameter m, which defines the proportional increase in difficulty associated with an increment of grade. We show that the data conform to assumptions that the climbing grade scale is a logarithmic scale of difficulty, like decibels or stellar magnitude. We estimate that an increment in Ewbank, French and UIAA climbing grade systems corresponds to 2.1, 2.09 and 2.13 times increase in difficulty respectively, assuming a logistic model of probability of success as a function of grade. Whereas we find that the Vermin scale for bouldering (V-grade scale) corresponds to a 3.17 increase in difficulty per grade increment. In addition, we highlight potential connections between the logarithmic properties of climbing grade scales and the psychophysical laws of Weber and Fechner.

Logs have been widely adopted in software system development and maintenance because of the rich runtime information they record. In recent years, the increase of software size and complexity leads to the rapid growth of the volume of logs. To handle these large volumes of logs efficiently and effectively, a line of research focuses on developing intelligent and automated log analysis techniques. However, only a few of these techniques have reached successful deployments in industry due to the lack of public log datasets and open benchmarking upon them. To fill this significant gap and facilitate more research on AI-driven log analytics, we have collected and released loghub, a large collection of system log datasets. In particular, loghub provides 19 real-world log datasets collected from a wide range of software systems, including distributed systems, supercomputers, operating systems, mobile systems, server applications, and standalone software. In this paper, we summarize the statistics of these datasets, introduce some practical usage scenarios of the loghub datasets, and present our benchmarking results on loghub to benefit the researchers and practitioners in this field. Up to the time of this paper writing, the loghub datasets have been downloaded for roughly 90,000 times in total by hundreds of organizations from both industry and academia. The loghub datasets are available at https://github.com/logpai/loghub.

Trading discipline often fails people. Our study tested whether four AI trading agents followed their strategies and risk rules. Offering traders the evidence and an agent evaluation toolkit to separate luck from following the rules, before giving agents meaningful autonomy or capital. Our study analysed 2,627 closed positions from 12 February to 27 August 2026 across the same asset universe and execution conditions. Most positions were simulated against live prices with a 0.09% round-trip fee; 18% involved real Hyperliquid orders. Each position declared a strategy, stop and target, with a limit of five open positions per agent. The fleet finished net positive after fees. Rule adherence was high across all four agents, including the unprofitable one. Profitability tracked how often agents won relative to their break-even win rates. Institutional-style controls ran by default and contained losses through a 29% market drawdown and recovery, with documented exceptions. The discipline held for all four agents. Agents kept 97.5% of gross loss within declared stops, and typical losses closed at declared levels. Declared risk remained stable after losses and broadly stable across calm and volatile months. Twenty-three of 24 runs respected the position limit; logs identify the exception's size and duration. The same live data produced different results across assigned strategies. The trade-log tests can be rerun from the published trade snapshot; regime tests also require the published Bitcoin prices and regime labels. Section 3.5 specifies the stop-breach tolerance. These trade-level results are not account-level returns or proof of a lasting edge. Our study provides an evaluation toolkit to help traders distinguish rule-following from luck before committing capital. For anyone considering allocating capital to agents to trade, discipline should be the entry test, not the only test.

Software systems often record important runtime information in logs to help with troubleshooting. Log-based anomaly detection has become a key research area that aims to identify system issues through log data, ultimately enhancing the reliability of software systems. Traditional deep learning methods often struggle to capture the semantic information embedded in log data, which is typically organized in natural language. In this paper, we propose LogLLM, a log-based anomaly detection framework that leverages large language models (LLMs). LogLLM employs BERT for extracting semantic vectors from log messages, while utilizing Llama, a transformer decoder-based model, for classifying log sequences. Additionally, we introduce a projector to align the vector representation spaces of BERT and Llama, ensuring a cohesive understanding of log semantics. Unlike conventional methods that require log parsers to extract templates, LogLLM preprocesses log messages with regular expressions, streamlining the entire process. Our framework is trained through a novel three-stage procedure designed to enhance performance and adaptability. Experimental results across four public datasets demonstrate that LogLLM outperforms state-of-the-art methods. Even when handling unstable logs, it effectively captures the semantic meaning of log messages and detects anomalies accurately.

Most benchmarks hand the model a question. EnigmaForge hands it a stack of old documents and no question at all. Buried in the letters, receipts, and logbook margins is a small logic puzzle whose solution is unique - proved by a SAT solver at generation time, with an ablation certificate showing every clue is load-bearing. Because instances are generated rather than collected, the corpus renews forever. The headline measure is intuition: task success when handed only the story, with world reconstruction as the secondary axis. Twenty-five frontier models ran over 600 instances (17,400 scored records) under three matched conditions. Intuition reshuffles the leaderboard: a 22x spread where fact recovery spans 1.6x, the second-best fact-recoverer ranks fourteenth, one model is indifferent to being told the question, and another is significantly better without it. Several models were blocked by their own content filters before reaching the puzzle - any benchmark scoring refusals as failure is quietly measuring filter behavior.

Automated log analysis is crucial to ensure high availability and reliability of complex systems. The advent of LLMs in NLP has ushered in a new era of language model-driven automated log analysis, garnering significant interest. Within this field, two primary paradigms based on language models for log analysis have become prominent. Small Language Models (SLMs) follow the pre-train and fine-tune paradigm, focusing on the specific log analysis task through fine-tuning on supervised datasets. On the other hand, LLMs following the in-context learning paradigm, analyze logs by providing a few examples in prompt contexts without updating parameters. Despite their respective strengths, we notice that SLMs are more cost-effective but less powerful, whereas LLMs with large parameters are highly powerful but expensive and inefficient. To trade-off between the performance and inference costs of both models in automated log analysis, this paper introduces an adaptive log analysis framework known as AdaptiveLog, which effectively reduces the costs associated with LLM while ensuring superior results. This framework collaborates an LLM and a small language model, strategically allocating the LLM to tackle complex logs while delegating simpler logs to the SLM. Specifically, to efficiently query the LLM, we propose an adaptive selection strategy based on the uncertainty estimation of the SLM, where the LLM is invoked only when the SLM is uncertain. In addition, to enhance the reasoning ability of the LLM in log analysis tasks, we propose a novel prompt strategy by retrieving similar error-prone cases as the reference, enabling the model to leverage past error experiences and learn solutions from these cases. Extensive experiments demonstrate that AdaptiveLog achieves state-of-the-art results across different tasks, elevating the overall accuracy of log analysis while maintaining cost efficiency.

As the IT industry advances, system log data becomes increasingly crucial. Many computer systems rely on log texts for management due to restricted access to source code. The need for log anomaly detection is growing, especially in real-world applications, but identifying anomalies in rapidly accumulating logs remains a challenging task. Traditional deep learning-based anomaly detection models require dataset-specific training, leading to corresponding delays. Notably, most methods only focus on sequence-level log information, which makes the detection of subtle anomalies harder, and often involve inference processes that are difficult to utilize in real-time. We introduce RAPID, a model that capitalizes on the inherent features of log data to enable anomaly detection without training delays, ensuring real-time capability. RAPID treats logs as natural language, extracting representations using pre-trained language models. Given that logs can be categorized based on system context, we implement a retrieval-based technique to contrast test logs with the most similar normal logs. This strategy not only obviates the need for log-specific training but also adeptly incorporates token-level information, ensuring refined and robust detection, particularly for unseen logs. We also propose the core set technique, which can reduce the computational cost needed for comparison. Experimental results show that even without training on log data, RAPID demonstrates competitive performance compared to prior models and achieves the best performance on certain datasets. Through various research questions, we verified its capability for real-time detection without delay.

Stock recommendation is vital to investment companies and investors. However, no single stock selection strategy will always win while analysts may not have enough time to check all S&P 500 stocks (the Standard & Poor's 500). In this paper, we propose a practical scheme that recommends stocks from S&P 500 using machine learning. Our basic idea is to buy and hold the top 20% stocks dynamically. First, we select representative stock indicators with good explanatory power. Secondly, we take five frequently used machine learning methods, including linear regression, ridge regression, stepwise regression, random forest and generalized boosted regression, to model stock indicators and quarterly log-return in a rolling window. Thirdly, we choose the model with the lowest Mean Square Error in each period to rank stocks. Finally, we test the selected stocks by conducting portfolio allocation methods such as equally weighted, mean-variance, and minimum-variance. Our empirical results show that the proposed scheme outperforms the long-only strategy on the S&P 500 index in terms of Sharpe ratio and cumulative returns. This work is fully open-sourced at https://github.com/AI4Finance-Foundation/Dynamic-Stock-Recommendation-Machine_Learning-Published-Paper-IEEE{GitHub}.

In economy, markets are denoted as efficient when it is impossible to systematically generate profits which outperform the average. In the past years, the concept has been tested in other domains such as the growing sports betting market. Surprisingly, despite its large size and its level of maturity, sports betting shows traits of inefficiency. The anomalies indicate the existence of strategies which shift betting from a game of chance towards a game of skill. This article shows an example for an inefficiency detected in the German soccer betting TOTO 13er Wette, which is operated by state-run lottery agencies. Gamblers have to guess the outcome (win, draw, loss) of 13 soccer matches listed on a lottery tip. Applying stochastic methods, a recipe is presented to determine hit rates for single match outcomes. More important, the recipe provides the number of lottery tips required to achieve a specific number of strikes (number of correct match forecasts per lottery tip) for any given level of safety. An approximation is derived to cope with large numbers in hypergeometric distributions, valid under certain constraints. Overall, the strategy does lead to returns exceeding the aggregated lottery fees, resulting in moderate, but consistent profits. It is briefly discussed if lessions learned from soccer betting can be transferred back to financial markets, because gamblers and retail investors face similar challenges and opportunities.

Logs play a crucial role in system monitoring and debugging by recording valuable system information, including events and states. Although various methods have been proposed to detect anomalies in log sequences, they often overlook the significance of considering relations among system components, such as services and users, which can be identified from log contents. Understanding these relations is vital for detecting anomalies and their underlying causes. To address this issue, we introduce GLAD, a Graph-based Log Anomaly Detection framework designed to detect relational anomalies in system logs. GLAD incorporates log semantics, relational patterns, and sequential patterns into a unified framework for anomaly detection. Specifically, GLAD first introduces a field extraction module that utilizes prompt-based few-shot learning to identify essential fields from log contents. Then GLAD constructs dynamic log graphs for sliding windows by interconnecting extracted fields and log events parsed from the log parser. These graphs represent events and fields as nodes and their relations as edges. Subsequently, GLAD utilizes a temporal-attentive graph edge anomaly detection model for identifying anomalous relations in these dynamic log graphs. This model employs a Graph Neural Network (GNN)-based encoder enhanced with transformers to capture content, structural and temporal features. We evaluate our proposed method on three datasets, and the results demonstrate the effectiveness of GLAD in detecting anomalies indicated by varying relational patterns.

The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence measures. Surprisingly, an equally important problem, estimating an unknown Markov chain from its samples, is still far from understood. We consider two problems related to the min-max risk (expected loss) of estimating an unknown k-state Markov chain from its n sequential samples: predicting the conditional distribution of the next sample with respect to the KL-divergence, and estimating the transition matrix with respect to a natural loss induced by KL or a more general f-divergence measure. For the first measure, we determine the min-max prediction risk to within a linear factor in the alphabet size, showing it is Omega(kloglog n / n) and O(k^2loglog n / n). For the second, if the transition probabilities can be arbitrarily small, then only trivial uniform risk upper bounds can be derived. We therefore consider transition probabilities that are bounded away from zero, and resolve the problem for essentially all sufficiently smooth f-divergences, including KL-, L_2-, Chi-squared, Hellinger, and Alpha-divergences.

Repeated event forecasting requires extracting predictive signals from noisy evidence and evaluating their value across successive decisions. We introduce JockeyBench, a benchmark and evaluation protocol that studies this problem through historical Japanese horse racing. The protocol combines time-gated evidence, priced tools, paired frozen-program controls, and two workflows: executing an LLM-written predictor or acquiring evidence for a fresh per-race LLM forecast. Evaluation separates forecast quality, benchmark-specific net utility, and retrospective betting returns and risk under fixed decision rules. Across 28 model--scaffold configurations on 324 races, paired tests identify seven revision gains and two declines after multiple-testing correction. Yet every configuration has negative mean profit under capped-Kelly settlement. In a four-model comparison, the reusable-program workflow has higher mean betting profit and lower research fees, although both workflows lose on average. Further diagnostics reveal that mean probability bias reverses on selected bets and that profitable individual runs can depend on concentrated returns. These findings motivate evaluating predictive competence, adaptation, resource use, and decision value separately when assessing agents for repeated event forecasting.

Logs, being run-time information automatically generated by software, record system events and activities with their timestamps. Before obtaining more insights into the run-time status of the software, a fundamental step of log analysis, called log parsing, is employed to extract structured templates and parameters from the semi-structured raw log messages. However, current log parsers are all syntax-based and regard each message as a character string, ignoring the semantic information included in parameters and templates. Thus, we propose the semantic-based parser SemParser to unlock the critical bottleneck of mining semantics from log messages. It contains two steps, an end-to-end semantic miner and a joint parser. Specifically, the first step aims to identify explicit semantics inside a single log, and the second step is responsible for jointly inferring implicit semantics and computing structural outputs based on the contextual knowledge base. To analyze the effectiveness of our semantic parser, we first demonstrate that it can derive rich semantics from log messages collected from six widely-applied systems with an average F1 score of 0.985. Then, we conduct two representative downstream tasks, showing that current downstream models improve their performance with appropriately extracted semantics by 1.2%-11.7% and 8.65% on two anomaly detection datasets and a failure identification dataset, respectively. We believe these findings provide insights into semantically understanding log messages for the log analysis community.

Survival analysis is the problem of estimating probability distributions for future event times, which can be seen as a problem in uncertainty quantification. Although there are fundamental theories on strictly proper scoring rules for uncertainty quantification, little is known about those for survival analysis. In this paper, we investigate extensions of four major strictly proper scoring rules for survival analysis and we prove that these extensions are proper under certain conditions, which arise from the discretization of the estimation of probability distributions. We also compare the estimation performances of these extended scoring rules by using real datasets, and the extensions of the logarithmic score and the Brier score performed the best.

System logs record detailed runtime information of software systems and are used as the main data source for many tasks around software engineering. As modern software systems are evolving into large scale and complex structures, logs have become one type of fast-growing big data in industry. In particular, such logs often need to be stored for a long time in practice (e.g., a year), in order to analyze recurrent problems or track security issues. However, archiving logs consumes a large amount of storage space and computing resources, which in turn incurs high operational cost. Data compression is essential to reduce the cost of log storage. Traditional compression tools (e.g., gzip) work well for general texts, but are not tailed for system logs. In this paper, we propose a novel and effective log compression method, namely logzip. Logzip is capable of extracting hidden structures from raw logs via fast iterative clustering and further generating coherent intermediate representations that allow for more effective compression. We evaluate logzip on five large log datasets of different system types, with a total of 63.6 GB in size. The results show that logzip can save about half of the storage space on average over traditional compression tools. Meanwhile, the design of logzip is highly parallel and only incurs negligible overhead. In addition, we share our industrial experience of applying logzip to Huawei's real products.

Users of music streaming, video streaming, news recommendation, and e-commerce services often engage with content in a sequential manner. Providing and evaluating good sequences of recommendations is therefore a central problem for these services. Prior reweighting-based counterfactual evaluation methods either suffer from high variance or make strong independence assumptions about rewards. We propose a new counterfactual estimator that allows for sequential interactions in the rewards with lower variance in an asymptotically unbiased manner. Our method uses graphical assumptions about the causal relationships of the slate to reweight the rewards in the logging policy in a way that approximates the expected sum of rewards under the target policy. Extensive experiments in simulation and on a live recommender system show that our approach outperforms existing methods in terms of bias and data efficiency for the sequential track recommendations problem.

As large language models become increasingly widespread, third-party providers that deploy open-weight models have become an important part of the ecosystem. Auditing the quality of their inference APIs is therefore an open problem. We formalize hosted model routing as a stochastic process and propose \textbf{Ventor-QTest}, a composite black-box audit that requires no probability information from the target API. Its repeated-request component sends each frozen constrained context to the target multiple times, reconstructs a categorical output distribution from the returned text counts, and reports average fidelity loss (AFL) as a null-bias-corrected, within-window mean coarsened-KL statistic. Its long-sequence component uses independent runs to report extreme fidelity loss (EFL) through the empirical upper tail of a run-level reference-centered-surprisal statistic. Across three logprob-capable route conditions, AFL shows strong linear descriptive agreement with a logprob-derived coarsened-KL comparator. Across seven route snapshots, 20-run sequence probes reveal route-specific EFL variation. AFL and EFL have little detectable route-level association with GPQA-Diamond accuracy. In contrast, pronounced EFL coincides with a decline in Terminal-Bench pass rate as task exposure increases. This pattern may arise because correctness in long-horizon tasks is more sensitive to extreme fidelity loss. These results motivate reporting AFL and EFL jointly, particularly when auditing long-horizon agentic tasks. The open-source implementation is available at https://github.com/Tencent/AI-Infra-Guard/tree/main/services/api_checker/ventor_qtest.

Words of estimative probability (WEP) are expressions of a statement's plausibility (probably, maybe, likely, doubt, likely, unlikely, impossible...). Multiple surveys demonstrate the agreement of human evaluators when assigning numerical probability levels to WEP. For example, highly likely corresponds to a median chance of 0.90+-0.08 in Fagen-Ulmschneider (2015)'s survey. In this work, we measure the ability of neural language processing models to capture the consensual probability level associated to each WEP. Firstly, we use the UNLI dataset (Chen et al., 2020) which associates premises and hypotheses with their perceived joint probability p, to construct prompts, e.g. "[PREMISE]. [WEP], [HYPOTHESIS]." and assess whether language models can predict whether the WEP consensual probability level is close to p. Secondly, we construct a dataset of WEP-based probabilistic reasoning, to test whether language models can reason with WEP compositions. When prompted "[EVENTA] is likely. [EVENTB] is impossible.", a causal language model should not express that [EVENTA&B] is likely. We show that both tasks are unsolved by off-the-shelf English language models, but that fine-tuning leads to transferable improvement.

We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small L^2 error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order moment, by either employing early stopping or assuming smoothness condition on the score function of the data distribution. Our result does not rely on any log-concavity or functional inequality assumption and has a logarithmic dependence on the smoothness. In particular, we show that under only a finite second moment condition, approximating the following in reverse KL divergence in epsilon-accuracy can be done in tilde Oleft(d log (1/delta){epsilon}right) steps: 1) the variance-delta Gaussian perturbation of any data distribution; 2) data distributions with 1/delta-smooth score functions. Our analysis also provides a quantitative comparison between different discrete approximations and may guide the choice of discretization points in practice.

There is a long history, as well as a recent explosion of interest, in statistical and generative modeling approaches based on score functions -- derivatives of the log-likelihood of a distribution. In seminal works, Hyv\"arinen proposed vanilla score matching as a way to learn distributions from data by computing an estimate of the score function of the underlying ground truth, and established connections between this method and established techniques like Contrastive Divergence and Pseudolikelihood estimation. It is by now well-known that vanilla score matching has significant difficulties learning multimodal distributions. Although there are various ways to overcome this difficulty, the following question has remained unanswered -- is there a natural way to sample multimodal distributions using just the vanilla score? Inspired by a long line of related experimental works, we prove that the Langevin diffusion with early stopping, initialized at the empirical distribution, and run on a score function estimated from data successfully generates natural multimodal distributions (mixtures of log-concave distributions).

Large language models (LLMs) often produce confident but incorrect answers in settings where abstention would be safer. Standard evaluation protocols, however, require a response and do not account for how confidence should guide decisions under different risk preferences. To address this gap, we introduce the Behavioral Alignment Score (BAS), a decision-theoretic metric for evaluating how well LLM confidence supports abstention-aware decision making. BAS is derived from an explicit answer-or-abstain utility model and aggregates realized utility across a continuum of risk thresholds, yielding a measure of decision-level reliability that depends on both the magnitude and ordering of confidence. We show theoretically that truthful confidence estimates uniquely maximize expected BAS utility, linking calibration to decision-optimal behavior. BAS is related to proper scoring rules such as log loss, but differs structurally: log loss penalizes underconfidence and overconfidence symmetrically, whereas BAS imposes an asymmetric penalty that strongly prioritizes avoiding overconfident errors. Using BAS alongside widely used metrics such as ECE and AURC, we then construct a benchmark of self-reported confidence reliability across multiple LLMs and tasks. Our results reveal substantial variation in decision-useful confidence, and while larger and more accurate models tend to achieve higher BAS, even frontier models remain prone to severe overconfidence. Importantly, models with similar ECE or AURC can exhibit very different BAS due to highly overconfident errors, highlighting limitations of standard metrics. We further show that simple interventions, such as top-k confidence elicitation and post-hoc calibration, can meaningfully improve confidence reliability. Overall, our work provides both a principled metric and a comprehensive benchmark for evaluating LLM confidence reliability.

The system log generated in a computer system refers to large-scale data that are collected simultaneously and used as the basic data for determining errors, intrusion and abnormal behaviors. The aim of system log anomaly detection is to promptly identify anomalies while minimizing human intervention, which is a critical problem in the industry. Previous studies performed anomaly detection through algorithms after converting various forms of log data into a standardized template using a parser. Particularly, a template corresponding to a specific event should be defined in advance for all the log data using which the information within the log key may get lost. In this study, we propose LAnoBERT, a parser free system log anomaly detection method that uses the BERT model, exhibiting excellent natural language processing performance. The proposed method, LAnoBERT, learns the model through masked language modeling, which is a BERT-based pre-training method, and proceeds with unsupervised learning-based anomaly detection using the masked language modeling loss function per log key during the test process. In addition, we also propose an efficient inference process to establish a practically applicable pipeline to the actual system. Experiments on three well-known log datasets, i.e., HDFS, BGL, and Thunderbird, show that not only did LAnoBERT yield a higher anomaly detection performance compared to unsupervised learning-based benchmark models, but also it resulted in a comparable performance with supervised learning-based benchmark models.

In the era of large language models, creative writing quality lacks a computable theoretical anchor. The dominant approaches are rubric scoring -- decomposing holistic aesthetic judgment into sub-scores -- and RLHF preference signals -- replacing quality with group votes. Both bypass the statistical structure of the text itself. This paper provides an information-theoretic foundation to fill this gap. We propose 'calibrated surprise' as the information-theoretic essence of excellent creative writing. This judgment matches reading intuition and covers its opposite. This literary judgment admits a precise mathematical formulation. Under full-dimensional constraints Y, feasible writing choices are forced into an extremely narrow space. The rare survivors are, from the unconstrained perspective, exactly the least predictable choices. Both are measured precisely by Shannon mutual information I(X;Y) = H(X) - H(X|Y) -- 'calibrated' corresponds to H(X|Y) approaching 0; 'surprising' corresponds to H(X) going high. The subtraction structure of the formula naturally separates 'well-grounded surprise' from 'pure noise'. We use token-level logprobs from Qwen1.5-7B as an operational proxy for the ideal reader's probability distribution. Across 20 pairs (12 Chinese / 8 English) of high-quality vs. systematically degraded literary passages, 20/20 pairs support the core prediction: high-quality passages have systematically higher I(X;Y) than their degraded versions.

We examine the potential of ChatGPT and other large language models in predicting stock market returns using news headlines. We use ChatGPT to assess whether each headline is good, bad, or neutral for firms' stock prices. We document a significantly positive correlation between ChatGPT scores and subsequent daily stock returns. We find that ChatGPT outperforms traditional sentiment analysis methods. More basic models such as GPT-1, GPT-2, and BERT cannot accurately forecast returns, indicating return predictability is an emerging capacity of complex language models. Long-short strategies based on ChatGPT-4 deliver the highest Sharpe ratio. Furthermore, we find predictability in both small and large stocks, suggesting market underreaction to company news. Predictability is stronger among smaller stocks and stocks with bad news, consistent with limits-to-arbitrage also playing an important role. Finally, we propose a new method to evaluate and understand the models' reasoning capabilities. Overall, our results suggest that incorporating advanced language models into the investment decision-making process can yield more accurate predictions and enhance the performance of quantitative trading strategies.

The proliferation of Large Language Models (LLMs) accessed via black-box APIs introduces a significant trust challenge: users pay for services based on advertised model capabilities (e.g., size, performance), but providers may covertly substitute the specified model with a cheaper, lower-quality alternative to reduce operational costs. This lack of transparency undermines fairness, erodes trust, and complicates reliable benchmarking. Detecting such substitutions is difficult due to the black-box nature, typically limiting interaction to input-output queries. This paper formalizes the problem of model substitution detection in LLM APIs. We systematically evaluate existing verification techniques, including output-based statistical tests, benchmark evaluations, and log probability analysis, under various realistic attack scenarios like model quantization, randomized substitution, and benchmark evasion. Our findings reveal the limitations of methods relying solely on text outputs, especially against subtle or adaptive attacks. While log probability analysis offers stronger guarantees when available, its accessibility is often limited. We conclude by discussing the potential of hardware-based solutions like Trusted Execution Environments (TEEs) as a pathway towards provable model integrity, highlighting the trade-offs between security, performance, and provider adoption. Code is available at https://github.com/sunblaze-ucb/llm-api-audit

We develop a statistical procedure to detect lookahead bias in economic forecasts generated by large language models (LLMs). Using a date-only recall query for a firm-date pair, we estimate the probability that the LLM has internalized information about the realized outcome, a statistic we term Lookahead Propensity (LAP). LAP is materially positive throughout the in-sample period and collapses essentially to zero right after the training-data cutoff. We show that a positive interaction between LAP and the LLM forecast in an accuracy regression indicates lookahead-bias contamination, and apply the test to two forecasting tasks: news headlines predicting stock returns and earnings call transcripts predicting capital expenditures. In both applications, the LLM forecast's predictive power is amplified on high-LAP firm-date pairs, and the interaction loses significance on post-training-cutoff samples. Our test provides a cost-efficient, diagnostic tool for assessing the validity and reliability of LLM-generated forecasts.

We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise. We provide a sharp analysis of the classical follow-the-regularized-leader (FTRL) algorithm to cope with the label noise. More specifically, for sigma-sub-Gaussian label noise, our analysis provides a regret upper bound of O(sigma^2 d log T) + o(log T), where d is the dimension of the input vector, T is the total number of rounds. We also prove a Omega(sigma^2dlog(T/d)) lower bound for stochastic online linear regression, which indicates that our upper bound is nearly optimal. In addition, we extend our analysis to a more refined Bernstein noise condition. As an application, we study generalized linear bandits with heteroscedastic noise and propose an algorithm based on FTRL to achieve the first variance-aware regret bound.

Crash datasets that carry an investigator narrative hold information the coded fields omit. Coding those narratives at scale has been blocked by three obstacles. Frontier large language models are costly at that scale, their generated text cannot be verified, and no rule says how much output a human must check. This paper formulates narrative coding as gated, typed decisions answered by Jev, a System One model that returns probabilities over analyst-defined options and generates no text. A screen covered 499,500 Texas narratives and 195,857 were coded with a 27-question schema. Cost is governed by schema size rather than narrative length. The probabilities are audited against coded fields and against 2,416 blinded human judgments drawn under a stated sampling design. Two frontier large language models are benchmarked on the same records. Against human labels the typed model attains an F1 of 0.908. One frontier model gains 0.059 and the other is indistinguishable from it. Calibration varies by model rather than by paradigm, so each model must be audited. Recalibration on the same labels reduces calibration error by a factor of 3.3. Agreement with coded fields understates fidelity to the narrative by a median of 0.26 in kappa. A resolution-floor bound covers any model that reports probabilities on a discrete grid. A review budget over flagged records gives the records a human must read per variable and per year. Adding the calibrated variables to the coded fields raises the injury and fatal crashes attributed to nine factors by 10,747 per year.

The output structure of database-like tables, consisting of values structured in horizontal rows and vertical columns identifiable by name, can cover a wide range of NLP tasks. Following this constatation, we propose a framework for text-to-table neural models applicable to problems such as extraction of line items, joint entity and relation extraction, or knowledge base population. The permutation-based decoder of our proposal is a generalized sequential method that comprehends information from all cells in the table. The training maximizes the expected log-likelihood for a table's content across all random permutations of the factorization order. During the content inference, we exploit the model's ability to generate cells in any order by searching over possible orderings to maximize the model's confidence and avoid substantial error accumulation, which other sequential models are prone to. Experiments demonstrate a high practical value of the framework, which establishes state-of-the-art results on several challenging datasets, outperforming previous solutions by up to 15%.

Wu et al. (2026) showed that most frontier large language models (LLMs) recommend a sponsored, roughly twice-as-expensive flight when their system prompt contains a soft sponsorship cue. We reproduce their evaluation on ten open-weight chat models plus the two of their twenty-three models that are still reachable today (gpt-3.5-turbo, gpt-4o). All reported rates in this paper are produced under the same judge the original paper used (gpt-4o); we additionally store every label under an open-weight (gpt-oss-120b) and a smaller proprietary (gpt-4o-mini) judge for an ablation. Three findings emerge. First, a prose description of an LLM evaluation pipeline is not, on its own, sufficient for accurate reproduction: we surfaced three silent implementation failures that each shifted a reported rate by tens of percentage points. Second, the central claims do generalise - the gpt-3.5-turbo logistic-regression intercept of alpha = 0.81 is within four points of the original alpha = 0.86, and 200 of 200 trials on gpt-3.5-turbo and gpt-4o promote a payday lender to a financially distressed user. Third, a thirty-token user prompt that asks the assistant for a neutral comparison table first cuts sponsored recommendation from 46.9% to 1.0% averaged across our ten open-source models, and from 53.0% to 0% averaged across the two OpenAI models. AI literacy and price-comparison portals are likely market-level mitigations; the harmful-product cell is bounded by neither. Raw data, labels and analysis scripts are at https://github.com/akmaier/Paper-LLM-Ads .

In this paper, we investigate the influence of claims in analyst reports and earnings calls on financial market returns, considering them as significant quarterly events for publicly traded companies. To facilitate a comprehensive analysis, we construct a new financial dataset for the claim detection task in the financial domain. We benchmark various language models on this dataset and propose a novel weak-supervision model that incorporates the knowledge of subject matter experts (SMEs) in the aggregation function, outperforming existing approaches. We also demonstrate the practical utility of our proposed model by constructing a novel measure of optimism. Here, we observe the dependence of earnings surprise and return on our optimism measure. Our dataset, models, and code are publicly (under CC BY 4.0 license) available on GitHub.

Probabilistic models are typically trained using task-agnostic objectives like log-loss, which can lead to significant errors in downstream estimation. This disconnect is especially critical in Inverse Probability Weighting (IPW) for causal inference, where propensity score errors near 0 and 1 often lead to high bias and variance. We propose a principled framework for deriving task-specific strictly proper scoring rules by matching the local curvature of the downstream error metric. We apply this to the Average Treatment Effect (ATE) estimation, deriving a closed-form loss and its corresponding canonical probability mapping that can be readily integrated with any model like a neural network or a gradient boosting algorithm. Extensive evaluations on causal inference benchmarks demonstrate that our tailored objective consistently outperforms standard likelihood-based and covariate-balancing approaches.

Verifying the provenance of content is crucial to the function of many organizations, e.g., educational institutions, social media platforms, firms, etc. This problem is becoming increasingly difficult as text generated by Large Language Models (LLMs) becomes almost indistinguishable from human-generated content. In addition, many institutions utilize in-house LLMs and want to ensure that external, non-sanctioned LLMs do not produce content within the institution. In this paper, we answer the following question: Given a piece of text, can we identify whether it was produced by LLM A or B (where B can be a human)? We model LLM-generated text as a sequential stochastic process with complete dependence on history and design zero-shot statistical tests to distinguish between (i) the text generated by two different sets of LLMs A (in-house) and B (non-sanctioned) and also (ii) LLM-generated and human-generated texts. We prove that the type I and type II errors for our tests decrease exponentially in the text length. In designing our tests, we derive concentration inequalities on the difference between log-perplexity and the average entropy of the string under A. Specifically, for a given string, we demonstrate that if the string is generated by A, the log-perplexity of the string under A converges to the average entropy of the string under A, except with an exponentially small probability in string length. We also show that if B generates the text, except with an exponentially small probability in string length, the log-perplexity of the string under A converges to the average cross-entropy of B and A. Lastly, we present preliminary experimental results to support our theoretical results. By enabling guaranteed (with high probability) finding of the origin of harmful LLM-generated text with arbitrary size, we can help combat misinformation.

Financial return forecasting is a difficult test case for time-series foundation models (TSFMs) due to low signal-to-noise ratios, structural breaks, heavy tails, and weak persistence. This paper benchmarks pretrained TSFMs against train-from-scratch neural baselines in a deliberately conservative financial setting. We evaluate TimeGPT/TimeGPT-LH, TimesFM-2.5, Moirai-2.0, Chronos, and Chronos-2 against NBEATS, NHITS, PatchTST, iTransformer, and KAN on five liquid U.S. equities (AAPL, AMZN, GOOG, JPM, META) using linear and log returns. Models are compared under an equalized context budget, a rolling-origin protocol, and against random-walk benchmarks. We provide a theoretical framing of pretraining as an inductive prior, linking PAC-Bayes transfer intuition, information-theoretic predictability limits, and attention geometry. This clarifies why strong model rankings need not imply economically meaningful predictability in noisy markets. Pragmatically, pretrained TSFMs dominate the ranking distribution, accounting for 8 of 10 task-level wins. Moirai-2.0 and TimesFM-2.5 achieve the strongest average ranks, leading tasks for AAPL, JPM, GOOG, and AMZN, while Chronos wins the remaining AMZN task. However, the iTransformer baseline wins both META tasks, showing local supervised learning can still outperform generic pretraining for specific assets. Crucially, gains over the random-walk benchmark are small and sparse. A one-sided Diebold-Mariano test rejects equal or inferior predictive accuracy only for Chronos on AMZN and Moirai-2.0 on GOOG. We conclude that TSFMs serve as useful practical priors that reduce model-development costs in low-data financial forecasting, but are not universal engines for statistically reliable alpha generation in realistic empirical deployment.

Gradient descent has proven to be a powerful and effective technique for optimization in numerous machine learning applications. Recent advances in computational neuroscience have shown that learning in standard gradient descent optimization formulation is not consistent with learning in biological systems. This has opened up interesting avenues for building biologically inspired learning techniques. One such approach is inspired by Dale's law, which states that inhibitory and excitatory synapses do not swap roles during the course of learning. The resulting exponential gradient descent optimization scheme leads to log-normally distributed synaptic weights. Interestingly, the density that satisfies the Fokker-Planck equation corresponding to the stochastic differential equation (SDE) with geometric Brownian motion (GBM) is the log-normal density. Leveraging this connection, we start with the SDE governing geometric Brownian motion, and show that discretizing the corresponding reverse-time SDE yields a multiplicative update rule, which surprisingly, coincides with the sampling equivalent of the exponential gradient descent update founded on Dale's law. Furthermore, we propose a new formalism for multiplicative denoising score-matching, subsuming the loss function proposed by Hyvaerinen for non-negative data. Indeed, log-normally distributed data is positive and the proposed score-matching formalism turns out to be a natural fit. This allows for training of score-based models for image data and results in a novel multiplicative update scheme for sample generation starting from a log-normal density. Experimental results on MNIST, Fashion MNIST, and Kuzushiji datasets demonstrate generative capability of the new scheme. To the best of our knowledge, this is the first instance of a biologically inspired generative model employing multiplicative updates, founded on geometric Brownian motion.

Large language models (LLMs) are increasingly deployed in high-stakes domains, where rare but severe failures can result in irreversible harm. However, prevailing evaluation benchmarks often reduce complex social risk to mean-centered scalar scores, thereby obscuring distributional structure, cross-dimensional interactions, and worst-case behavior. This paper introduces Social Harm Analysis via Risk Profiles (SHARP), a framework for multidimensional, distribution-aware evaluation of social harm. SHARP models harm as a multivariate random variable and integrates explicit decomposition into bias, fairness, ethics, and epistemic reliability with a union-of-failures aggregation reparameterized as additive cumulative log-risk. The framework further employs risk-sensitive distributional statistics, with Conditional Value at Risk (CVaR95) as a primary metric, to characterize worst-case model behavior. Application of SHARP to eleven frontier LLMs, evaluated on a fixed corpus of n=901 socially sensitive prompts, reveals that models with similar average risk can exhibit more than twofold differences in tail exposure and volatility. Across models, dimension-wise marginal tail behavior varies systematically across harm dimensions, with bias exhibiting the strongest tail severities, epistemic and fairness risks occupying intermediate regimes, and ethical misalignment consistently lower; together, these patterns reveal heterogeneous, model-dependent failure structures that scalar benchmarks conflate. These findings indicate that responsible evaluation and governance of LLMs require moving beyond scalar averages toward multidimensional, tail-sensitive risk profiling.

Point-adjustment (PA), for years the default scoring protocol in time-series anomaly detection (TSAD), was shown by Kim et al. (2022) to award near-perfect F1 to random anomaly scores. The field adopted a suite of replacement metrics (PA%K, range-based precision/recall, affiliation precision/recall, and Volume-Under-the-Surface, VUS, ROC/PR). We ask, independently and adversarially, whether these resist no-skill detectors on real benchmarks, and find the answer turns entirely on one overlooked variable: N, the number of random attempts an adversary reports the best of. Under a single honest run (N=1), not one replacement metric is gameable on any of six benchmarks (UCR, SMD, SMAP, MSL, NAB, PSM): a random detector reaches 90% of the best real detector's score on at most 11% of series for affiliation-F1, 5% for the ROC family, and 2% for the PR-based metrics and PA%K. But under best-of-N reporting, the seed-shopping endemic to ML, the metrics split sharply. affiliation-F1 and every ROC-based metric inflate steeply, affiliation crossing gameable (25% of series) by N=3 and reaching 0.98 at the full pool (N=41), the ROC family crossing by N=9-11; the PR-based metrics and PA%K stay near-flat at every N, floored near the anomaly prevalence (the lone exception is NAB at large N). A paired test finds VUS-ROC inflated on 131 series where its sibling VUS-PR is not, and never the reverse. The ROC-vs-PR split follows from the order-statistic behaviour of AUC under extreme class imbalance (a random PR-AUC is floored at prevalence); affiliation inflates by a second route, its extreme single-run leniency (already fragile at N=1). We release a pip-installable stress-test harness, and recommend reporting single-run scores or disclosing N and preferring PR-based metrics, which resist best-of-N inflation on nearly every benchmark.

This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

Predicting trends in stock market prices has been an area of interest for researchers for many years due to its complex and dynamic nature. Intrinsic volatility in stock market across the globe makes the task of prediction challenging. Forecasting and diffusion modeling, although effective can't be the panacea to the diverse range of problems encountered in prediction, short-term or otherwise. Market risk, strongly correlated with forecasting errors, needs to be minimized to ensure minimal risk in investment. The authors propose to minimize forecasting error by treating the forecasting problem as a classification problem, a popular suite of algorithms in Machine learning. In this paper, we propose a novel way to minimize the risk of investment in stock market by predicting the returns of a stock using a class of powerful machine learning algorithms known as ensemble learning. Some of the technical indicators such as Relative Strength Index (RSI), stochastic oscillator etc are used as inputs to train our model. The learning model used is an ensemble of multiple decision trees. The algorithm is shown to outperform existing algo- rithms found in the literature. Out of Bag (OOB) error estimates have been found to be encouraging. Key Words: Random Forest Classifier, stock price forecasting, Exponential smoothing, feature extraction, OOB error and convergence.

The fluency and factual knowledge of large language models (LLMs) heightens the need for corresponding systems to detect whether a piece of text is machine-written. For example, students may use LLMs to complete written assignments, leaving instructors unable to accurately assess student learning. In this paper, we first demonstrate that text sampled from an LLM tends to occupy negative curvature regions of the model's log probability function. Leveraging this observation, we then define a new curvature-based criterion for judging if a passage is generated from a given LLM. This approach, which we call DetectGPT, does not require training a separate classifier, collecting a dataset of real or generated passages, or explicitly watermarking generated text. It uses only log probabilities computed by the model of interest and random perturbations of the passage from another generic pre-trained language model (e.g, T5). We find DetectGPT is more discriminative than existing zero-shot methods for model sample detection, notably improving detection of fake news articles generated by 20B parameter GPT-NeoX from 0.81 AUROC for the strongest zero-shot baseline to 0.95 AUROC for DetectGPT. See https://ericmitchell.ai/detectgpt for code, data, and other project information.

We study the classic Text-to-Pattern Hamming Distances problem: given a pattern P of length m and a text T of length n, both over a polynomial-size alphabet, compute the Hamming distance between P and T[i, ., . , i+m-1] for every shift i, under the standard Word-RAM model with Theta(log n)-bit words. - We provide an O(nm) time Las Vegas randomized algorithm for this problem, beating the decades-old O(n m log m) running time [Abrahamson, SICOMP 1987]. We also obtain a deterministic algorithm, with a slightly higher O(nm(log mloglog m)^{1/4}) running time. Our randomized algorithm extends to the k-bounded setting, with running time Obig(n+nk{m}big), removing all the extra logarithmic factors from earlier algorithms [Gawrychowski and Uzna\'{n}ski, ICALP 2018; Chan, Golan, Kociumaka, Kopelowitz and Porat, STOC 2020]. - For the (1+epsilon)-approximate version of Text-to-Pattern Hamming Distances, we give an O(epsilon^{-0.93}n) time Monte Carlo randomized algorithm, beating the previous O(epsilon^{-1}n) running time [Kopelowitz and Porat, FOCS 2015; Kopelowitz and Porat, SOSA 2018]. Our approximation algorithm exploits a connection with 3SUM, and uses a combination of Fredman's trick, equality matrix product, and random sampling; in particular, we obtain new results on approximate counting versions of 3SUM and Exact Triangle, which may be of independent interest. Our exact algorithms use a novel combination of hashing, bit-packed FFT, and recursion; in particular, we obtain a faster algorithm for computing the sumset of two integer sets, in the regime when the universe size is close to quadratic in the number of elements. We also prove a fine-grained equivalence between the exact Text-to-Pattern Hamming Distances problem and a range-restricted, counting version of 3SUM.

Cricket, "a Gentleman's Game", is a prominent sport rising worldwide. Due to the rising competitiveness of the sport, players and team management have become more professional with their approach. Prior studies predicted individual performance or chose the best team but did not highlight the batter's potential. On the other hand, our research aims to evaluate a player's impact while considering his control in various circumstances. This paper seeks to understand the conundrum behind this impactful performance by determining how much control a player has over the circumstances and generating the "Effective Runs",a new measure we propose. We first gathered the fundamental cricket data from open-source datasets; however, variables like pitch, weather, and control were not readily available for all matches. As a result, we compiled our corpus data by analyzing the commentary of the match summaries. This gave us an insight into the particular game's weather and pitch conditions. Furthermore, ball-by-ball inspection from the commentary led us to determine the control of the shots played by the batter. We collected data for the entire One Day International career, up to February 2022, of 3 prominent cricket players: Rohit G Sharma, David A Warner, and Kane S Williamson. Lastly, to prepare the dataset, we encoded, scaled, and split the dataset to train and test Machine Learning Algorithms. We used Multiple Linear Regression (MLR), Polynomial Regression, Support Vector Regression (SVR), Decision Tree Regression, and Random Forest Regression on each player's data individually to train them and predict the Impact the player will have on the game. Multiple Linear Regression and Random Forest give the best predictions accuracy of 90.16 percent and 87.12 percent, respectively.

Operational telemetry can be jointly anomalous while every individual stream stays inside its familiar range. TRACE-C is an auditable strictly-prior rank-calibrated detector for aligned multi-stream telemetry: same-regime rolling median/MAD residuals feed three window channels -- a maximum normalized local sum, a Gaussian copula-form dependence contrast on robust-z residuals, and a worst standardized AR(1) innovation -- whose channel ranks are Fisher-aggregated and ranked against earlier aggregates. We evaluate six Great Britain grid streams with a January-April 2019 fit, July-December 2019 development evidence, and a 2020 hold-out frozen before inspection. TRACE-C ranks Storm Atiyah first among 2019 test windows, but a disclosed channel ablation attributes that rank to the local channel, not the copula-form channel: copula-only ranks Atiyah 59th. The short 9 August frequency event is ranked far lower by the fused detector (143) than by the temporal channel alone (40), and reconstruction baselines rank it first. In 2020 no window is selected, which is consistent with record-rule saturation rather than an uneventful year; the highest-ranked frozen window was later interpreted as Storm Ellen. Three interpretive limits carry throughout. The resulting p-values are selection quantities, not event probabilities. The copula-form channel is not a literal copula density: the method applies no probability-integral or normal-score transform. Empirical rank counts are diagnostics, not coverage or false-discovery proofs. Every table and figure in this paper is generated from committed machine-readable reports.

Detecting anomalous events in online computer systems is crucial to protect the systems from malicious attacks or malfunctions. System logs, which record detailed information of computational events, are widely used for system status analysis. In this paper, we propose LogBERT, a self-supervised framework for log anomaly detection based on Bidirectional Encoder Representations from Transformers (BERT). LogBERT learns the patterns of normal log sequences by two novel self-supervised training tasks and is able to detect anomalies where the underlying patterns deviate from normal log sequences. The experimental results on three log datasets show that LogBERT outperforms state-of-the-art approaches for anomaly detection.

Machine learning classifiers for bearing fault detection produce scalar confidence scores that conflate confident errors with genuinely ambiguous predictions, and the conventional truth/falsity pair (F = 1 - T) is algebraically redundant by construction. We operationalize a refined neutrosophic decomposition of a Random Forest + XGBoost + Logistic Regression ensemble into four indicators -- T-hat (top-class evidence), F-hat (best-competitor evidence), predictive entropy I1-hat, and decision disagreement I2-hat -- evaluated on two bearing benchmarks (CWRU and JNU, 600-1000 rpm) under a leave-one-condition-out protocol. On CWRU, after correcting a file-to-class mapping error, the ensemble reaches 100.00 percent accuracy on three of four held-out loads (92.27 percent on the fourth), leaving too few errors for uncertainty analysis. On JNU, holding out 1000 rpm, accuracy collapses to 40.64 percent, below a majority-class baseline; Logistic Regression (57.91 percent) generalizes far better than the tree ensembles. I1-hat shows a robust association with error beyond T-hat/F-hat, while I2-hat contributes little; standalone Logistic Regression confidence outperforms the full decomposition, a boundary condition we report honestly. Two further results extend this: fusing a time-domain and a frequency-domain model of the same signal and scoring their Jensen-Shannon divergence beats that model own entropy (AURC 0.29 vs. 0.36 on the standard split; 0.54 vs. 0.73 under a harder single-condition reproduction), the only indicator moving correctly under a CWRU-versus-JNU distributional-shift contrast; and, on CWRU alone, literature-verified bearing fault frequencies, correctly demodulated via the envelope spectrum, separate most fault classes almost perfectly (99.57 percent) using three interpretable features. Code, logs, and figures are released for independent verification.

Knowing domain rules does not guarantee applying them to a case. We study this distinction in traditional Chinese Bazi through 3,000 Chinese multiple-choice questions spanning 14 Theory and 11 Case categories. Six endpoint systems are evaluated, with primary results reported on a 2,492-item model-informed refinement. Theory accuracy exceeds Case accuracy for every system, and gaps of 16.60-29.56 percentage points remain when invalid responses are excluded. The contrast is more specific than a general case-reasoning deficit. Across six systems, Twelve Stages and Nayin reach mean accuracies of 89.10% and 88.62%, while Shensha Basics reaches 75.96%. Within Case, Luck Pillars averages 84.62%, but Career and Family Relations average only 36.98% and 38.19%. Overall rankings also conceal different category strengths. On the original 3,000 items, paired DeepSeek native/disabled comparisons associate native configurations with Theory gains of 6.53 and 12.20 points for Flash and Pro, respectively; Case changes are -3.67 and +1.27 points. These are provider-configuration associations, not isolated causal effects of reasoning. The results motivate task-specific evaluation of cultural-domain applications rather than reliance on aggregate knowledge scores. The benchmark measures agreement with a model-generated, model-verified answer key, not real-world predictive validity. Final-set results are post-selection descriptions, and incomplete provenance and expert validation constrain their interpretation.

The Growth-at-Risk (GaR) framework has garnered attention in recent econometric literature, yet current approaches implicitly assume a constant Pareto exponent. We introduce novel and robust econometrics to estimate the tails of GaR based on a rigorous theoretical framework and establish validity and effectiveness. Simulations demonstrate consistent outperformance relative to existing alternatives in terms of predictive accuracy. We perform a long-term GaR analysis that provides accurate and insightful predictions, effectively capturing financial anomalies better than current methods.

Current question-answering benchmarks predominantly focus on accuracy in realizable prediction tasks. Conditioned on a question and answer-key, does the most likely token match the ground truth? Such benchmarks necessarily fail to evaluate LLMs' ability to quantify ground-truth outcome uncertainty. In this work, we focus on the use of LLMs as risk scores for unrealizable prediction tasks. We introduce folktexts, a software package to systematically generate risk scores using LLMs, and evaluate them against US Census data products. A flexible API enables the use of different prompting schemes, local or web-hosted models, and diverse census columns that can be used to compose custom prediction tasks. We evaluate 17 recent LLMs across five proposed benchmark tasks. We find that zero-shot risk scores produced by multiple-choice question-answering have high predictive signal but are widely miscalibrated. Base models consistently overestimate outcome uncertainty, while instruction-tuned models underestimate uncertainty and produce over-confident risk scores. In fact, instruction-tuning polarizes answer distribution regardless of true underlying data uncertainty. This reveals a general inability of instruction-tuned LLMs to express data uncertainty using multiple-choice answers. A separate experiment using verbalized chat-style risk queries yields substantially improved calibration across instruction-tuned models. These differences in ability to quantify data uncertainty cannot be revealed in realizable settings, and highlight a blind-spot in the current evaluation ecosystem that folktexts covers.

CI failure logs are large (median 5k lines, max 200k in this corpus) and noisy. Coding agents that try to debug them depend on an upstream tool to reduce the log to a manageable context, but the field has had no public empirical comparison of which reductions preserve enough evidence for downstream LLM diagnosis. We introduce LogDx-CI, a benchmark that compares 11 context-reduction tools (raw, tail, grep, three RTK modes, two real LLM map-reduce summarizers, three hybrid routers) on 35 real GitHub Actions failure cases, scored by 3 LLM debugger families (Claude Haiku 4.5, Claude Sonnet 4.6, OpenAI gpt-5-mini) plus a Sonnet 4.6 tool-using agent. We report three load-bearing findings. (1)~Hybrid grep+tail routers dominate the cost-quality Pareto frontier; the top two methods score 0.670 / 0.666 at sim \0.03 per case, same-ballpark quality as standalone grep at 4.5\times fewer tokens. (2)~In the agent-loop regime, the quality range across reduction tools collapses 7\times (single-shot spread 0.42 \to agent-loop spread 0.059); the agent rescues weak contexts via follow-up tool calls. However, cost differences persist: weak contexts force the agent to issue 2--4\times more tool calls to recover. (3)~A cross-family LLM-summary pair (gpt-5-mini summarizer feeding a Claude Haiku debugger) beats the same-family pair by +0.071 averaged across four diagnoser variants, falsifying the self-call-bias hypothesis on this task. The gpt-5-mini summarizer is also the agent-loop #1 method (score 0.749) at 0.37 tool-calls per case and 10\times lower reducer cost than the Haiku summarizer (0.18 vs \$1.75 per case). All data, code, per-case bundles, and reproducibility infrastructure are public.

The widespread adoption of large language models (LLMs) makes it important to recognize their strengths and limitations. We argue that in order to develop a holistic understanding of these systems we need to consider the problem that they were trained to solve: next-word prediction over Internet text. By recognizing the pressures that this task exerts we can make predictions about the strategies that LLMs will adopt, allowing us to reason about when they will succeed or fail. This approach - which we call the teleological approach - leads us to identify three factors that we hypothesize will influence LLM accuracy: the probability of the task to be performed, the probability of the target output, and the probability of the provided input. We predict that LLMs will achieve higher accuracy when these probabilities are high than when they are low - even in deterministic settings where probability should not matter. To test our predictions, we evaluate two LLMs (GPT-3.5 and GPT-4) on eleven tasks, and we find robust evidence that LLMs are influenced by probability in the ways that we have hypothesized. In many cases, the experiments reveal surprising failure modes. For instance, GPT-4's accuracy at decoding a simple cipher is 51% when the output is a high-probability word sequence but only 13% when it is low-probability. These results show that AI practitioners should be careful about using LLMs in low-probability situations. More broadly, we conclude that we should not evaluate LLMs as if they are humans but should instead treat them as a distinct type of system - one that has been shaped by its own particular set of pressures.