Science & Mathematics

BACKGROUND: After a software incident, organizations attempt to improve the reliability of their software systems by conducting post-incident analysis and identifying actions to prevent or mitigate similar future incidents. Despite the importance of this activity, there is a limited understanding of the nature and characteristics of the software evolution triggered by the analysis process. AIMS: This study seeks to bridge this gap by providing the first empirical characterization of post-incident software evolution. We aim to establish an understanding of how these changes manifest, specifically focusing on how their characteristics (such as effort, location, and timing) differ from standard maintenance and evolutionary changes. METHOD: We conducted a mixed-methods analysis of a 10-year longitudinal dataset from Wikimedia, examining 1,302 tasks and 2,203 code reviews. We categorized these changes across five dimensions: target, effort, abandonment rate, prioritization, and time-to-resolve. RESULTS: Our results show that the post-incident evolution is distinct from other change types. Post-incident changes are more time-consuming, with a median completion time over twice that of other changes and are disproportionately concentrated in a server configuration repository. CONCLUSION: By identifying a few of the characteristics of post-incident evolution, this work provides a foundation for future research into reliability engineering and learning from failure. We highlight further avenues for exploration necessary to fully understand post-incident evolution. Lastly, our work enables researchers to move beyond high-level analysis and begin developing specialized methods and tooling tailored to the nature of post-incident evolution.

AI coding agents now contribute to software repositories at scale, yet their documentation practices remain uncharacterised. We analyse 29,669 AI-generated pull requests from 2,585 repositories in the AIDev dataset, measuring documentation co-change: whether code-file modifications are accompanied by a documentation-file update in the same PR. We find that 63.2% of AI PRs change code without updating any documentation. This varies sharply by task type: 55.2% for features and 77.5% for refactoring. Undocumented code files are followed by a fix to the same file 8.6 to 11.7% more often than documented files across 30 to 90-day windows. A raw PR-level comparison shows the opposite because documented PRs are 3.9 times larger and therefore attract more fixes. Controlling for size exposure reverses this result. Documented changes also merge faster despite their larger size (median: 40 seconds versus 184 seconds), although merging is largely automated in this dataset. Documentation drift also compounds: within 90 days, a file changed without documentation is later re-documented at roughly half the rate of a file changed with documentation (24% versus 48%). This suggests that documentation debt tends to accumulate rather than be revisited.

Finding vulnerabilities early, before they can affect the production system, is important for reducing the risk of any software attacks. However, detecting vulnerabilities during secure code review is still difficult because the vulnerable code logic may depend on lines found across different repository files. Recent approaches such as AgenticSCR have shown that LLM agents can explore repository files and use security knowledge to improve secure code review. However, these approaches mainly rely on external commercial LLMs and can provide a large amount of security knowledge to the agent at once. This creates an important question of whether agentic secure code review can also be performed effectively using locally deployed open-weight LLMs with more focused and relevant security knowledge. In this paper, we propose AgenticVulHunter, an agentic secure code review approach and tool that can run with a locally deployed open-weight LLM. We evaluate AgenticVulHunter on 144 vulnerability cases from SCRBench using Qwen3-Coder-30B and DeepSeek V3.1 Terminus. We measure what percentage of generated review comments correctly identify the vulnerable location, match the vulnerability type, and provide a relevant security review comment together. AgenticVulHunter achieves an accuracy of 18.4% with Qwen3- Coder-30B and 23.8% with DeepSeek V3.1 Terminus, compared with 11.8% for our AgenticSCR-style reproduction using Qwen3-Coder-30B and 17.5% for AgenticSCR using Claude Sonnet 4.

We analytically study the evolution of the energy function of Dense Associative Memories (DenseAMs) as they train on randomly sampled codewords of random expander low-density parity-check codes (a.k.a. solutions of random XORSAT problems). We identify two distinct regimes and a transition between them, reminiscent of grokking in neural networks. A regime of small training set size is where the model memorizes a few training examples but cannot discover the underlying rules of the entire codeword dictionary generative process. The opposite regime, corresponding to a larger training set size, is where the model has uncovered the sparse constraints that generated the entire data set after seeing only polynomially many patterns. We also design a novel class of DenseAMs with a thresholding learning rule, and show that any amount of thresholding enables the model to perform simplified sparse Hamiltonian learning, which exponentially reduces the number of training examples needed to learn the true underlying data set. In this regime, the model learns how to discover $\exp[\mathrm{O}(n)]$ solutions from only $\mathrm{O}(\log n)$ training samples, which is asymptotically optimal for any learning algorithm. When training on codewords of certain random codes, the model can even learn the underlying code when a small O(1) fraction of bits are latent variables. These latent variables are not shown to the model during learning, but will be discovered by sparsifying observed higher-order correlations. For certain random codes, we show that a simple and conservative algorithm learns a minimal latent representation for the data set. This provides a transparent, physics-motivated, and analytically tractable toy model for how deep latent representations emerge in an associative memory training.

We study turn-based deterministic zero-sum games with discounted and long-run average costs. For discounted costs, we establish exponential and superpolynomial iteration lower bounds for the simple strategy-iteration method with Dantzig's rule under unrestricted costs and unit weights, respectively. To the best of our knowledge, this shows for the first time that the method is not strongly polynomial even when all action costs belong to $\{-1,0,1\}$. For long-run average costs, we establish an exponential iteration lower bound for termination of a Dantzig counterpart with unrestricted costs and prove that it admits a strongly polynomial implementation with unit weights.

Variance reduction techniques improve the efficiency of drawing conclusions from data. Recent proposals for variance-reduction use two complementary techniques to reduce variance: incorporating machine learning predictions into estimators and weighted sampling. A popular weighted sampling algorithm is Poisson Sampling (PS), which independently flips a biased coin at each unit and includes all heads in the sample. A fundamental flaw with PS is that it has a random sample size, which presents practical challenges and introduces variance into the estimator. We show that a fixed-size alternative, known in survey sampling as Conditional Poisson Sampling (CPS), is a drop-in replacement for PS on general multivariate Z-estimation problems, which include convex M-estimation considered in prior work. Notably, we show that the asymptotic variance of CPS is no worse than that of PS, and can be substantially better in realistic scenarios where predictions are imperfect. We illustrate these advantages on both synthetic and real datasets, and release a Python package implementing CPS. In light of our contributions, there is no need to suffer a variable sample size.

Urban park accessibility shapes mental health, physical well-being, and community cohesion. Measuring it is thus central to urban and landscape planning. Although researchers have debated the impacts of different accessibility measures on analysis results, scant attention has been paid to variability from data source selection. Do the results of accessibility analyses vary depending on the dataset used to define park locations and attributes? We compare four widely used geospatial data sources - OpenStreetMap, Esri, SafeGraph, and The Trust for Public Land - by validating their data and measuring park access across two cities. These datasets purport to cover the same spatial features, but our findings reveal wide discrepancies in accessibility results, driven by differences in dataset completeness, coverage, and accuracy between the sources. We provide guidelines for selecting and carefully validating data for accessibility analyses, as these decisions directly impact the accuracy and equity of downstream urban park planning and decision-making.

Mechanistic interpretability asks which language model components matter for a behavior, and activation patching answers by changing one component's activation and measuring its effect, at a cost growing with components and prompts. Attribution patching estimates these effects from one gradient pass, but its estimates can be far off, and verifying each one restores the cost. Can the structure of these errors reduce this cost? We propose Guided-AP, which uses a few exact measurements to reveal attribution patching's errors and correct unmeasured estimates. On a single prompt, many components' errors share one sign, so a small exact sample yields one correction for the rest. Over many prompts of one task, components are misestimated similarly, so a few measured prompts show what to verify and how to correct each component's average effect. Our analysis shows that choosing what to verify needs error size, while correction also needs sign. On a single prompt, the correction lowers error by up to 26% across three behaviors at the compute of verifying the largest estimates and also on larger models. Over many prompts, learned corrections cut the error of average effects on factual completion by 75% to 79%, repaying their cost in long analyses.

For Black women in the mathematical sciences, histories have frequently been fragmented or omitted from official records, an absence that itself constitutes a form of exclusion. This project addresses this critical gap by constructing a curated dataset of 147 Black women who have earned doctoral degrees in mathematics and related mathematical sciences in the United States. By integrating archival research, institutional records, digital databases, and community knowledge, we establish a reproducible methodology for identifying, verifying, and documenting Black women mathematicians. We situate this dataset within a broader history of efforts to document Black mathematicians and describe how prior archival and community based initiatives informed its development. We then demonstrate the utility of the dataset through exploratory analyses of doctoral production, institutional pathways, undergraduate preparation, mentorship networks, and research areas. This revealed patterns including large concentrations of doctoral production among a small number of institutions and advisors. Additionally, our analysis highlights the vital role of Historically Black Colleges and Universities (HBCUs) in preparing Black women who have earned doctoral degrees in the mathematical sciences. By transforming historical documentation into structured research infrastructure, this work provides a foundation for future investigations of mathematical communities using historical as well as mathematical, statistical, and computational methods. More broadly, the framework developed here offers a model for constructing datasets that support the study of underrepresented communities within the mathematical sciences.

Learned post-training quantization (PTQ) calibration fits quantizer parameters on a small calibration set, and for a text embedder the natural supervision is retrieval relevance. We ask two questions that are usually conflated: how far to calibrate, and whether to calibrate at all. Across three embedders (e5-base-v2, BGE-M3, EmbeddingGemma-300m) at 4-bit weight quantization, 161 calibration runs, the outcome of a fixed procedure ranges from a gain to catastrophic degradation, and the driver is the dose of the update, measured as the functional displacement D_func of the quantized model from its uncalibrated start. On EmbeddingGemma the same learning-rate grid gives +1.47 to -71.53 points of in-domain NDCG@10 change; a label-free cosine objective collapses at the same dose (-69.52 vs -71.63), so the collapse is a property of learnable calibration rather than of retrieval supervision. Objective sensitivity is heterogeneous: on e5, ranking calibration is substantially more robust than cosine at matched displacement (+14.16 +/- 4.34 pp, 95% t-CI [+3.37, +24.96], three paired slates), whereas on BGE-M3 the ordering is directionally opposite but unresolved ([-5.18, +2.38]). Dose is the main axis but not a sufficient statistic: equal D_func reached along different paths differs by up to 1.61 pp. We therefore treat calibration as an optional intervention. A pre-registered rule that accepts a checkpoint only when a per-query paired confidence interval on a 25% calibration-validation split clears the uncalibrated baseline was run on 6 independent slates and five arms. It never selected a checkpoint below its slate's baseline (0 harmful selections in 30 decisions), retained 8 of 11 beneficial updates, and paid a mean oracle regret of 1.52 pp with one abstention that forfeited 11.13 pp, a safety-opportunity trade-off, not a free improvement. We report what remains open, including label efficiency.

Probabilities of causation (PoCs) have developed steadily, from the binary measures first introduced by Pearl to the non-binary setting recently studied by Shu et al. As the theory has matured, PoCs have found applications in a growing range of areas, including personalized medicine, marketing and legal attribution. Shu et al. proposed closed-form bounds for multi-valued treatments and outcomes and proved them valid, but left their sharpness in high dimensions open. We close this gap with a mathematical proof. We further show that $\PNS$, $\PSub$, $\PRep$ and $\PN$ are all special cases of a single, more general formula. Combined with their equivalence classes, this settles the question of sharp bounds for discrete PoCs from experimental and observational data: in every dimension, they are given in closed form by a single theorem.

Large language model (LLM) agents are moving beyond reactive responses toward proactive assistance that anticipates user needs without explicit requests. However, existing proactive agents primarily address immediate needs, while many everyday situations involve delayed intentions that can only be acted on hours or days later. Humans handle such intentions through prospective memory, the ability to remember to act on an intention when the right moment arises. In this paper, we introduce ProMemAgent, the first proactive agent to incorporate prospective memory over everyday sensory contexts for long-horizon proactive assistance. ProMemAgent organizes past sensory perceptions (e.g., egocentric video and audio) into context-aware memory, generating prospective cues and linking earlier events with subsequent developments for future retrieval. Given the current context, it retrieves relevant past events and performs memory-augmented proactive reasoning to determine whether assistance is needed. We further introduce CPMBench, the first benchmark for evaluating long-horizon proactive assistance over sensory contexts, comprising 1,000 instances across eight everyday categories. Extensive experiments show that ProMemAgent achieves the best memory retrieval performance and consistently outperforms all baselines on long-horizon proactive assistance.

Motivated by the notion of features from machine learning, we study the complexity of representing data that allows for evaluation with a given family of functions. Concretely, we consider a deterministic encoder that observes $X\sim D$ and produces a finite encoding before a task $f\in\mathcal{F}\subseteq\{0,1\}^{\mathcal{X}}$ is specified. For each task, a decoder must predict $f(X)$ with error at most $\varepsilon$ under $D$. We construct an encoder that outputs a representation with $O(d^{*}\log(1/\varepsilon))$ bits, where $d^{*}$ is the dual VC dimension of $\mathcal{F}$. Our encoder greedily selects $O((d^{*}/\varepsilon)\log(1/\varepsilon))$ functions from the class and uses their joint label pattern to produce the encoding. The key idea in our upper bound is a novel potential function argument, where we compare the entropy gained from each greedy selection with the number of patterns allowed by the dual VC dimension. We present lower bounds showing that the representation length achieved by our encoder is worst-case optimal for every $d^* \ge 1$ and $\varepsilon < 1/4$ up to a universal constant factor, and instance-wise optimal for every family $\mathcal{F}$ up to an $O(\log(1/\varepsilon))$ factor. We give two ways to learn the representation from unlabeled samples, with different guarantees on the representation size and sample complexity. Experimentally, we verify the greedy construction's accuracy-size tradeoff and explore its connection to neural sparse autoencoders.

Text-to-speech systems built on residual vector quantization often generate audio in two stages: a transformer backbone emits the first level of each frame's token stack, and a smaller depth model generates the rest autoregressively. We ask which components of such a model are responsible for prosodic intonation, more precisely for generating the English nuclear tune (for instance, the falling pitch melody that distinguishes an assertion from a question's rising melody), and whether interventions on those components can be used to control intonation. Prompt-based control mostly fails; only a final question mark is a reliable lever. Interchange interventions in CSM and S2 locate the tune: the backbone's hidden state carries it to the waveform through the depth model, and the first level of the stack carries little or none of it. Steering the backbone state with a difference-of-means vector computed on new material generated with a final period or question mark moves the tune, but the push toward an assertion degrades the voice. Steering vectors computed instead from the backbone states associated with human imitations of theoretically-specified tunes, whose text carries no punctuation, and applied inside the generation loop, move most recordings to the other condition in both systems (even when fitted without the speaker being steered), at a small cost in predicted naturalness. These imitation-derived vectors are aligned with the one obtained from the two punctuated conditions far beyond a shuffled-label null, so the backbone state of a punctuated prompt already represents intonation. The steered recordings broadly become falling or rising, according to the intent, but the edge tone moves more coherently than the pitch accent, and the target tune cannot be selected precisely beyond this broad tendency.

LLM agents can improve across tasks without updating model parameters by storing experience from their own executions in external memory and reusing it to guide later decisions. A central design question is whether to retain only observed trajectories and outcomes or also the rules, summaries, and skills inferred from them. Retaining these abstractions allows agents to reuse strategies without repeatedly deriving them from raw trajectories. However, errors in stored abstractions can propagate to subsequent decisions through retrieval and reuse. They can also shape execution trajectories, which then become the basis for new abstractions that reproduce the original errors. We term this feedback mechanism error reproduction: errors are regenerated through a cycle of abstraction, execution, and re-abstraction, extending their persistence beyond direct reuse of the original faulty knowledge. We propose Anti-Persistence, a memory design that accumulates trajectories and outcomes while reconstructing task-specific guidance on demand. An adaptive selector uses prior outcomes to decide whether and how to synthesize guidance, which is discarded after execution. This prevents its direct reuse as a stored object, although indirect feedback through retained trajectories remains possible. Across different benchmarks and backbones, Anti-Persistence achieves higher overall held-out success and the lowest average LLM-call cost among the evaluated memory designs. These results support separating experience accumulation from abstraction persistence in memorybased self-improvement.