#01Jul 23, 2026
math.OC
Barzilai-Borwein Fails Superlinear Convergence on an Open Set of Quadratics for Every Dimension $n\geq 4$
Dawei Li, Xiaotian Jiang, Mingyi Hong
Barzilai--Borwein (BB) method has shown strong practical performance in continuous optimization, yet its convergence dynamics remains poorly understood. In particular, a central unresolved question is whether BB converges superlinearly for almost every strictly convex quadratic problem and initialization. We provide a negative answer to this question. Specifically, for every finite dimension $n\geq4$, we construct a nonempty open, hence positive-Lebesgue-measure, family of strictly convex quadratic problems and initial points for which the long Barzilai--Borwein method (BB1) converges but cannot converge root-superlinearly. More precisely, with the explicit constants $ρ_{\min}=10^{-6},ρ_{\max}=0.61$, every spectral component of the gradient is bounded above and below by the corresponding geometric sequence. Consequently, the gradient norm and the energy norm of the error satisfy two-sided geometric estimates with the same rates, while the objective gap satisfies the corresponding estimates with squared rates. In particular, all three quantities are bounded below by geometric sequences, ruling out superlinear convergence. The construction is highly nontrivial, based on a computer-assisted proof of a nonresonant, attracting seven-cycle of the projectivized BB dynamics in dimension four.
#02Jul 23, 2026
cs.SE
From Resource Flow to Executable Tests: Petri-Net-Guided LLM Test Generation for Concurrent Stateful Rust APIs
Kaiwen Zhang, Guanjun Liu
Concurrent stateful library APIs expose behavior through evolving resource ownership, lifecycle states, and competing interleavings. Large language models can synthesize executable Rust tests, but their outputs often violate API preconditions, remain shallow, or reduce concurrency to accidental sequential traces. Conversely, model-based and systematic testing techniques provide semantic control but commonly require substantial handwritten code to turn abstract scenarios into executable tests. This paper addresses the gap between formal scenario design and low-cost test concretization. We present a Petri-net-guided methodology for test generation over concurrent stateful Rust APIs. The method represents API resources, lifecycle conditions, and causal dependencies as colored tokens and transitions; derives legal deep-state, near-legal, and partial-order concurrent scenarios; and uses these scenarios as a constrained intermediate representation for LLM-based code synthesis. A local-faithfulness contract and structural repair loop preserve the modeled intent during concretization, while Petri-guided schedule shaping prioritizes high-conflict concurrency skeletons for systematic exploration. A layered semantic oracle then distinguishes synthesis failures from violations of the target API's expected behavior.
#03Jul 23, 2026
cs.AI
Unsupervised Consensus-Based Anomaly Detection for Spatiotemporal Malaria Incidence in Ghana
T. Ansah-Narh, Y. Asare Afrane
A consensus anomaly detection framework was applied to monthly malaria surveillance data from Ghana (2014-2023) to identify atypical transmission patterns. Anomalies were highly structured in space and time. Ashanti and Northern Regions accounted for most recurrent anomalies, with persistent hotspots at Tamale, Kumasi, and Accra. A key finding was the spatial distinction between anomaly burden (cumulative cases during anomalous periods) and anomaly frequency (persistence of unusual behaviour). Tamale had the highest burden during anomalies, whereas the highest anomaly rates clustered in Ashanti districts, showing that high-burden areas are not necessarily those with the most frequent anomalous transmission. Anomalous months formed a statistically distinct group, with much higher case counts (Cohen's $d = 3.252$) and large seasonal deviations ($d > 1.2$) compared with normal months. Malaria burden alone provides an incomplete picture of transmission dynamics. By distinguishing where malaria is most prevalent from where transmission behaves most unusually, this framework can strengthen surveillance, prioritise investigations, and support targeted control strategies.
#04Jul 23, 2026
cs.CL
What, Where, and How: Disentangling the Roles of Task, Language, and Model in Code Model Representations
Piotr Wilam
Do independently trained language models come to represent the same thing in the same way? We answer for code, extending a recently introduced concept-circuit extraction method to a 2x2 design -- Python and Rust crossed with Qwen2.5-Coder-7B and DeepSeek-Coder-V1-6.7B -- and measuring a complete inventory of grammatical concepts (58 Python, 57 Rust) identically in all four cells: the smallest design that separates what depends on the task, the language, and the model. The answer splits into three parts. What earns dedicated circuitry is set by the task: the models agree on which concepts receive circuits (Spearman $ρ$ = 0.638 for Python, 0.673 for Rust, both p < $10^{-7}$). Where those circuits sit is set by the model: Qwen processes concepts in a late band (~L17-19), DeepSeek at L6-7, for both languages. How circuits grow across layers is also set by the model: Qwen gives its atomic concepts an early spike that DeepSeek does not. "Are circuits universal?" thus has no single answer: yes for What, no for Where and How -- universality is a property of representational content, not of computational organisation. None of this structure was fixed in advance. The agreement could have landed anywhere between independence and identity; it lands at $ρ\approx 0.65$. Rust constructs receive 2-3x more concept-specific circuitry than their Python equivalents, in both models. Both models share neurons between the languages (6/7 and 7/7 paired constructs), DeepSeek 1.94x more than Qwen -- a direction no prior result predicts. And Qwen binds nine keywords of Rust's type-and-trait machinery into one tight neuron cluster (Jaccard 0.535 vs null 0.112, p < 0.001), a semantic dimension invisible in surface syntax. Ablation and linear probes confirm the circuits are functional. All claims are scoped to this 2x2; whether the per-model profile predicts a third model is the designed next test.
#05Jul 23, 2026
cs.CL
Artificial Epanorthosis: Why large language models overuse a classical rhetorical figure, and how to mitigate it
Federico Boggia
A rhetorical figure that Cicero and Quintilian catalogued two thousand years ago reappears, systematically, in the text of large language models: epanorthosis, the self-correction of the specimen «This is not a course. It is a journey of transformation». This essay argues that the overuse is a trained disposition, driven mainly by a training distribution rich in promotional prose and by preference tuning (RLHF) that rewards confident, emphatic phrasing; the left-to-right nature of generation is an amplifier rather than the root cause. Building on evidence that models diverge from human rhetorical style, and on Fontanier's classification of epanorthosis as a figure of thought, it sets out a programme that scores the figure against genre-specific human baselines through an Epanorthosis Index (density relative to the human rate). A first measurement, on three sizes of one instruction-tuned model family, finds mis-calibration by register in both directions: the models overshoot in oratory (about twofold, near threefold in Italian, concentrated in the larger tiers) and undershoot in informal question-and-answer writing, while matching humans in argument, journalism, and encyclopedic prose. Three constructive contributions follow: a survey of mitigation techniques centred on lightweight LoRA adapters; a demonstration, in Italian, that a one-line instruction cuts the figure by half to nearly three-quarters and that a supervised-fine-tuning adapter removes it almost entirely, with a scaling coefficient that dials the reduction back onto the human rate; and the argument that the target is calibration to the human rate for each genre, not elimination. It closes on the stakes: the real risk is that we begin to write like the machines.