Papers

Long-form live-streaming TTS requires context-dependent prosody and paragraph-level coherence. However, many existing instruction-based TTS systems use global or uniform conditions, providing limited explicit control over clause-level relative prosodic changes. We introduce Speaker-Relative Inline Prosody Control, where each Pitch, Energy, or Speed instruction targets a clause relative to the preceding clause from the same speaker, while Pause uses an absolute duration interval. In codec-based TTS, Speed and Pause affect sequence length, whereas Pitch and Energy rely on residual codebooks. By analyzing Qwen3-TTS RVQ codebooks, we find that Energy concentrates in early residual codebooks, whereas Pitch accumulates across a deeper prefix. We therefore propose Scope- and Codebook-Aware Instruction Conditioning (SCIC), combining a Temporal Instruction Router for frame-level tag activation with Tag-Specific Codebook Weighting over residual codebooks. SCIC improves speaker-relative Pitch and Energy control over standard instruction fine-tuning using text-token tags. We further apply multi-reward GDPO post-training to jointly optimize control and quality, improving control accuracy while preserving CER and speaker similarity. In long-form synthesis, SCIC produces a more distinct paragraph-level expressive hierarchy than speaker-adapted SFT without instructions. Audio demos are available at: https://taoliveaigc.github.io/SCIC/

We investigate primordial tensor perturbations in a Lorentz violating inflationary framework with non-canonical scalar field dynamics. Using an Einstein-Æther type with a higher order kinetic term $K_3X^2$, we derive the tensor propagation speed and its dependence on an effective Lorentz violating coupling. We consider an analytically tractable potential free background and study two representative couplings, $q_k=\lambda_T\phi_k^2$ and $q_k=\lambda_T\phi_k^4$. The resulting tensor spectral index $n_T$ and its running $\alpha_T$ satisfy distinct consistency relations, providing potential signatures of Lorentz violation in the primordial gravitational wave spectrum. We derive corresponding constraints from the tensor tilt and running and compare them with the stringent late-time bound on the gravitational wave speed from GW170817/GRB170817A. We emphasize that translating this bound into primordial constraint requires an assumption about the evolution of tensor sector coupling between inflation and the late Universe. Our results demonstrate that primordial tensor observables can provide a complementary probe of Lorentz violation and its interplay with non-canonical inflationary dynamics.

Runtime error healing lets a crashed program continue by generating code that repairs its live runtime state. Recent work shows that LLMs can generate such healing code, but it is evaluated only on small competition programs, and executing LLM-generated code inside a live process raises safety concerns that remain unaddressed. In this paper, we take LLM-based runtime healing toward practical use in real-world repositories. We first build HealBench, a benchmark of 265 runtime errors from 18 real-world repositories, each paired with a reference execution on the patched version. HealBench also provides a unified framework that lets LLM agents heal with cross-file context and live runtime state. We then design HealGuard, which requires healing code to be written in HealCore, an analyzable subset of Python, and uses static and dynamic taint analysis to check whether state changed by healing reaches operations protected by developers. We evaluate a dedicated healing method and three general coding agents with three backbone LLMs. The best setting resumes execution in 38.11% of instances and passes the target test in 28.68%, showing that existing agents can already heal a meaningful share of real repository-level crashes. However, among executions that pass, HealGuard flags 17.4% whose healing-changed state may reach a protected operation. On 684 controlled cases, HealGuard detects all unsafe cases, at the cost of a 68.42% false positive rate.

We study the complex saddle structure of singly rotating Kerr–AdS$_5$ black holes using a two-variable reduced model in the grand canonical ensemble at fixed angular velocity, $\Omega$. The small and large black hole saddles merge at a critical point where one Takagi singular value of the complex Hessian vanishes, identifying the soft mode associated with the merger. This merger remains distinct from the Hawking–Page transition throughout the physical domain $|\Omega| < 1$. For the reduced integral with the standard measure, we show that thermal AdS dominates uniformly in a complex neighborhood of each real merger point when Newton's constant $G$ is sufficiently small. Consequently, this neighborhood contains no zeros of the partition function, even though the local saddle merger is described by Airy-type behavior. The Fisher zeros instead accumulate near the Hawking–Page coexistence line, with spacing of order $G$, through interference between thermal AdS and the large black hole saddle. We also show that the real quasi-Euclidean Kerr–AdS$_5$ family satisfies a strict asymptotic Kontsevich–Segal–Witten (KSW) phase bound for $|\Omega| < 1$, with the merger point lying inside the allowed domain. In the fixed angular momentum extended ensemble, two such merger points combine into a cusp with a contour-dependent Pearcey approximation. These results distinguish local saddle degeneracies from global phase coexistence and clarify the different roles of Takagi modes, phase transitions, and zeros of the partition function in the complex black hole saddle structure.

Engineering dissipation has emerged as a powerful strategy for controlling quantum many-body dynamics, complementing purely coherent control for state preparation. However, finite-time driving across a quantum critical point generates nonadiabatic excitations and coherences, and existing dissipation-engineering approaches have largely characterized how a fixed environment modifies critical dynamics rather than actively steering a system toward a prescribed thermal trajectory. Here we develop a Markovian dissipative framework for finite-time thermal-state tracking based on engineered population currents with non-negative transition rates, and apply it to the transverse-field Ising model driven across its quantum critical point. Compared with unitary dynamics and a natural thermal bath, the engineered dynamics strongly suppresses thermal excitation deviations and provides additional control over coherence damping through a free common current $Q_k$, while exhibiting a substantially steeper residual scaling, $\delta n_{\mathrm{ex}}^{\mathrm{th}}\sim(v/v_{\mathrm{ch}})^2$, than the Kibble–Zurek behavior recovered for unitary evolution. These results point toward engineered dissipation as a route for controlling thermal-state preparation in driven quantum critical systems.

Super-resolution and quality enhancement of 1.5\,T brain MRI are normally validated with image-fidelity metrics, although their purpose is to improve downstream analysis. We study whether enhancement improves tissue segmentation, and for which segmenters. We propose an unpaired, physics-guided training pipeline for a lightweight ($\le$2.5\,M parameter) recurrent convolutional enhancer: a six-module stochastic 1.5\,T degradation operator, a residual adversarial network that adds scanner-specific texture without moving anatomy, and a cycle-consistent objective with an anti-identity penalty that rules out the copy solution. We then train U-Net, Swin-UNet and wavelet token-mixing segmenters \citep{jeevan2023wavemix} from scratch on either raw or enhanced 1.5\,T images of the same subjects, using identical labels and subject-level splits, for three enhancer variants and two datasets. On ABIDE (41 held-out subjects, FreeSurfer labels) enhancement significantly improves the wavelet segmenter (mean Dice $+0.014$, Wilcoxon $p=3.5\times10^{-5}$; CSF $+0.018$, grey matter $+0.013$), significantly degrades the U-Net ($-0.008$, $p=5.1\times10^{-4}$) and leaves Swin-UNet unchanged. On IXI, whose labels come from FSL-FAST, enhancement lowers Dice for all nine pairings, almost entirely through CSF; we trace this to spatially implausible CSF voxels in the labels that penalise smoother predictions. Enhancement of low-field MRI should therefore be validated per downstream model and against reliable labels.

As new evidence arrives, a sequence model must update what it remembers and how memory influences predictions. While Transformers incur computation and cache costs scaling with context length, fixed-state recurrent models offer constant-memory inference. However, linear and spectral recurrences traditionally rely on static transitions, failing to dynamically revise how stored representations decay or rotate. While recent selective architectures introduce input-dependent transitions, they assign independent controls to every memory mode, coupling control cost to state capacity. We show that high-dimensional spectral memory does not require high-dimensional control, and introduce Shared Phase and Retention Control for Efficient Adaptive Spectral Recurrence (SPARC). SPARC employs just two input-dependent scalar signals to coordinate memory retention and phase rotation across heterogeneous complex modes, while preserving mode-specific baseline timescales and frequencies. Its diagonal affine recurrence supports parallel associative scans for sequence-level BPTT as well as exact structured Real-Time Recurrent Learning (RTRL) for online credit assignment. Across partially observable continuous control, POPGym, and sequence classification, SPARC achieves a 9.09% relative return improvement on Walker-P and a 1.36% relative accuracy gain on FordA over second-best methods. On an NVIDIA Blackwell GPU, our implementation reduces recurrent-mixer training latency by 18.2%-34.2% in fixed-token workloads and accelerates scans by 3.1x-4.7x over an optimized RG-LRU baseline. These results show that two shared control signals can efficiently govern adaptive spectral memory across online and full-sequence settings. Code is available at https://github.com/Botwwt/sparc.

We spent five weeks using an LLM coding agent on open problems in coding theory: finding large sets of four-letter words, such as DNA barcodes, that stay far apart in edit distance. The agent wrote the verifiers and search code; a human chose the problem and set the verification protocol. Restricting the search to codes with a prescribed symmetry, a classical technique, shrank the problem about fourfold and raised the best known code of length 6 and minimum edit distance 3 from 114 to 120 words ($E_4(6,3) \geq 120$). The same pipeline improved twelve further lower bounds at lengths 6 to 9 and distances 3 to 6. We give the failures equal space. Our own search stopped at 116 and recorded the last symmetry class as topping out at 112; a second agent session, running the same search with a better operator, found the 120. A later verdict that the method did not carry over to length 7 was wrong for the same reason, and an earlier instance cost three weeks. Each time, an intermediate result was written down, never rechecked, and treated as a fact that ruled out further search. Checking final outputs, as our protocol required, does not catch such errors.

Intracortical motor decoders degrade across sessions because the set of recorded units changes and persisting units can alter how their firing relates to behavior. Most existing methods update network weights on each new session or rely on unlabeled activity, which does not directly reveal such changes. We present APST, an Association Profile-conditioned Set-Temporal transformer that adapts to new sessions with all network weights frozen. From a few labeled calibration trials, APST summarizes how each unit's firing relates to behavior in a four-dimensional association profile computed in closed form. The profiles condition a set-attention encoder that accepts any number and order of units, followed by a causal transformer for streaming decoding. On held-out DANDI688 sessions from two monkeys, APST reaches velocity $R^2$ of $0.78$ and $0.81$, versus $0.40$ and $0.58$ for a variant that uses neural activity alone, and matches or exceeds an RNN fine-tuned on the same trials. On FALCON private held-out evaluation, it attains $R^2$ of $0.65$, $0.42$, and $0.44$ on M1, M2, and H1.

We study the singularities of orbit closures in loop symmetric varieties, extending our previous work https://arxiv.org/abs/2310.20006 to the twisted setting. We prove that the IC complexes of orbit closures are pointwise pure and satisfy a parity-vanishing property. We apply these geometric results to the study of twisted affine Lusztig–Vogan modules, establishing foundational results, including positivity properties of the twisted affine Kazhdan–Lusztig–Vogan polynomials. Along the way, we construct conical symplectic transversal slices in loop symmetric spaces. We provide applications to Langlands duality for real groups.

Representations are routinely used across machine learning, psychology, and neuroscience to draw inferences about the computations of biological and artificial systems. Such inferences presume a meaningful link between representational geometry and the computation being performed. For artificial neural networks, however, the extent to which function constrains representation remains unclear. One key obstacle is that these networks admit parameter symmetries: changes in parameterization that preserve function exactly while reshaping representational geometry. Here, we show that a broad class of parameter symmetries acts on representations through just three primitive feature transformations: addition, duplication, and scaling. This feature-level characterization yields a closed-form decomposition of representational geometry into essential and auxiliary components, which makes precise how degeneracy in representational geometry can grow with overparameterization even when function is held fixed. Finally, we show that implementation-level selection rules can resolve this degeneracy, yielding identifiable geometries in which features are weighted according to their contributions to the network's function. Together, our results delineate when representations can support inferences about computation, and when they cannot.

An advisor knows who would benefit from using a resource but cannot assign its use. Individuals have private assessments and may ignore advice. We study how their choices can respect a fixed usage limit. In our model, whenever coordination is possible, eliciting private assessments makes some harmful use unavoidable. Policies that maximize welfare, or even minimize harm, also forgo beneficial uses that direct assignment would permit. In those environments, observing assessments instead allows advice to achieve as much beneficial use as direct assignment, without harmful use. The loss therefore reflects the incentive cost of eliciting private beliefs while leaving use voluntary.

A pool of language models can collaborate and improve collectively by learning from one another's responses. These interactions depend on the instructions used during training. Existing methods typically sample instructions uniformly, even though their usefulness may change as the models improve: an instruction on which models' responses once differed in quality may later be answered equally well, while a previously difficult instruction may begin to provide a useful learning signal. We propose Stackelberg Alignment, a game-theory-inspired leader-follower framework that turns instruction selection into an adaptive curriculum. An EXP3 bandit acts as the leader, allocating a fixed sampling budget across instructions and updating its sampling distribution using a reward that combines instruction difficulty and response discriminability. The language models act as followers: they respond to the selected instructions, evaluate one another's responses, and learn from the resulting preference signals through DPO or GRPO. The framework uses Elo-style reputation-weighted peer judgment and reputation-based opponent matching to support reliable and competitive model interactions. Experiments across three heterogeneous model pools and 12 benchmarks spanning scientific discovery, reasoning, code, instruction following, and knowledge show that Stackelberg Alignment achieves the highest macro-average across three diverse model pools, outperforming the strongest training-time baseline by up to 7.4% and the best static inference baseline by 12-25%. Analysis confirms that the adaptive leader concentrates duels on the most informative instructions, and ablations show that both reputation-weighted judgment and reputation-based matching improve the effectiveness of multi-LLM evolution.

Retrieval-augmented generation (RAG) systems need inexpensive ways to route generated answers: accept low-risk outputs, review uncertain ones, and reserve strong verifiers for the expensive tail. We present RAGScope, a leakage-controlled protocol for evaluating local evidence gates that use only the task input, retrieved context, and answer text. The protocol combines context-grouped splits, fold-scoped preprocessing, group bootstrap intervals, deployment operating points, end-to-end runtime, and explicit source-shift stress tests. On three RAGTruth tasks, the enhanced gate RAGScope-E reaches 0.798 AUROC and 0.660 average precision (AP) in pooled grouped cross-validation. Its pooled AP exceeds ROUGE-L by 0.034 with a 95% context-group interval of [0.002, 0.064], although the AUROC gain is not significant and ROUGE-L remains stronger on data-to-text. At a top-10% review budget, RAGScope-E attains 0.748 precision; accepting the lowest-risk 50% yields 0.141 residual unfaithfulness. RAGScope-E runs in 6.22 ms/example on CPU, versus 145.75 and 223.07 ms/example for the tested DeBERTa-NLI and HHEM settings. A 14,900-example HaluBench stress test exposes the deployment boundary: an in-domain calibrated gate reaches 0.879 AUROC, but leave-source-out calibration averages only 0.466. Target-only calibration recovers to 0.675 AUROC with 100 labels per source and 0.685 with 200. Cheap evidence gates are therefore useful routing components, but learned calibration must be validated and adapted within the target domain.

Federated learning (FL) on memory-constrained edge devices faces a dilemma: first-order (FO) optimization (i.e., backpropagation) demands substantial memory, whereas zeroth-order (ZO) optimization suffers from severe convergence slowdown. To resolve this dilemma, we introduce HO-FL, a hybrid-order FL framework that trains a model's bottom segment with ZO optimization and its top segment with FO optimization. Each device can flexibly select its order boundary according to its memory budget while participating in the training of the same global model. Moreover, our convergence analysis reveals a new, fundamental trade-off: clients with larger FO-trained segments can provide more accurate updates, but favoring them can underrepresent other clients' data. We connect this trade-off to the bias and variance of actual multi-step local updates, yielding a sampling optimization problem and a practical dimension-aware approximation with direct model averaging. Experiments on language tasks examine task performance, client memory, and sampling under data heterogeneity. The results show that hybrid-order local training can retain much of the full-FO performance with substantially lower client memory requirements. Our code is available at https://github.com/HKU-WILL-Lab/HO-FL.

The charge-carrier lifetime in halide perovskites often varies by orders of magnitude with the injection level, complicating the analysis of conventional time-resolved photoluminescence and comparisons of reported lifetimes. We use intensity-modulated photoluminescence spectroscopy (IMPLS) as a frequency-domain alternative. Carried out under operating conditions, it yields the lifetime at a specific injection level, e.g., one-sun-equivalent illumination. On thin films, IMPLS and steady-state photoluminescence yield comparable lifetimes. For perovskite/transport-layer stacks, the IMPLS response becomes more complex. A dedicated transfer function disentangles charge transfer from interface recombination and predicts an upper limit on the charge-carrier lifetime in the solar cell. In devices, electrical methods such as intensity-modulated photovoltage spectroscopy (IMVS) often fail to measure the lifetime due to capacitive effects. IMPLS shows not only the same two characteristic frequencies as IMVS, but also a third one, thereby resolving the lifetime itself.

Emotion recognition in conversation has been widely studied, but applying Large Language Models (LLMs) to continuous dimensional emotion evaluation in multimodal dialogue remains largely unexplored. We propose an LLM-based framework that performs discrete emotion recognition and Valence-Arousal-Dominance (VAD) dimensional evaluation on IEMOCAP, incorporating acoustic cues as natural language descriptions following the SpeechCueLLM approach. We evaluate six models spanning the LLaMA, GPT, and Qwen families under zero-shot prompting, few-shot prompting, and LoRA fine-tuning. LoRA fine-tuned LLaMA models substantially outperform prompt-engineered GPT models on both tasks despite GPT's larger scale, a gap we attribute to domain adaptation rather than model capacity. Our best model achieves a Valence CCC of 0.7822, a new state-of-the-art on IEMOCAP. Ablation studies confirm that textual audio descriptions meaningfully improve smaller models (+3.5 to 3.6 weighted F1) while contributing little for the largest model, suggesting audio cues are most valuable when linguistic capacity is limited. The performance asymmetry across VAD dimensions closely mirrors the annotator agreement hierarchy in IEMOCAP's own annotations.

Legal language models require reward signals that capture not only answer correctness but also the multidimensional quality of legal responses. Existing reward methods, however, often rely on coarse-grained holistic judgments, providing limited domain specificity and interpretability. We introduce LexReward, a taxonomy-driven framework for legal reward modeling. LexReward characterizes legal response quality along three complementary dimensions: Style, covering lexical and syntactic quality; Element, assessing legal subjects, facts, statutes, and decisions; and Chain, evaluating the order, completeness, correctness, and non-redundancy of legal reasoning. For each dimension, we develop rubrics that specify evaluation criteria and quality levels. The resulting rewards are used to construct pairwise preference data for Direct Preference Optimization (DPO) and reward-model training. Experiments show that the rubric-based rewards reliably distinguish legal responses of different quality and that DPO training on the preference data improves performance across all three dimensions. The learned reward models, LexRM, also support effective downstream optimization: each dimension-specific reward model improves policy performance in its corresponding dimension through reinforcement learning, without requiring reference answers at reward time. Dimension-wise analyses further support the effectiveness of the proposed taxonomy and reward construction.

How does an inherited cross-type wage gap enter Markov-perfect discretionary monetary policy when transfers are passive? In a two-agent New Keynesian model with sticky prices and type-specific own-lag wage adjustment, the gap changes implementable allocations and the second-order welfare loss. A positive lower bound establishes its value relevance; explicit rank conditions characterize when current price inflation, wage inflation, and the output gap fail to determine the implementing nominal rate. An illustrative parameterization satisfies these conditions, although the additional state explains little nominal-rate variance after conditioning on all three aggregate variables. Welfare comparisons with fixed rules are driven mainly by aggregate wage-inflation stabilization and do not isolate the value of distributional information. Unrestricted targeted transfers separate aggregate allocation from the legacy wage-gap transition. In the CES-consistent distribution block, optimal smoothing eliminates consumption dispersion, improves on immediate wage-gap elimination, and coincides under discretion and date-0 commitment.

Test-time reasoning systems often respond to failure by restarting or revising the latest step, even when an earlier decision caused the error. We introduce CORE, a search controller that requests a certified conflict core from a verifier, backjumps to the latest decision in that core, and caches the conflict to avoid repeating it. Under sound verification, finite branching and depth, and exhaustive proposals, the uncapped search is complete and never prunes a valid solution. On 2,000 planted graph-coloring instances with matched proposals and an exact verifier, CORE reduces median verifier calls by 39.8% at 30 variables and 35.0% at 36 variables relative to chronological repair; caching further improves on backjumping alone. Across five reasoning tasks, CORE achieves 75.9% mean success with Qwen2.5-7B-Instruct and 84.2% with Qwen3-8B, compared with 72.5% and 81.8% for Tree of Thoughts. It also uses fewer verifier calls and generated tokens on both backbones. These results show the value of using certified failure explanations to direct language-model search.

Long-context LLM agents accumulate interaction histories that strain KV-cache memory and attention computation. Although sparse attention reduces these costs, heterogeneous cache representations and workflows hinder integration with existing inference engines, while prior sparse-serving abstractions support only specific layouts or workflows. We present SparseEngine, a ground-up, sparse-first inference engine whose shared lifecycle contract lets each method control its KV representation and computation while coordinating state transitions with common serving infrastructure. SparseEngine supports 15 methods across four categories and enables cross-request state management through Chain Cache, which resumes KV-eviction methods from retained history, and controllable Prefix-Cache Pruning, which removes KV from selected history regions while preserving logical-prefix matching. While maintaining method quality, SparseEngine delivers over 10x higher throughput with KV eviction, over 2.5x faster decoding at matched concurrency than vLLM, and over 2x end-to-end speedup on agent benchmarks. The code is available at https://github.com/CURRENTF/SparseEngine.

Elastic Compute Cloud (EC2) Spot is 60% to 90% cheaper than On-Demand but can be reclaimed on just a 2-minute notice; for expensive multi-node training this loss can be severe, with one reclaim costing hours of synchronous progress. We build Argus, a Kubernetes operator, and ask empirically, on a CIFAR-10 testbed, when predicting interruptions beats simple checkpointing. Argus on real EKS survives a real Spot drain with a graceful SIGTERM checkpoint, resuming from epoch 8 and losing only the in-progress epoch. Alongside, we further find that in an 80-trial benchmark, the reactive-on-notice degrades toward no protection once interruption outpaces the fixed 2-minute notice, and predictive wasted compute is driven to zero, but with an oversized fixed lead it over-migrates so severely that at the fastest rate only one of five runs completes, while periodic is a strong ML-free baseline. A lead-time sweep turns the lead prediction into a guideline where a small lead suffices for zero waste, but excess lead is wasteful. The predictor built is advisory (a proxy label); real interruption labels and large-model-scale validation are future work.

Conventional image forgery detection methods produce binary scores or pixel-level masks without interpretable evidence, while recent multimodal large language model (MLLM)-based approaches generate post-hoc explanations of predetermined classification results rather than reasoning from evidence. Inspired by the forensic workflow of human judicial experts, we propose Agentic Tool-Augmented Reasoning (ATAR), a framework integrating 22 specialized forensic tools across seven complementary domains to autonomously detect, localize, and explain image forgeries through multi-turn reasoning. A Dual-Stream Forensic Reasoning paradigm combines a high-level semantic anomaly path, which magnifies suspicious regions for fine-grained inspection, with a low-level forgery artifact path, which invokes forensic tools to extract objective evidence. We further introduce Forensics Curriculum Learning: during General Experience SFT, an automated teacher-student mentoring pipeline synthesizes multi-turn tool-usage reasoning trajectories; during Forensic Scene RL, a Tool Prior Curriculum guides early tool exploration and progressively transfers control to the agent, while a Structured Evidence Reward provides fine-grained process-level supervision. Experiments across IMDL, Deepfake detection, DMDL, and AIGC detection show that ATAR achieves 78.5% average image-level F1 on six zero-shot IMDL benchmarks, surpassing the strongest MLLM baseline by 11.8 percentage points, and remains competitive with specialized detectors on other tasks while producing substantially more faithful and grounded explanations.

LLM agents increasingly rely on installable skills, which are packages of instructions, code, and resources that equip them with task-specific capabilities and, once installed, can be automatically invoked across subsequent user tasks. This creates a chain of trust in which users delegate authority to agents, while agent frameworks admit skill-provided content into the agents' context with insufficient validation, allowing malicious skills to influence agent behavior under that delegated authority. Yet, little is known about whether this trust model adequately constrains untrusted skill content before it reaches security-sensitive operations, or how frequently such trust violations arise in real-world agents. We present TrustProbe, a framework for uncovering unsafe chains of trust in skill-based LLM agents. First, TrustProbe analyzes agent source code to identify source-to-sink call paths from skill-controlled inputs to security-sensitive operations. Second, it generates semantically realistic SKILL.md seeds with injected canaries and evolves them through feedback-guided scheduling and mutation. Finally, it validates vulnerabilities using an oracle that confirms attacker-controlled flows and verifies observable harm. Across 11 open-source agents, eight with more than 10,000 GitHub stars, TrustProbe identifies 104 taint-style vulnerabilities. Validation on a large corpus of real-world skills collected from public hubs such as ClawHub further shows that 25.1% of skill-agent trials exercise the identified vulnerable paths, with payload injection successfully weaponizing 15 of the vulnerabilities. These results reveal a systematic trust failure in skill-based LLM agents: untrusted skill content can reach security-sensitive operations and exercise authority delegated by users to their agents.

Transport authorities comparing urban station plans need to distinguish plan differences from differences in evaluation inputs. Reconstructing spatial units, included trips, or candidate blocks from each plan's access outcomes can make scores incomparable. Freeze–Validate–Report fixes an evaluation contract: target trips, proxy groups, reporting cells, candidate pools, and a lexicographic selection rule. A two-point example shows that plan-specific observation selection can reverse the target mean ordering. We compare seven generators spanning clustering, facility location, fairness-oriented adaptations, and a grid control. All plans are scored on common validation evidence using endpoint distance: the sum of origin and destination distances to their nearest stations. A five-metric rule selects one plan for a single test report. In Porto, it selects IFkCO, an adaptation of individually fair $k$-center with outliers; test overall and worst-group 90th percentiles are 805 m and 872 m. In Chicago, it selects Grid; values in a later test window on the same day are 1404 m and 1656 m. Post hoc checks show input sensitivity: expanding candidates from 300 to 600 changes selection in both cities, while holding the hour fixed across three Chicago dates selects Priority. A proportional mean fairlet diagnostic shows that plan-specific proposal pools can change diagnostic ranks; admissibility and solver bounds apply only to the sampled pool. The package supplies code, hashes, decision logs, and proposal pools. We establish auditability within a declared contract, not stable performance after deployment; proxy definitions and metric priorities remain the authority's choices.

We give a new proof of the fact that every 2-coloring of the positive integers contains a monochromatic Pythagorean triple. This result was originally proven by Heule, Kullmann, and Marek with SAT solvers in 2016, answering a decades-old question of Graham. This proof uses elementary techniques and requires neither lengthy computation nor difficult analytic machinery.

We give a randomized algorithm for Directed Hamiltonian Cycle on $n$-vertex directed graphs that runs in $O^*(1.9133^n)$ time. For general directed graphs, this is the first improvement in the exponential base over the classical $O(2^n n^2)$-time algorithms of Bellman and Held–Karp (1962). To obtain this improvement, we reduce Hamiltonicity to weighted parity counting using the isolation lemma of Mulmuley, Vazirani, and Vazirani (STOC 1987). If a Hamiltonian path from $s$ to $t$ exists, assigning random polynomially bounded integer weights to the arcs gives a unique minimum-weight Hamiltonian path from $s$ to $t$ with constant probability. In particular, the path count at its total weight is odd. To compute these parities, we give a $(2-2^{-d})^n n^{O(1)}$-time algorithm for instances in which the arcs entering each vertex have at most $d$ distinct polynomially bounded integer weights. The algorithm applies the random linearization idea of Arvind and Guruswami (IPEC 2021) to the Laplacian determinant construction of Björklund, Kaski, and Koutis (ICALP 2017). To keep $d$ small, we randomly delete and duplicate arcs and partition the incoming copies at each vertex into $d$ groups, assigning a common weight to all arcs in each group. We prove that, if the input graph has a Hamiltonian path from $s$ to $t$, then with positive, albeit exponentially small, probability one can select one group at each vertex so that their union contains an odd number of such paths.

Regression analysis for stochastic processes has been an important topic over the last decades. Typically, regressing a dependent process $Y$ on an explanatory $Z$ results in an integral relationship of the form $dY_t = \beta_t dZ_t + dX_t$ with some residual process $X$, and often with constant or piecewise constant $\beta$. In the case of jump processes such a relationship essentially boils down to $\Delta Y_t = \beta \Delta Z_t + \Delta X_t$ on the level of the jumps. Here the residual process $X$ is such that it never jumps together with $Z$, and so any jump in $Y$ is either exactly proportional to $Z$ or purely idiosyncratic. In this paper we discuss a related setup which appears more realistic and is closer to classical regression, namely $\Delta Y_t = (\beta + \eta_t) \Delta Z_t$ for i.i.d. $(\eta_t)_{t \ge 0}$. We propose an estimator for $\beta$ based on high-frequency observations of $(Y,Z)$ and discuss consistency and associated central limit theorems in two different asymptotic regimes.

Artificial intelligence (AI) has expanded the accessible space for catalyst discovery, yet executing complex screening campaigns still requires constant human intervention to bridge high-level reaction objectives with underlying computational pipelines. Here, we present Autocata, a knowledge-embedded autonomous agent that scales catalytic expertise by encoding multistep reaction pathways into reusable, language-invocable capabilities. Powered by a Transformer pretrained on two million catalyst-adsorbate structures, the system incorporates a capability registry of 79 adsorbate-specialized generative models spanning complex reaction networks across carbon, nitrogen, oxygen, and hydrogen intermediates. Given a high-level natural-language prompt, Autocata deconstructs reaction networks, queries and configures matching generative models, generates candidate surface configurations, enforces physical and geometric validity filtering, and coordinates machine-learning potentials evaluations to rank promising materials. Crucially, the agent adaptively reconfigures workflows when encountering capability boundaries or task bottlenecks. We demonstrate these capabilities across CH4 activation, nitrogen reduction reaction (N2RR), and CO2-to-methanol pathways. By shifting from static toolkits to an adaptive, language-driven computational infrastructure, Autocata lowers the barrier for expert-level catalyst discovery and offers a scalable paradigm for self-driving catalytic research.

We prove sharp volume bounds (up to dimensional constants) for the $\delta$-neighbourhoods of a general family of Besicovitch-Rado-Kinney (BRK) type sets associated with surfaces of revolution in $\mathbb R^n$, $n\ge 3$, which, in particular, include spheres, elliptic paraboloids, and cones. As a result, we obtain sharp $L^{p}$-$L^q$ bounds for their associated Wolff-type maximal operators for all $1\le p,q\le \infty$. In $\mathbb R^3$, it is worth noting that our result necessitates a variant of Sogge's cinematic curvature condition.