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01.
arXiv (CS.AI) 2026-06-12

Arbor: Tree Search as a Cognition Layer for Autonomous Agents

arXiv:2606.12563v1 Announce Type: new Abstract: Arbor is a multi-agent framework that introduces structured tree search as a cognition layer for autonomous agents operating in large, stateful action spaces. Prior autonomous optimization systems operate on isolated targets with stateless evaluation. Arbor instead maintains an explicit search tree of scored hypotheses that serves as the shared working memory across agents, evolving with every measurement, treating failures as diagnostic signal that reshapes subsequent exploration, and expanding as prior successes shift the bottleneck distribution. We validate Arbor on full-stack LLM inference optimization, a domain where achieving peak performance has historically required coordinated effort from engineering teams across the application, framework, compiler, kernel, and hardware stack. Arbor pairs an Orchestrator agent, which drives optimization by delegating to Domain Specialists across the inference stack, with a Critic agent that safeguards stability through root-cause analysis, introspection, and measurement validation – a checks-and-balances architecture where neither agent can unilaterally drive the system. Agent capabilities are decomposed into hard skills (domain expertise) and soft skills (coordination protocols that determine how contributions compose), enabling fully autonomous multi-day campaigns. Arbor achieves up to 193% inference throughput-latency Pareto improvement over vendor-optimized baselines, while a single agent without the harness plateaus at +33% throughput improvement and crashes irrecoverably within hours. Arbor generalizes to multiple generations of hardware platform, and run-to-run variance is within 2 percentage points demonstrating that the method is hardware-agnostic and reproducible.

02.
arXiv (CS.LG) 2026-06-19

Influence-Guided Concolic Testing of Transformer Robustness

arXiv:2509.23806v2 Announce Type: replace-cross Abstract: Concolic testing for neural networks alternates concrete execution with constraint solving to search for inputs that flip model decisions. We present a concolic tester for Transformer classifiers that uses SHAP estimates to rank pending path predicates by their impact on the current prediction. To support self-attention with multiple heads in execution backed by SMT solving, we implement attention semantics in pure Python that are compatible with the solver and make the softmax boundary explicit by concretizing exponentiation arguments. We evaluate our method on CIFAR-10 across three compact Transformer classifiers, ResNet18, and VGG16 under a one-pixel budget and a 900s horizon. Across the 500 model–input pairs in this matched comparison, our method achieves 60% success, compared with 15% for a differential evolution baseline that treats the model as a black box. In the primary two-layer Transformer branch-ordering study, SHAP-based predicate prioritization raises success from 56% to 60% and reduces median attack time by 51%. These results show that influence-guided path exploration can make concolic testing a practical way to find adversarial examples in Transformer models.

03.
arXiv (CS.CV) 2026-06-16

Scribby: A Multi-Level LLM Framework for Semantic Video Analysis

As video content continues to expand across educational platforms, recorded lectures, and live-streamed entertainment, the need for efficient and structured analysis of long-form footage has increased [1]. Although many existing AI programs provide high-level video summaries based on AI-generated transcripts [2,3,4,5], these approaches are often limited to coarse overviews and lack detailed analysis of a video's structure, thematic progression, and semantic relationships, all of which are required for comprehensive video analysis. This paper proposes an LLM-based video summarization framework that balances macro-level comprehension with micro-level semantic analysis [6,12,13]. The first stage of the process indexes the video at a micro level by (1) analyzing the full transcript, (2) analyzing individual transcript sentences, and (3) grouping these sentences by semantic similarity using an LLM as a judge [6,13]. Contextual continuity is retained during sentence-level processing by incorporating both the global transcript analysis and adjacent sentence information into each evaluation prompt. This framework establishes a foundation for video analysis tools that visualize semantic chunking and semantic matching through relevance-based heatmaps. Limitations and future expansions of the framework are also discussed.

04.
arXiv (math.PR) 2026-06-17

Limit theorems for random Dirichlet series with summation over primes, with an application to Rademacher random multiplicative functions

arXiv:2508.15032v2 Announce Type: replace Abstract: It is shown that two conjectures put forward in the recent article Iksanov and Kostohryz (2025) are true. Namely, we prove a functional central limit theorem (FCLT) and a law of the iterated logarithm (LIL) for a random Dirichlet series $\sum_p \frac{\eta_p}{p^{1/2+s}}$ as $s\to 0+$, where $\eta_1$, $\eta_2,\ldots$ are independent identically distributed random variables with zero mean and finite variance, and $\sum_p$ denotes the summation over the prime numbers. As a consequence, an FCLT and an LIL are obtained for $\log \sum_{n\geq 1} \frac{f(n)}{n^{1/2+s}}$ as $s\to 0+$, where $f$ is a Rademacher random multiplicative function.

05.
arXiv (CS.LG) 2026-06-12

Viral Proteins Reveal Geometry of Protein Language Models

arXiv:2606.12609v1 Announce Type: new Abstract: Protein language models are trained on highly imbalanced datasets, raising the question of how they represent underrepresented biological sequences. Using viral proteins as a case study across ESM model families, we identify a dominant nativeness axis in embedding space, aligned with masked reconstruction perplexity, that orders sequences from well-modeled cellular proteins through viral proteins to shuffled and random sequences. Scaling contracts this axis unevenly across viral families. Despite this, protein language model embeddings retain viral-specific signal: viral proteins remain linearly separable beyond zero-shot perplexity and shallow sequence features. Together, these results suggest that pLM representations are structured by a general notion of nativeness while preserving information specific to distinct biological groups.

06.
Nature Medicine 2026-06-15

Adaptive deep brain stimulation for dynamic gait control in Parkinson’s disease: a randomized feasibility trial

A randomized crossover study of five patients with Parkinson’s disease (PD) demonstrates that gait-synchronized adaptive deep brain stimulation is feasible and safe, and reduces falls compared with continuous stimulation. Gait dysfunction in PD is a major source of disability and is often insufficiently treated by continuous deep brain stimulation (cDBS). Although adaptive DBS (aDBS) has shown efficacy for other motor symptoms using β-based, state-driven neural signals, gait is a dynamic, cyclical behavior that may require temporally precise modulation. Here we evaluated a behavior-contingent aDBS approach that synchronizes stimulation to gait phase. We reported a single-center, blinded, randomized, crossover study evaluating the feasibility of identifying patient-specific biomarkers to drive aDBS. The primary outcome was feasibility of successful identification of gait-phase biomarkers to implement aDBS. Five participants with PD undergoing pallidal DBS and subdural electrode paddle implantation were enrolled. We successfully identified personalized gait-phase biomarkers from cortical or pallidal field potentials in all five patients and embedded them into a bidirectional neurostimulator. During acute in-clinic testing, aDBS improved step variability and step symmetry versus cDBS. Three participants subsequently completed a double-blinded, multi-day crossover phase. In this setting, aDBS maintained general motor symptom control, reduced falls and yielded patient-specific gait improvements. No adverse events occurred and aDBS was well tolerated. These findings establish the feasibility of biomarker-driven, movement-synchronized neuromodulation and support the development of a larger randomized trial to determine clinical efficacy. ClinicalTrial.gov registration: NCT04675398 . A randomized crossover study shows that gait-phase-synchronized adaptive deep brain stimulation is feasible and safe, and reduces falls compared to continuous stimulation in Parkinson’s disease.

07.
arXiv (math.PR) 2026-06-16

Interplay of insurance and financial risks in a non Levy-Renewal environment

arXiv:2606.15596v1 Announce Type: new Abstract: In this paper we consider a multivariate risk model, with common counting process and common process of logarithmic returns for the investment portfolio. We assume that the claim-vectors, the counting process and the logarithmic returns of the investment portfolio satisfy a weak dependence structure. Further, we consider that the counting process represents an inhomogeneous renewal process, and the logarithmic returns represent a cadlag process with independent but not necessarily stationary increments. Under these conditions we provide an asymptotic expression for the infinite-time entrance probability of the discounted aggregate claims into some rare set xA, where A denotes a set from a general set family, crucial for the actuarial practice, when the common distribution of the claim vectors belong to a multivariate heavy-tailed distribution class. This result, is derived under a moment condition for the financial risks, and underlines the multivariate linear single big jump principle. When we restrict the distribution class of the claim-vectors to multivariate regular variation, we find more explicit asymptotic expressions, weakening the moment conditions on the financial risks. The asymptotic formulas, derived through double dependence solution, become more direct and practical in applications. With respect to the technical part, due to non Levy-Renewal framework, the classical Kesten-Goldie theorems are not applicable, nor their extensions. The way we make the discretization of the process of the discounted aggregate claims permits to derive uniform asymptotics with respect to the number of summands, that facilitate the approximation of the infinite sums of the main results.

08.
arXiv (CS.CL) 2026-06-17

Moderating Illicit Online Image Promotion for Unsafe User-Generated Content Games Using Large Vision-Language Models

Online user generated content games (UGCGs) are increasingly popular among children and adolescents for social interaction and more creative online entertainment. However, they pose a heightened risk of exposure to explicit content, raising growing concerns for the online safety of children and adolescents. Despite these concerns, few studies have addressed the issue of illicit image-based promotions of unsafe UGCGs on social media, which can inadvertently attract young users. This challenge arises from the difficulty of obtaining comprehensive training data for UGCG images and the unique nature of these images, which differ from traditional unsafe content. In this work, we take the first step towards studying the threat of illicit promotions of unsafe UGCGs. We collect a real-world dataset comprising 2,924 images that display diverse sexually explicit and violent content used to promote UGCGs by their game creators. Our in-depth studies reveal a new understanding of this problem and the urgent need for automatically flagging illicit UGCG promotions. We additionally create a cutting-edge system, UGCG-Guard, designed to aid social media platforms in effectively identifying images used for illicit UGCG promotions. This system leverages recently introduced large vision-language models (VLMs) and employs a novel conditional prompting strategy for zero-shot domain adaptation, along with chain-of-thought (CoT) reasoning for contextual identification. UGCG-Guard achieves outstanding results, with an accuracy rate of 94% in detecting these images used for the illicit promotion of such games in real-world scenarios.

09.
arXiv (CS.CL) 2026-06-15

Every Eval Ever: A Unifying Schema and Community Repository for AI Evaluation Results

AI evaluations are widely used for testing and understanding progress. However, the diverse evaluators bring with them inconsistencies that challenge analysis and comparison. First, results are saved in incompatible formats, scattered across leaderboards, papers, blog posts, evaluation harness logs, and custom repositories. Second, results are created by different evaluation frameworks, which produce divergent scores for nominally identical evaluations and record metadata inconsistently, hindering comparison, cross-community evaluation science, cost reduction, and reuse. We introduce Every Eval Ever, the first shared schema and community-crowdsourced repository for AI evaluation results. The schema standardizes how evaluations are represented in a unified, single JSON document. It is source-agnostic by design, ingesting results from evaluation harnesses and papers alike, and optionally stores per-instance outputs for fine-grained analysis. We contribute: (i) a community-governed metadata schema with a companion instance-level schema, the first standardization effort of its kind; (ii) automatic converters from popular formats, evaluation harnesses, and leaderboards to the unified schema; and (iii) a crowdsourced community database hosted on Hugging Face, currently spanning to date 22,235 models, 2,273 unique benchmarks, and 31 evaluation formats.

10.
arXiv (quant-ph) 2026-06-15

Simultaneous Estimation of Partial-Transpose Moments with Active Memory Independent of the Moment Order

arXiv:2606.14204v1 Announce Type: new Abstract: We study the simultaneous estimation of partial-transpose moments $p_j(\rho_{AB})=\mathrm{Tr}[(\rho_{AB}^{T_B})^j]$, $j=2,\ldots,K$, of an unknown bipartite $n$-qubit state from independent copies under an explicit active-memory constraint. We give a sequential qubit-reuse realization of the partial-transpose permutation that uses at most $2n+1$ active qubits, independent of $K$, and estimates all moments $p_2,\ldots,p_K$ to uniform additive error $\epsilon$ with total copy complexity $O(K\log K/\epsilon^2)$. We also prove two converse bounds. First, any uniformly accurate simultaneous estimator requires $\Omega(K/\epsilon^2)$ copies in the worst case. Second, the same scaling holds on an explicit isospectral two-qubit negative-partial-transpose (NPT) family whose ordinary moments are constant while the partial-transpose moments vary. These results characterize the copy complexity of the partial-transpose moment hierarchy up to a logarithmic factor and extend simultaneous nonlinear-functional estimation from ordinary state powers to partial-transpose spectral data under active quantum memory independent of the target moment order.

11.
medRxiv (Medicine) 2026-06-12

Association of circulating endothelial progenitor cell count and functional outcome in patients with acute ischemic stroke due to intracranial large vessel occlusion

Background: Circulating endothelial progenitor cells (cEPCs) contribute to vascular repair following an ischemic stroke. The aim of the study was to evaluate the association between cEPCs and functional outcomes in patients with acute ischemic stroke (AIS) due to large vessel occlusion (LVO) who received endovascular therapy (EVT). Methods: Prospective study of patients with LVO-AIS who received EVT. Blood samples were obtained within 24 +- 12 hours and on day 7+-1 from stroke onset. cEPCs were detected using flow cytometry (CD34+/VEGFR2+/CD133+). The primary endpoint was a favourable functional outcome (modified Rankin Scale 0-2) at three months of follow-up. Secondary endpoints include baseline to 24 hours/day 7 changes in the National Institutes of Health Stroke Scale (NIHSS) score and collateral circulation (CC) status. Bivariate and multivariable logistic regression analyses were performed. Results: Included were 90 patients (73.2+-12.7 years, 41.1% women) in 42 of whom (46.7%) cEPCs were detected at 24 hours. On day 7, cEPCs were detected in 27 (43.6%) of 62 patients for which this information was available. Atrial fibrillation, prior anticoagulant treatment and stroke onset-to-door time

12.
arXiv (math.PR) 2026-06-12

Counterintuitive problems in discrete probability

arXiv:2606.07516v2 Announce Type: replace Abstract: This manuscript contains a collection of counterintuitive problems in discrete probability, together with detailed solutions. The dataset was constructed as part of a broader research project investigating the capabilities of the latest-generation Large Language Models (LLMs) in solving discrete probability problems, in order to assess whether LLMs tend to make systematic reasoning errors associated with known cognitive biases. The problems collected here are specifically designed to challenge heuristic reasoning strategies that often lead to intuitively appealing but mathematically incorrect conclusions. The dataset combines several types of problems. Some are adapted from classical probabilistic paradoxes and cognitive-bias literature, while others originate from recreational mathematics sources or were developed by ourselves following similar principles. The primary purpose of this document is to provide a transparent and publicly accessible reference for the problems used in our experimental evaluation of language models, as well as providing detailed human-made solutions. At the same time, we believe that this collection may also prove useful for future research on probabilistic reasoning, cognitive biases, and the evaluation of reasoning capabilities in artificial intelligence systems.

13.
arXiv (math.PR) 2026-06-12

Conditional means, vector pricings, amenability and fixed points in cones

Authors:

arXiv:2512.13829v4 Announce Type: replace Abstract: We develop a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized probabilities can be stationary, respectively invariant. Our results deviate from the setting of classical probability and lead to a new criterion for amenability and for fixed points in cones.

14.
arXiv (CS.AI) 2026-06-16

The Model Knows, the Decoder Finds: Future Value Guided Particle Power Sampling

arXiv:2605.02427v3 Announce Type: replace Abstract: A recurring pattern in "reasoning without training" is that base LLMs already assign non-trivial probability mass to correct multi-step solutions; the bottleneck is locating these modes efficiently at inference time. Power sampling provides a principled way to bias decoding toward such modes by targeting p_theta(x)^alpha with alpha > 1, but practical approximations must account for future-dependent correction factors that determine which prefixes remain promising. We introduce Auxiliary Particle Power Sampling (APPS), a blockwise particle algorithm for approximating the sequence-level power target with a bounded population of partial solutions. APPS propagates hypotheses in parallel using proposal-corrected power reweighting and refines their survival through future-value-guided selection at resampling boundaries. This redistributes finite compute across competing prefixes rather than committing to a single unfolding path, while providing a direct scaling knob in the particle count and predictable peak memory. We instantiate the future-value signal with short-horizon rollouts and also study an amortized variant that replaces rollouts with a lightweight learned selection head. AMore broadly, APPS improves the accuracy–runtime trade-off of training-free decoding, further supporting the view that inference-time power approximation can recover gains often attributed to post-training.

15.
arXiv (CS.AI) 2026-06-11

Subliminal Learning Is Steering Vector Distillation

arXiv:2606.00995v3 Announce Type: replace Abstract: Subliminal learning refers to a student language model acquiring a teacher's traits (e.g. a system-prompted preference for owls) when fine-tuned on the teacher's outputs, despite the outputs being semantically unrelated to those traits. It remains poorly understood how data without semantic meaning can transfer specific semantic traits. In this work, we show that subliminal learning is mediated by a single steering vector, i.e. a vector added to the model's activations. Across two open-source models, we find that the teacher's system prompt is well approximated by a steering vector, and that the student's behavior is driven by learning an aligned vector over fine-tuning. System prompts that are not well approximated by steering vectors are not subliminally learned. This is a special case of steering vector distillation, in which a student trained on the outputs of a steered teacher learns to imitate that steering. We demonstrate steering vector distillation on a range of semantic and random vectors. Adding a semantic vector to a model's activations can have both model-independent and model-specific (i.e. non-semantic) effects on its behavior, so generated data that is non-semantic can transmit a vector with semantic effects, enabling subliminal learning. This also explains why subliminal learning does not transfer between models. We find that adaptive optimizers are necessary for subliminal learning in language models: activation gradients on steered data carry a small but consistent component along the steering direction, and non-adaptive optimizers impede this by allowing outlier gradients to dominate.

16.
arXiv (quant-ph) 2026-06-16

Optimal learning of quantum channels in diamond distance

arXiv:2512.10214v3 Announce Type: replace Abstract: Quantum process tomography, the task of estimating an unknown quantum channel, is a central problem in quantum information theory. A long-standing open question is how many uses of an unknown channel are required to learn it in diamond distance, the standard metric for distinguishing quantum processes. While quantum state tomography is well understood, for general channels the problem remained open beyond the unitary case. Here we establish the query complexity of channel tomography with optimal dependence on the dimension parameters, at any fixed constant accuracy. We design an algorithm showing that any channel with input/output dimensions $d_{\mathrm{in}},d_{\mathrm{out}}$ and Kraus rank at most $k$ can be learned to accuracy $\varepsilon$ using $O(d_{\mathrm{in}}d_{\mathrm{out}}k/\varepsilon^{2})$ channel uses. Conversely, we prove that $\Omega(d_{\mathrm{in}}d_{\mathrm{out}}k)$ uses are necessary at constant accuracy and that, for non-minimal Kraus rank, a separate $\Omega(1/\varepsilon^{2})$ contribution is unavoidable. Since channels subsume states, unitaries, isometries, and measurements as special cases, our protocol provides a unified framework for these tomography tasks, yielding new guarantees for isometry and measurement tomography while recovering known optimal scalings for state and unitary tomography. Our algorithm follows the natural strategy of performing optimal tomography on the Choi state. The main technical contribution is to show that this suffices to control the induced diamond-distance error, avoiding the dimension loss incurred by a naive conversion from Choi-state trace distance to channel diamond distance. The protocol uses the channel non-adaptively to prepare Choi-state copies, purifies them in parallel, and performs optimal pure-state tomography on the resulting purifications. Hence, we reduce channel tomography to pure-state tomography.

17.
arXiv (quant-ph) 2026-06-15

New Identity for Cayley's First Hyperdeterminant with Applications to Symmetric Tensors and Entanglement

Authors:

arXiv:2512.03093v3 Announce Type: replace Abstract: In this article, a new formula for computing Cayley's first hyperdeterminant in terms of the Levi-Civita symbol is given. It is then shown that this formula can be used to compute the hyperdeterminant of symmetric tensors in polynomial time with respect to their order (assuming fixed side length). Applications to quantifying the entanglement of states of bosonic quantum systems are then discussed. Additionally, in order to obtain the fast calculation of the hyperdeterminant on symmetric tensors, generalized elimination and duplication matrices are defined and their explicit formulas are derived.

18.
arXiv (CS.AI) 2026-06-17

MODE: Modality-Decomposed Expert-Level Mixed-Precision Quantization for MoE Multimodal LLMs

arXiv:2606.17118v1 Announce Type: cross Abstract: Mixture-of-Experts Multimodal Large Language Models (MoE-MLLMs) offer remarkable performance but incur prohibitive GPU memory costs, making compression essential. Among PTQ methods, expert-level mixed-precision quantization has proven effective for MoE-LLMs, yet suffers notable degradation on MoE-MLLMs due to two overlooked biases in expert importance estimation. (1) At the cross-modal level, the numerical dominance of vision tokens causes expert selection frequency to be dominated by vision tokens, masking experts that are critical to the text modality; (2) at the intra-vision level, the large proportion of redundant vision tokens further skew frequency statistics, obscuring experts critical for informative visual content. To bridge gaps, we propose MODE, a modality-decomposed expert-level mixed-precision quantization framework for MoE-MLLMs that decomposes expert selection frequency by modality, filters redundant vision tokens to obtain denoised visual frequency, and further evaluates quantization sensitivity per modality as a complementary signal to frequency-based estimation. These signals are integrated into an Integer Linear Programming formulation to assign per-expert bit-widths under a given budget. Extensive experiments show that MODE is particularly well-suited for MoE-MLLMs, limiting average performance loss to within 2.9% at W3A16, with larger gains at the extreme 2-bit setting.

19.
arXiv (CS.CL) 2026-06-12

Operadic consistency: a label-free signal for compositional reasoning failures in LLMs

Detecting LLM reasoning failures at inference time without ground-truth labels has motivated a wide range of confidence baselines, including self-consistency, semantic entropy, and P(True), built on within-question sampling and self-evaluation. Operad theory, the formalism for systems built by iterated substitution, suggests a complementary diagnostic: a model's direct answer to a compositional query should agree with the answer it produces by composing a stated decomposition of the same query. We instantiate this idea as operadic consistency (OC), a per-question signal. Across twelve instruction-tuned LLMs (4B to 671B parameters, open-weights and closed-source) on four multi-hop QA datasets, OC is strongly correlated with accuracy on every dataset (Pearson $r \in [0.86, 0.94]$, all $p \leq 0.0004$), and is the only signal we evaluate with $r \geq 0.85$ uniformly across all four datasets. Chain-of-thought self-consistency (CoT-SC; Wang et al., 2023) matches OC on HotpotQA and DROP ($r = 0.93, 0.87$) but drops to $r \approx 0.45$ on MuSiQue and StrategyQA. At the per-question level, OC contributes information beyond CoT-SC and semantic entropy on every dataset (cluster-robust $p \leq 10^{-16}$ for the OC coefficient), and the conclusion is robust to additionally controlling for constructed decomposition-aware baselines ($p \leq 10^{-13}$). The same signal yields selective-prediction improvements (accuracy at fixed coverage) over a tuned CoT-SC baseline at the equal-cost $K = 3$ budget (AUARC lifts of +0.086 to +0.096 and AUROC lifts of +0.092 to +0.164; 95% CIs exclude zero on every cell). On five frontier thinking models, where the decomposition is extracted from the model's own chain of thought, the same equal-cost comparison gives positive selective-prediction point-estimate lift on all 16 (dataset, budget, metric) cells tested, with 95% CIs excluding zero on 12 of the 16.

20.
arXiv (CS.CL) 2026-06-16

Cross-lingual Embedding Clustering for Hierarchical Softmax in Low-Resource Multilingual Speech Recognition

We present a novel approach centered on the decoding stage of Automatic Speech Recognition (ASR) that enhances multilingual performance, especially for low-resource languages. It utilizes a cross-lingual embedding clustering method to construct a hierarchical Softmax (H-Softmax) decoder, which enables similar tokens across different languages to share similar decoder representations. It addresses the limitations of the previous Huffman-based H-Softmax method, which relied on shallow features in token similarity assessments. Through experiments on a downsampled dataset of 15 languages, we demonstrate the effectiveness of our approach in improving low-resource multilingual ASR accuracy.

21.
arXiv (CS.LG) 2026-06-18

TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs

arXiv:2601.20361v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space-time PINNs take time as an input but reuse a single network with shared weights across all times, forcing the same features to represent markedly different dynamics. This coupling degrades error performance and can destabilize training when enforcing PDE, boundary, and initial constraints jointly. We propose Time-Induced Neural Networks (TINNs), a novel architecture that parameterizes the network weights as a learned function of time, allowing the effective spatial representation to evolve over time while maintaining shared structure. The resulting formulation naturally yields a nonlinear least-squares problem, which we optimize efficiently using a Levenberg-Marquardt method. Experiments on various time-dependent PDEs show up to 4 times improved relative error and 10 times faster convergence compared to PINNs and strong baselines.

22.
arXiv (math.PR) 2026-06-11

On the $d$-rigidity phase transition in random graphs

Authors:

arXiv:2605.25711v2 Announce Type: replace-cross Abstract: We study generic $d$-dimensional rigidity in sparse random graphs. Our main result is that for every $d\ge 2$, the Erdős–Rényi random graph $G\sim G(n,c/n)$ undergoes a $d$-rigidity phase transition at the known, explicit, $d$-orientability threshold $c_d$: If $cc_d$, then $G$ is a.a.s. not independent in the generic $d$-rigidity matroid, and we give a sharp asymptotic estimate for its rank. In addition, the $d$-rigidity closure of $G$ has a giant clique of linear size, which contains all but at most $o(n)$ vertices of the $((d+1)+d)$-core of the graph. More generally, we compute, up to a $1+o(1)$ factor, the generic $d$-rigidity rank of random graphs with a given degree distribution. For example, we show that the uniform $n$-vertex $k$-regular graph a.a.s. has rank $\min(k/2,d)n+o(n).$ Our approach is to estimate the rigidity rank of a random graph from its Galton–Watson local weak limit, using a parameter that we call local flexibility.

23.
arXiv (quant-ph) 2026-06-12

Vacuum photon emission and mean electromagnetic field in pair-creating external backgrounds

arXiv:2606.12547v1 Announce Type: cross Abstract: We develop a perturbative description of vacuum radiative processes in quantum electrodynamics with a prescribed external electromagnetic background capable of producing electron-positron pairs. Since the initial vacuum is then unstable and the in- and out-vacua are inequivalent, radiative observables require a real-time formulation beyond the ordinary in-out approach of vacuum-stable QED. Using the Keldysh-Schwinger-Fradkin nonequilibrium technique, we derive the mean number density of emitted photons through the second nonvanishing order in the fine-structure constant. The leading term, of order $\alpha$, reproduces the known vertex and tadpole mechanisms, while the complete order-$\alpha^2$ correction contains interference, loop, and induced-current contributions. We also give an independent derivation based on the spectral decomposition of the identity operator in the in-Fock space, where the photon number density is represented as a sum of squared transition amplitudes and vacuum-disconnected terms are canceled by the optical theorem generalized to an unstable vacuum. In addition, we compute the mean electromagnetic field through order $e^3$, including the electromagnetic dressing of the induced vacuum current, and verify it using the corresponding Schwinger-Dyson equations. The final formulas are expressed in terms of exact solutions and propagators of the Dirac equation in the external background and apply to general spacetime-dependent field configurations.

24.
arXiv (CS.CV) 2026-06-16

FireRed-Image-Edit-1.0 Technical Report

We present FireRed-Image-Edit, a diffusion transformer for instruction-based image editing that achieves state-of-the-art performance through systematic optimization of data curation, training methodology, and evaluation design. We construct a 1.6B-sample training corpus, comprising 900M text-to-image and 700M image editing pairs from diverse sources. After rigorous cleaning, stratification, auto-labeling, and two-stage filtering, we retain over 100M high-quality samples balanced between generation and editing, ensuring strong semantic coverage and instruction alignment. Our multi-stage training pipeline progressively builds editing capability via pre-training, supervised fine-tuning, and reinforcement learning. To improve data efficiency, we introduce a Multi-Condition Aware Bucket Sampler for variable-resolution batching and Stochastic Instruction Alignment with dynamic prompt re-indexing. To stabilize optimization and enhance controllability, we propose Asymmetric Gradient Optimization for DPO, DiffusionNFT with layout-aware OCR rewards for text editing, and a differentiable Consistency Loss for identity preservation. We further establish REDEdit-Bench, a comprehensive benchmark spanning 15 editing categories, including newly introduced beautification and low-level enhancement tasks. Extensive experiments on REDEdit-Bench and public benchmarks (ImgEdit and GEdit) demonstrate competitive or superior performance against both open-source and proprietary systems. To support future research, our code, models, and benchmark suite are publicly available at https://github.com/FireRedTeam/FireRed-Image-Edit/ .

25.
arXiv (CS.CL) 2026-06-15

A Computational Audit of Demographic Association Encoding in ClinicalBERT Language Predictions

Transformer-based clinical language models are increasingly integrated into high-stakes clinical decision support pipelines, yet the computational mechanisms through which demographic associations encoded in medical documentation propagate into model probability distributions remain empirically underspecified. We present a systematic computational audit of representational bias in ClinicalBERT (Alsentzer et al., 2019), a BERT-based model pretrained on MIMIC-III discharge summaries, employing two complementary probing methodologies: Log Probability Bias Analysis (LPBA), which quantifies demographic descriptor-induced shifts in masked token probability distributions across behavioral and evaluative semantic categories, and Masked Language Model-based analysis (MLM), which probes internal representational structure for demographic agency attribution encoding across 98 real clinical sentence templates and eight intersectional race-gender combinations. Corpus frequency analysis operationalizes the distinction between statistical disparity and bias amplification by benchmarking model outputs against empirical term frequencies in the MIMIC-III training corpus. Of 32 statistically significant findings, 65.6% contradict observed corpus distributions, rising to 80% for Black patients and 87.5% for agency attribution under MLM probing, providing direct empirical evidence that representational bias in ClinicalBERT operates predominantly through model-internal amplification rather than training data inheritance. Keywords: natural language processing, clinical documentation, algorithmic auditing, representational bias, health equity 1