Papers

We study rectified flows for denoising without clean training targets. For an unconditional rectified flow trained on Noise2Noise pairs, the optimal velocity field yields the minimum mean squared error (MMSE) denoiser in one step. In a jointly Gaussian model, we show that integrating the flow before applying its denoising readout increases error with integration time. The flow transports between noisy distributions, so its endpoint is not a clean-image estimate. Experiments on low-dose CT and Gaussian-corrupted natural images follow this pattern: one-step flow performs similarly to direct regression on the same pairs, whereas additional Euler steps reduce PSNR. A direct regressor using spatially separated, similar patches gives our best label-free CT result, a $1.99$\,dB gain over the noisy input. We report these results in CTDenoiser, a benchmark covering five architectures, supervised and self-supervised training, and two per-image methods. Supervised CNNs gain about $4$\,dB, while label-free performance depends strongly on how training pairs account for correlated CT noise. A channelized Hotelling observer also shows that fidelity gains need not improve lesion detectability: detectability falls at $160$\,HU despite higher PSNR and SSIM, while changes at $40$–$80$\,HU are small. Code, model definitions, and data-loading utilities will be released publicly; the repository link is withheld for anonymous review.

We present NanoForecast v0.5, a 6.5M-parameter forecaster that competes with models 31x its size (TimesFM, 200M parameters) after training pipeline fixes and no architecture change. Retraining the v0.3 architecture with corrected loss-scope handling, tensor shape alignment, and wider augmentation coverage cuts overall Mean Absolute Scaled Error by 43.8% under one fixed protocol (MASE 3.030 to 1.704) on the same data and compute budget. NanoForecast v0.5 beats TimesFM on all three ETT datasets (MASE 0.676/1.110/0.287 vs. 0.705/1.360/0.545) and on exchange rate (4.317 vs. 4.383); TimesFM keeps a clear lead on the high-cardinality electricity and traffic sets. Against PatchTST (15M+ parameters, official configuration), v0.5 wins all three ETT sets. Training takes about 12 hours on a single cloud GPU (NVIDIA T4, Google Colab) and inference needs no GPU (measurements in this paper are on an Apple M4 CPU). We release all code, pretrained checkpoints, and evaluation framework under Apache 2.0 at https://github.com/eulogik/NanoForecast

Multimodal large language models (MLLMs) process multimodal inputs by converting text, images, and videos into token sequences that are subsequently processed by a backbone language model. While MLLMs have achieved excellent performance in understanding the content of individual images, video understanding remains significantly more difficult because videos contain large number of video frames. MLLMs typically process only a subset of these frames, usually ranging from 8 to 64. MLLMs usually sample frames uniformly, regardless of their relevance to the question being answered. To address this limitation, several training-free, model-agnostic methods for selecting question-relevant frames have recently been proposed. In this work, we introduce a frame-selection method designed specifically for multiple-choice questions. We extend the query text by appending semantic cues derived from the answer choices and employ a direct query-frame alignment scoring mechanism. To the best of our knowledge, our method is the first to directly utilize answer choices as inference-time cues for selecting frames relevant to answering a question. The method first constructs a compact candidate pool by subsampling video frames at a fixed rate. The frames are then scored according to their maximum cosine similarity across all question-answer pairs to identify the most relevant frames for a given query. This approach preserves a fixed token budget while improving the relevance of the visual evidence provided to the downstream MLLM. We evaluate the effectiveness of our frame-selection method on the MLVU, Video-MME, and LongVideoBench benchmarks using three MLLMs: LLaVA-Mini, Qwen2-VL, and LLaVA-Video. Experimental results demonstrate that answer-aware frame selection generally outperforms uniform sampling and existing training-free frame-selection methods under the same frame budget.

Digital pens are widely used to capture handwriting on digital devices, enabling precise trace recording and enhancing human-computer interaction. However, most are bundled with tablets and lack cross-brand compatibility. Recent digital pens equipped with kinematic sensors have emerged, designed for use on any surface. This especially opens significant potential for supporting handwriting acquisition in classrooms. Handwriting reconstruction from such an IMU-equipped pen poses a challenge due to the significant variability in sensor signals between adults and children. Even when producing visually similar traces, variations in writing dynamics, motor control, pen holding, and user confidence introduce substantial discrepancies in the captured signals. Additionally, the high variability in children's handwriting requires collecting large amounts of data, which is not feasible to implement in a school environment at scale. Furthermore, models trained exclusively on adult data fail to generalize to children's handwriting, and conversely, models trained on children's data perform poorly on adult writers. This crosspopulation degradation highlights the need for a unified model that can be deployed directly on the pen, without any user-specific adaptation. To address this issue, we propose a cross-domain learning, using an original neural network architecture based on a Temporal Convolutional Network and multiple prediction heads. The model is designed to be robust across age groups by leveraging shared features while effectively handling variability induced by differences in graphomotor development. This approach aims to improve handwriting trace reconstruction from sensor data, where each domain benefits from additional data provided by the other domain.

Action anticipation predicts future human actions from partial video under incomplete context and temporal uncertainty. Recent systems introduce large language models (LLMs), vision-language models (VLMs), or language-derived semantics at different stages, but reported gains are difficult to interpret when task formulation, visual pretraining, supervision, decoder design, and evaluation code change simultaneously. The central contribution of this review is an evidence-aware design map that crosses task regime with the point at which language-derived information intervenes. We characterise task regimes along six axes. These axes organise the literature into five broad task families: single-action, sequence, object-interaction, cross-view, and planning-oriented settings. C1-C3 locate interventions in context construction, goal/intention modelling, and future decoding, while C4 is treated as an adjacent, emerging grounding/executability extension. Unlike a generic processing pipeline, the map links each intervention to an appropriate counterfactual, failure diagnosis, and permissible evidence claim. Supporting contributions include a protocol-level audit of Ego4D-LTA and EPIC-KITCHENS-100, a multidimensional evidence profile, and the Backbone-Aware Comparison and Ablation Protocol (BCAP). The unresolved EK-100 record is treated as a reporting-comparability case study and is not used as a leaderboard. Evidence for LLM benefits, goal ambiguity, and horizon effects is therefore formulated as testable hypotheses requiring matched validation, not as causal conclusions. The accompanying package contains the coded evidence, source locators, protocol metadata, and versioned catalogue used in the review.

Recent work suggests that obscure language registers can weaken large language model refusal behavior, especially when paired with black-box prompt optimization. It remains unclear whether failures stem from non-standard surface form, culturally grounded framing, or optimization over an expressive prompt-strategy space. We study Chinese registers by extending a classical-Chinese red-teaming framework to Shanghainese and Cantonese and running a 36-cell ablation across surface forms, strategy-bank variants, and two target models. The main finding is corrective: dialectal surface form is neither necessary nor sufficient for high attack success. Non-optimized English, Mandarin, and naive dialect translations remain below 8% attack success rate, whereas all conditions that retain an optimizer-controlled strategy bank reach 98–100%. A culture-neutral generic strategy bank reaches the same ceiling at near-single-query cost, further indicating that strategy-bank expressiveness, rather than dialectal or cultural content, accounts for most of the observed effect. Dialect choice still affects query efficiency and response severity, and qualitative coding identifies recurring high-level mechanisms such as semantic glossing and procedural scaffolding. We qualify the absolute ceiling-level attack success rate by showing sensitivity to judge calibration and noting that the design does not fully separate one-shot strategy construction from iterative search.

Ontology-driven knowledge graph construction from industrial text remains challenging due to the domain specificity of documents, the scarcity of annotated resources, and the complexity of ontology engineering workflows. This paper presents and investigates the applicability of an ontology learning pipeline that combines compact open-source Large Language Models (LLMs), reusable prompting strategies, and open knowledge bases to support the extraction, structuring, enrichment, and evaluation of knowledge from textual corpora. The approach is tested and evaluated on a private French corpus of power-grid incident reports, using locally deployable open-source LLMs ranging from 7B to 32B parameters. Starting from unstructured reports, the approach extracts entities and relations, generates RDF triples, constructs related OWL ontology, enriches it using external knowledge sources, assesses the quality of the ontology, and subsequently constructs a populated knowledge graph grounded in the resulting ontology schema. Experiments on 80 manually annotated private reports show that schema-guided prompting significantly improves extraction quality, while quantized models provide an effective trade-off between performance and computational cost. These results demonstrate the feasibility of transforming domain-specific industrial text into ontology-based knowledge graphs using locally deployed open-source LLMs, while supporting the generalization of the extraction process through reusable prompting strategies.

Face Image Quality Assessment determines the suitability of captured face images for automated face recognition (FR), a critical capability for reliable biometric systems. Existing state-of-the-art FR-integrated FIQA methods suffer from temporal instability: as the feature space evolves during training, single-epoch quality estimates fluctuate, creating a moving target that undermines reliable quality prediction. We introduce CARPM-FIQA, a stabilization strategy for FR-integrated FIQA that accumulates relative point margin measurements, the ratio between intra-class compactness and inter-class separation, across the entire training trajectory rather than relying on single-epoch estimates. This cumulative averaging approach provides theoretically grounded advantages: reduced variance in quality estimates, improved mean squared error, and enhanced ranking stability with convergence guarantees as training progresses. Through controlled experiments on the SynFIQA dataset with labeled quality groups, we demonstrate that cumulative averaging achieves superior discriminative ability, and ablation studies across different training configurations confirm consistent improvements. Evaluated against twelve FIQA methods on eight challenging benchmarks with four FR models at two FMR thresholds, CARPM-FIQA places 4th (CARPM-FIQA(L)) and 6th (CARPM-FIQA(S)) of 17 compared methods by pAUC-EDC and AUC-EDC averaged across FR models and, after per-benchmark normalization, across benchmarks, staying within a few percent of the best method's normalized average for every FR model, providing a principled solution to training instability while maintaining the performance benefits of FR integration. More broadly, our work demonstrates that temporal aggregation strategies can stabilize training objectives in deep learning systems where target values inherently fluctuate due to evolving feature representations.

Reliable face forgery detection is critical to the security of online identity verification systems, where missed attacks compromise security and excessive false positives disrupt legitimate users. Specialized forensic detectors achieve strong detection performance but provide limited interpretability, while multimodal large language models (MLLMs) offer strong semantic understanding and interpretable reasoning yet remain substantially weaker for face forgery detection. We argue that a key limitation lies in how visual evidence is acquired: subtle forensic artifacts may be poorly represented at standard resolution, while uniformly processing all cases at higher resolution is computationally inefficient. We therefore introduce ForensicZoom, an industrial-grade MLLM framework for adaptive visual inspection. ForensicZoom first equips a general-purpose MLLM with forensic-aware visual representations and aligns the language model with these features. Its central mechanism, NEED_ZOOM, enables the model to autonomously request magnified views of suspicious regions when the initial evidence is insufficient, turning fixed-pass classification into adaptive multi-round forensic reasoning. The zoom behavior is learned through reward shaping that balances detection accuracy with unnecessary visual inspection, concentrating additional computation on difficult cases. A final attribution optimization stage improves natural-language forensic reports while preserving detection performance. On large-scale industrial identity verification data, ForensicZoom achieves over 97% TPR at 0.1% FPR, substantially outperforming both specialized detectors and existing MLLM-based methods while producing actionable forensic attributions. These results demonstrate that ForensicZoom can provide an effective path toward accurate, interpretable, and scalable MLLM-based face forgery detection.

Retrieval-augmented generation (RAG) pipelines are typically assembled from independently-chosen components – a document parser, a chunking strategy, and an embedding model – yet these choices are rarely evaluated jointly, and evaluations that do combine them are usually run on a single document or corpus. We present a controlled factorial study of 3 parsers, 3 chunking strategies, and 5 dense embedding models, together with a sparse BM25 baseline, evaluated against 800 question instances, each with one or more required evidence strings, with evidence strings automatically validated against source text and a 10% random sample manually reviewed, across four structurally distinct Indian central-government regulatory documents. We fit linear mixed-effects models with document-query-level random intercepts to the resulting 72,000-row result set, run Holm-corrected paired comparisons between matched dense and sparse configurations, and report clustered bootstrap confidence intervals for all 54 unique retriever configurations. We find that no single retriever family dominates across documents; parser and chunker choice interact significantly; MPNet-base is a consistent underperformer with a severe failure mode on table-derived questions; and the corpus exhibits a near-saturated evidence-preservation ceiling above 98%, indicating that retrieval differences are driven primarily by ranking quality rather than information loss during ingestion. We additionally report embedding-dimension and chunk-size/overlap ablations and an efficiency/quality Pareto analysis. We release our full evaluation harness, corpus manifest, and 800-question benchmark.

Power magnetic materials are characterized on the sinusoidal and triangular waveforms that excitation hardware conveniently produces, whereas deployed converters expose cores to trapezoidal, PWM-shaped flux trajectories, so loss models must predict exactly where their training data are thinnest. The final test of the MagNet Challenge embeds a deliberately extreme instance of this characterization-deployment mismatch: for material D, trapezoids form 16.4% of the test set but only 1.4% of the training set. The 95th-percentile relative error, hereafter p95, of the best submission, built on sequential transfer learning, stalled at 15.9%, the worst among the five materials. This paper shows that the obstacle is missing information under covariate shift rather than class imbalance, and that the missing support can be borrowed from sibling materials instead of being extrapolated. Controlled experiments first refute the imbalance reading: four standard remedies fail, and raising the trapezoidal share to the test-set level degrades accuracy further. The proposed material-identity support transfer, MIST, then trains one 2784-parameter predictor jointly on all five challenge materials. Material identity enters through feature-wise linear modulation, or FiLM, the scarce material's true-label loss is reweighted, and material D receives no fine-tuning, so that the bias of its trapezoid-free training set is never re-installed. MIST lowers the five-seed material-D p95 from 20.39+/-2.03% to 12.38+/-0.92% and the trapezoidal-class p95 from 37.4+/-8.8% to 15.16+/-1.69%, surpassing the best submission with one-sixth of its parameters and no fine-tuning stage; removing material identity at matched capacity inflates the error by an order of magnitude. These results argue that scarce materials should be characterized jointly with their siblings.

Ship classification from Synthetic Aperture Radar (SAR) imagery is a critical computer vision task, yet the robustness of models under deployment shifts remains unclear. While models are often trained on one dataset and deployed on another, we lack a comprehensive understanding of their cross-dataset generalization. To address this, we evaluate six pretrained models on two SAR ship datasets in three settings: in-domain classification, cross-dataset transfer, and unknown-class detection. For unknown detection, we hold out all classes one at a time. In-domain, SARDet100K gives the best balanced accuracy on both datasets (73.4% on FUSARShip and 53.2% on OpenSARShip). In cross-dataset transfer, we observe strong failures: some models show moderate accuracy but near-chance balanced accuracy (for example, 64.5% accuracy but 33.3% balanced accuracy for OpenSARShip to FUSARShip). In unknown detection, performance depends on the held-out class and dataset, while MC-dropout variance is often close to random. These findings show that cross-dataset generalization in SAR remains limited and that task-specific uncertainty scores are often more informative than MC-dropout variance for held-out-class detection, although their relative ranking depends on the dataset and held-out class.

Remote-sensing foundation models offer strong representations for SAR imagery, but their behavior under severe long-tail class imbalance is still not well characterized. We benchmark DOFA and SAR-JEPA on the imbalanced OpenSARShip dataset and compare them with ImageNet-pretrained baselines under a fixed, training-efficient protocol that keeps the backbone frozen. To mitigate imbalance without fine-tuning, we apply four oversampling methods in embedding space exclusively to minority classes and train a lightweight classifier head on the augmented embeddings. Across both foundation models, oversampling improves Macro-F1 and test accuracy relative to their respective baselines, with the largest Macro-F1 gains observed for DOFA using ADASYN (34.39 to 38.56) and for SAR-JEPA using SVM-SMOTE (25.89 to 32.30). We also report class-wise behavior, showing that aggregate improvements can coexist with persistent failures on specific rare classes. Code for embedding extraction and reproducible multi-seed evaluation is provided to support rapid experimentation on free-tier hardware.

Data quality is a major bottleneck for the reliable deployment of graph neural networks (GNNs) in real-world graph mining tasks. Among various sources of degradation, label noise and feature distribution shift (hereafter referred to as distribution shift) are two common yet fundamentally different challenges. To study their effects under controlled conditions, this paper constructs a synthetic homophilic graph regression benchmark in which the two factors can be manipulated separately. A total of 41 configurations and 410 runs are conducted to evaluate the behavior of representative GNN models under varying noise and shift conditions. The results show two distinct patterns. First, under additive label corruption, performance remains relatively stable over a broad range of noise settings and begins to deteriorate sharply only after an observed transition region around the 50 percent noise ratio. Second, under extreme feature distribution shift, all tested models suffer substantial degradation, with test MSE increasing by 48 times to 316 times and correlation dropping by 73 percent to 89 percent. These findings suggest that, in the present controlled setting, GNNs are considerably more tolerant to moderate label perturbation than to severe distribution mismatch. The study provides a controlled empirical baseline for understanding how data quality affects GNN-based graph mining systems and offers practical implications for deployment-oriented monitoring and model maintenance.

Generative priors reconstruct accelerated 3D MRI well but pay heavily at deployment: tens of network evaluations per volume, and protocol-specific hyperparameter tuning. A third hidden cost is the scanner's fixed sampling pattern. We treat the whole operating point as an input. A 3D MeanFlow patch network (a one-step flow model) is fine-tuned end-to-end through a warm-started, five-iteration differentiable conjugate-gradient projection. A small hypernetwork maps the operating point (data-consistency weight, acceleration, and the Cartesian sampling pattern itself) to the network's per-channel modulation. Three findings follow. (i) Learning the acquisition is worth more than any other operating point: on clinical knee data, the learned mask gains up to +2.34 dB over the protocol's variable-density mask. This gain requires the solver: with a feed-forward reconstructor the same learned mask hurts at 4x (-1.7 dB), but with the data-consistency projection it adds +4.6 dB. (ii) One evaluation is highly effective: it beats a 20-step patch-diffusion prior by up to +3.1 dB on brain and +2.9 dB on knee. Three to five evaluations extend the front to +6 dB while using a quarter of the prior's network calls. (iii) Fully sampled targets are optional: trained self-supervised on a split of acquired samples, the reconstructor matches its supervised twin at 4x on real data. Finally, we report what failed and why: subject-adaptive acquisition from measured energy, combining self-supervision with learned acquisition, and amortising the data-consistency weight.

Scientific progress is a key driver of economic growth and prosperity. There is great excitement - but also concerns - about the impacts of AI on science, but so far little data. We provide early insights on this from three data sources: a sample of 15 million Gemini interactions, an inventory of over 2,600 specialized AI models across disciplines, and a survey of over 600 scientists. We map these data to a new taxonomy of scientific tasks to study how scientists are using AI. Four main findings emerge. First, we find broad adoption and coverage: scientists use AI more than most other occupations. Specialized AI models have broad disciplinary coverage and are highly cited. Nearly half of the scientists surveyed report using some form of AI every day. Second, we document evidence that LLMs (proxied through Gemini usage) and specialized models act as complements– LLMs are used for general analysis, coding, and manuscript preparation, while specialized models provide domain-specific predictions, data generation and classification. Third, scientists report large productivity gains from using AI: a saving of nearly 7 hours per week, time which is primarily re-invested in more research. Finally, we show that AI is already changing the scientific process. As some stages of scientific research become easier, bottlenecks shift downstream. Scientists report an increased backlog of untested hypotheses and substantial demand for output verification. Our findings suggest that AI holds significant potential to increase scientific productivity. However, as with other sectors, its ultimate impact will be governed by complex task interdependencies and investment into the elimination of emerging bottlenecks.

For the neutral periodic one-dimensional Riesz gas with pair potential locally $-|x|^a$, $0<a<1$, we prove a particle-displacement variance bound of order $\beta^{-1}$, uniformly in the number of particles. Log-concavity also gives exponential displacement tails. Every stationary periodic thermodynamic limit is simple, has intensity one, and admits a stationary ordered matching to the unit lattice with the same bounds. Each limit satisfies the canonical Gibbs equations for the full-line interaction, with an ordinary symmetric spatial principal value for the exterior potential. The matching implies uniformly bounded interval number variance and a positive limiting second moment of the reciprocal-lattice Fourier average at sufficiently low temperature. The main estimate compares the inverse random Hessian, through deterministic electrical flows, to a transient long-range network.

Knowledge tracing (KT) models predict student performance opaquely, limiting pedagogical action. This study contributes a validation protocol testing predictive competitiveness (RQ1), explanation stability (RQ2) and retraining-based faithfulness (RQ3) together. Thirteen behavioral features across five pedagogical themes were engineered from ASSISTments 2009 and 2012, with history features computed from temporally preceding interactions and current response latency retained only for retrospective analysis. ASSISTments 2009 was rebuilt: the uncorrected skill-builder release duplicates each multi-skill interaction across one row per skill, and because those rows share one correctness label, they leak it into preceding-interaction features. Rebuilding lowered model AUC and reordered the explanation results. An Extreme Gradient Boosting (XGBoost) model explained with Tree SHapley Additive exPlanations (TreeSHAP) was compared against four deep baselines (DKT, SAKT, AKT and SimpleKT) under an information-matched protocol giving the deep models the same behavioral signals and restricting XGBoost to what is derivable from the identifier-and-correctness stream they consume. XGBoost reached an area under the curve (AUC) of 0.777 on 2012 and 0.786 on rebuilt 2009, with prediction-time AUCs of 0.771 and 0.775, respectively, after excluding current response latency; restricted to the baselines' information it performed as they did (0.697 against 0.700, and 0.717 against 0.720), locating the difference in information supplied, not model family. Rankings were consistent across folds, seeds and conditioning schemes (Spearman rho = 0.989-1.000), and removing top-ranked TreeSHAP features harmed AUC more than random removal, though split-gain and permutation rankings performed comparably. Student-level examples are illustrative interpretations, not validated recommendations.

Mixers protect privacy by concealing deposit–withdrawal links, but are also abused to launder illicit funds. Existing anti-money laundering studies do not specifically target mixer laundering, while mixer research focuses on deanonymization rather than identifying laundering-related transactions. Public reports remain fragmented, leaving no public case-level dataset for systematic measurement and detection. To fill this void, this paper presents the first comprehensive study of mixer laundering on Ethereum. We first construct MixLaunder, the first public case-level dataset of mixer laundering. It covers 27 cases involving Tornado Cash and Railgun from 2020 to 2025 and labels 9,300 laundering-related transactions with case identities and observable upstream and downstream fund flows, including deposits totaling approximately \$1.1 billion. By comparing these transactions with background mixer usage, we identify five common strategies, showing that laundering evidence spans complementary behavioral and fund-flow contexts, while same-case activity is locally tight but weakly connected across bursts. Our analysis further reveals coverage gaps in mixer-side risk screening and representative deanonymization heuristics. Guided by these findings, we develop MixGuard, which combines tri-view representation learning with two-stage grouping for transaction-level detection and case-aware grouping. Under strict case-level holdout evaluation, MixGuard outperforms representative baselines, achieving 97.89% detection precision and 98.73% group purity, while its top ten groups cover 95.09% of each case's transactions on average.

It is a well-known result of Gustafson, Halmos and Radjavi, dating back to 1976, that any matrix $A$ in $SL_n(\mathbb{C})$ is a product of at most 4 involutions. We consider a natural continuous and holomorphic parameter dependence of this result in the spirit of Vaserstein and Gromov. Our main result shows that null-homotopy characterizes exactly those matrices in the special linear group over rings of continuous or holomorphic functions that are finite products of involutions. We give an upper bound $I(n, d)$, depending only on the size $n$ of the matrices and the dimension $d$ of the parameter space, for the number of involutions needed in the factorization. Our upper bound is not optimal, however we show that for fixed $n$ the optimal upper bound tends to infinity as $d\to \infty$. In some cases we are able to determine the optimal bound.

For the hard-sphere Boltzmann equation, we derive an exact nonlinear generating vertex for collisional stress and heat-flux production. The complete two-input Hermite hierarchy for stress resums to a universal traceless tensor times one scalar radial law, while the heat-flux vertex follows from the same law by an exact contraction. Taylor differentiation yields universal bilinear collision tensors with exact stress and heat-flux gradings, without a finite moment closure. DSMC tests, including wall-driven flows and a bimodal Mach-5 shock, recover independently sampled Boltzmann productions and the predicted convergence, while the converged production is independent of the thermal Gaussian foot used for its Hermite representation.

Image restoration is inherently challenging due to the diverse and highly input-dependent nature of real-world degradations. While recent architectures like Transformers and state-space models have advanced the field, they predominantly rely on static, globally shared parameters, which struggle to fully accommodate instance-specific degradation patterns. Test-Time Training (TTT) offers a promising paradigm for generating data-dependent operators, yet its standard self-supervised inner loop lacks the explicit guidance required to transition degraded features toward clean structures. To address this, we propose TTTIR, a novel framework that reformulates image restoration as an instance-specific state evolution process. Specifically, we design Progressive State Sequence Generation (PSSG) to construct complementary spatial-frequency target states (defining what to recover), and State Transition Evolution (STE) to adapt lightweight transition operators via a restoration-oriented TTT inner loop (determining how the features should evolve). Extensive experiments demonstrate that TTTIR consistently outperforms state-of-the-art models across multiple image restoration benchmarks, achieving dynamic instance-specific recovery with favorable computational scalability. The code is available at https://github.com/Elysiaaaaaaaa/TTTIR.git.

Let $X$ be a three-dimensional real Banach space and let $f:S_X\to S_Y$ be a surjective isometry. We study the propagation of an affine formula for $f$ on a relatively open part of $S_X$. A finite family of antipodal distance coordinates propagates a linear anchor except at three explicitly described degeneracies: a facet, an open face-star, or a family of chord cones with a common cylindrical kernel. We prove that, if the norm has no fixed-direction cylindrical open cone, every affine open anchor is linear and global. This yields a source-geometric criterion for the Mazur–Ulam property and covers, among other non-strictly-convex examples, the Euclidean double cone. We also give a segment-saturation criterion which proves the property for every prism $Z\oplus_\infty\mathbb R$, where $Z$ is an arbitrary real Banach plane. Finally, in the remaining cylindrical regime, we prove that a chord-saturated same-kernel network cannot be confined to one proper projective quotient arc. We then show that this multi-arc difficulty and the transverse-ruled part of producing an initial affine anchor reach the same final obstruction: upgrading norm calibration on an ambient open cone, together with calibration on a few spherical segments, to pointwise calibration of the sphere map on a two-dimensional open patch.

In this paper, we study de Rham realizations for finite orientifold quotients. On the orientation preserving inertia of an almost complex global quotient we construct an anti-linear involution of the Chen-Hu algebra whose fixed subalgebra is a real form of the Chen-Ruan algebra. For genuine orientation reversing fixed sectors we prove that no coordinate invariant single sector fractional age exists. When a Calabi-Yau volume line is preserved, the relative phases define a canonical class $[\mu_{\mathbb R}]\in H^2(\widehat G;\mathbb Z_\epsilon)$. We identify this class with the Bockstein obstruction to a coherent real phase lift and prove that its vanishing is equivalent, after rephasing the volume form, to a phase trivial orientifold action. We then formulate a general Euler-Gysin realization theorem using relative Fredholm bundles and determinant-line sewing. For phase trivial Calabi-Yau surfaces we verify the admissibility conditions directly and obtain a canonically defined associative graded cohomology algebra containing the Chen-Hu even sector and the odd fixed surfaces. For an Eisenstein abelian surface with an order six dihedral action we compute the centralizer invariant algebra explicitly; it is a $16$ dimensional Frobenius algebra whose odd sector multiplication is noncommutative in the shifted grading. We also explain the relation with earlier unoriented orbifold cohomology constructions.

Training spike detectors on real recordings is challenging because algorithmically generated labels can be noisy and incomplete. We propose VanillaSort, combining multichannel detection with spatially augmented, template-guided clustering. VanillaDet uses visibility-aware masking, truncated Gaussian targets and a temporally tolerant positive-bag loss, followed by conditional event-SNR gating. VanillaCluster combines HuiduRep embeddings with relative-amplitude features for Gaussian mixture clustering and refines assignments using cross-fitted waveform templates built from selected core events. VanillaDet improves detection accuracy over SimSort by two and three percentage points on the static and drift subsets of Hybrid Janelia, respectively. The complete pipeline also improves sorting performance over the corresponding HuiduRep baselines. These results support learning from imperfect real-data labels and incorporating waveform consistency into neuronal assignment.

We develop an interdisciplinary framework for evaluating the epistemic robustness of social-scientific inquiry through Hadamard's criteria for well-posed problems: existence, uniqueness, and stability. Reinterpreting these criteria not as demands for deterministic certainty but as methodological guardrails, we show how they diagnose recurrent failures of identification and inference across quantitative and qualitative paradigms. In quantitative research (e.g., econometric modeling), instability manifests when substantive conclusions depend sensitively on model specifications or data filtering. In interpretivist qualitative research, non-uniqueness and non-falsifiability arise when theoretical frameworks are elastic enough to accommodate contradictory observations without pre-specified rejection criteria. We frame these failures as inverse problems where the mapping from empirical data to substantive claims fails to satisfy existence, uniqueness, or stability. Finally, we propose cross-paradigmatic safeguards: ex-ante falsification criteria, empirical boundary conditions, multiverse sensitivity auditing, and cross-observer validation, to ensure social-scientific claims remain appropriately constrained, falsifiable, and robust to perturbations in evidence and interpretation.

Motivations and derivations for Heron's triangle area formula abound. But how would one discover the formula? We recount the challenge of designing a laboratory experiment to discover Heron's formula, and of doing so in the morning, in time for a noon class—a snapshot of collaboration with AI in fall 2025. We then reflect on extensions and generalizations.

The rapid progress of artificial intelligence is reshaping robotics and accelerating the adoption of learning-based approaches. While purely data-driven methods have achieved remarkable success in computer vision and natural language processing, robotics remains constrained by limited data, complex real-world interactions, and the need for reliable operation. These challenges have motivated the exploration of physics-embedded robot learning, which embeds physics priors into learning algorithms. By encoding the underlying physical laws and constraints, physics priors can complement limited data with robotics-specific inductive biases, potentially improving generalization, interpretability, and sample efficiency. However, the literature on physics-embedded robot learning remains fragmented across terminology, methodologies, and application domains, making it difficult to assess this growing body of work. This survey reviews physics-embedded robot learning across a broad range of physics priors, robotics applications, and machine learning models, from single-layer perceptrons to generative foundation models. We adopt a unified taxonomy that classifies existing approaches according to their physics embedding: physics-guided inputs, data, and representations; physics-encoded model architectures; and physics-informed training loss functions. Building on this taxonomy, we review methods for robot dynamics learning, trajectory planning, prediction, control, and estimation, together with the corresponding open-source software ecosystem. We identify key open challenges, and outline promising future research directions. Overall, we argue that physics priors provide a particularly relevant robotics-specific inductive bias, complementing rather than replacing data-driven learning, and paving the way toward more generalizable, data-efficient, and trustworthy robotic systems.

We conjecture an explicit evaluation of the pure fifth Bessel moment $\int_0^\infty K_0(t)^5\,dt$ as a quadratic expression in the critical value $L(f,2)$ of the weight-three, level-60 newform $f$ (LMFDB orbit 60.3.b.a) identified in the twisted fifth-moment modularity theorem of Lim, Tu and Yu, with coefficients in $\mathbb{Q}(\sqrt{5})$ and the square taken before the real and imaginary parts. Directed interval computations, using no stored Bessel or $L$-values, bound the absolute discrepancy by $10^{-358}$. We prove three exact modular identities for $f$: the Petersson-norm formula $\langle f,f\rangle_{60} = \frac{3(5-\sqrt{5})}{2\pi^4}|L(f,2)|^2$, the coefficient-conjugation relation $L(f^{\sigma},2) = \kappa L(f,2)$ with explicit $\kappa \in \mathbb{Q}(\sqrt{5},i)$, and the twisted symmetric-square evaluation $L(\chi_{-4}\mathrm{Sym}^2 f,2) = \sqrt{15}\,\pi^2 \langle f,f\rangle_{60}$, together with $L(\chi_{-4}\mathrm{Sym}^2 f,3) = \pi^4\langle f,f\rangle_{60}/8$, in the full Euler-factor normalization of Lim, Tu and Yu. The last identity shows that the companion norm conjecture $D_{5,\mathrm{odd}} = \frac{3\sqrt{15}(5-\sqrt{5})}{2}|L(f,2)|^2$ is equivalent to the symmetric-square conjecture $D_{5,\mathrm{odd}} = \pi^2 L(\chi_{-4}\mathrm{Sym}^2 f,2)$ of Lim, Tu and Yu, while the exact relation $D_{5,\mathrm{even}} = \pi^2 D_{5,\mathrm{odd}}/(2\sqrt{15})$ follows from Chuang's period formulas. Every Bessel-to-modular equality, including the individual-period formula, remains conjectural. Complete proofs, exact rational certificates and verification programs are included as ancillary files.

World models support autonomous driving by predicting the scene evolution associated with candidate trajectories. Driving dynamics differ in predictability, motivating a distinction between regular evolution and event-induced deviations that call for selective correction. We propose EditWM, a world model that decomposes future prediction into normal evolution and event-driven incremental correction in compact visual feature space. A trajectory-conditioned normal predictor provides the base forecast and is then frozen for correction learning. A correction decoder compares this forecast with observation history and planned actions, producing a bounded feature update whose contribution is regulated by a learned gate. The corrected future features condition trajectory scoring through candidate-specific cross-attention, linking world modeling to plan selection. At inference, EditWM uses only past and current observations, ego state, and candidate trajectories. Across all 12,146 NAVSIM navtest scenes, expert-trajectory-conditioned evaluation shows a 5.35% reduction in future-feature MSE over Normal, with improvements in 83.54% of scenes. The system achieves 91.05 EPDMS on a 100-point scale using the official EPDMS evaluator. These results demonstrate improved future-feature prediction and competitive trajectory selection when corrected future representations are integrated into planning.