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Test-time compute (TTC) scaling has emerged as a powerful paradigm for improving large language model (LLM) reasoning by allocating additional compute during inference, e.g., via multi-sample generation and verifier-based reranking. Existing TTC scaling strategies and reasoning scorers remain fragmented, evaluated under inconsistent protocols, and are rarely analyzed through the lens of quality-cost trade-offs. We introduce ThinkBooster, a unified framework for seamless test-time compute scaling of LLM reasoning, which consists of (i) a modular Python library implementing state-of-the-art TTC scaling strategy and scorer families, (ii) a benchmark that jointly evaluates performance and computational efficiency, and (iii) a deployable OpenAI-compatible proxy service that enables drop-in integration of adaptive reasoning into real-world applications. We further provide a demo visual debugger for inspecting the reasoning trajectories, intermediate selection decisions, and alternative reasoning paths. Empirical results on mathematical and coding tasks reveal the performance-compute trade-offs of TTC scaling strategies and scoring methods and demonstrate that ThinkBooster provides practical gains in real-world tasks. The code is available online under an MIT license.

Forward-Forward (FF) learning [Hinton, 2022] replaces backpropagation with strictly layer-local goodness updates. Recent FF-CNN work has narrowed the gap to BP on 32x32 benchmarks, raising the question of whether layer-local training is becoming a viable alternative at realistic scale. To probe this rigorously, we develop DTG-FF -- dynamic temperature goodness, decoupled normalization, and multi-layer fusion -- as an instrument that sets FF-family state of the art across nine real-data benchmarks (91.8% CIFAR-10 and the first FF baseline at ImageNet-100 224x224), and use it to audit how far layer-local training actually scales. (1) Real-data scaling. Under identical recipe and backbone, an architecture-matched BP-DeepSup baseline beats DTG-FF by 2.40/5.93 pp on CIFAR-10/CIFAR-100, and the gap widens with class count. At 224x224 the same instrument reaches only 49.4% -- the first FF baseline at this scale, versus typical BP above 75% [Tian et al., 2020] -- exposing a real-data ceiling invisible at 32x32. (2) Synthetic vs. real K-conflict. DTG-FF increasingly outperforms BP as class count K grows on synthetic teacher-student tasks, yet on real images the FF-BP gap reverses sign and widens with K. A within-dataset CIFAR-100 coarse vs. fine probe isolates label-hierarchy from image distribution: synthetic K-sweeps confound output dimensionality with fine-grained discrimination difficulty and thereby overstate FF transferability. (3) Systems audit. FF can be implemented without storing depth-wide activations, but on commodity 8 GB hardware standard BP+gradient-accumulation reaches 4.18 GB / 157 imgs/s versus DTG-FF's 7.90 GB / 138 imgs/s, so a memory-based justification for FF at this scale is not supported under fair baselines.

Scaling laws for dense LLMs under infinite data are well explored, but how sparsity interacts with limited data is not. In this work, we study sparse training in data-constrained regimes where limited unique tokens require multi-epoch training. Our experiments span models up to 1.92B parameters in the fitting set, sparsity up to 93.75%, unique data budgets up to 2.6B tokens, and total training tokens up to 41.6B over 16 epochs; we further validate extrapolation on held-out dense-equivalent models up to 7.68B parameters. We find that: 1. Sparse scaling in data-limited settings: We introduce a scaling law that models loss as a function of active parameters, unique tokens, data repetition, and sparsity, accurately predicting performance across compute and data budgets. 2. Delayed data saturation: sparse training postpones diminishing returns from repeated data, making multi-epoch training more effective. 3. Resource trade-offs: With fixed data, loss-optimal sparsity is moderate ~ 50%, while compute-optimal sparsity is higher and grows with data scale. Overall, sparsity is not just a tool for efficiency, but a mechanism for improving scaling trade-offs under data scarcity. Our code is available at: https://github.com/boqian333/sparse-dc-scaling.

We present a functional form (that we refer to as a Unified Neural Scaling Law (UNSL)) that accurately models and extrapolates the scaling behaviors of deep neural networks as multiple dimensions all vary simultaneously (i.e. how the evaluation metric of interest varies as one simultaneously varies the number of model parameters, training dataset size, number of training steps, number of inference steps, amount of compute, and various hyperparameters) for various architectures and for each of various tasks within a varied set of upstream and downstream tasks. This set includes large-scale vision, language, math, and reinforcement learning. When compared to other functional forms for neural scaling, this functional form yields extrapolations of scaling behavior that are considerably more accurate on this set.

Existing scaling laws for Large Language Models (LLMs), predominantly monotonic power laws, fail to explain emerging non-monotonic phenomena such as catastrophic overtraining and quantization-induced degradation, where performance deteriorates despite increased compute. We propose the Shannon Scaling Law, a unified theoretical framework that models LLM training as information transmission over a noisy channel, grounded in the Shannon-Hartley theorem. By mapping model parameters to channel bandwidth and training tokens to signal power, our formulation explicitly captures the interaction between learning signal and intrinsic noise. This perspective reveals a fundamental Shannon capacity for LLMs: scaling model size or data without preserving a sufficient signal-to-noise ratio (SNR) inevitably amplifies noise, inducing a transition from monotonic improvement to U-shaped performance degradation. We validate our theory through experiments on Pythia and OLMo2 under perturbations, including Gaussian noise, quantization and supervised fine-tuning on math, QA and code tasks. The Shannon Scaling Law consistently outperforms classical scaling laws and recent perturbation-aware laws, achieving strong $R^2$ scores and accurately capturing loss basins missed by prior approaches. It also extrapolates: fitted on $\leq$6.9B Pythia models with $\leq$180B tokens, it predicts the unseen 12B model up to 307B tokens at pooled $R^2{=}0.847$, while monotonic baselines collapse.

A common failure mode in long-horizon agentic test-time scaling is error propagation, where factual errors or invalid deductions introduced at intermediate steps persist in the agent's belief state and contaminate later reasoning. Existing test-time scaling methods provide limited control over this process, as they often rely on agents to detect their own mistakes, select among flawed trajectories, or refine solutions only after errors have already shaped the reasoning path. We propose ExComm, a communication protocol for exploration-stage agentic test-time scaling. ExComm is motivated by the empirical observation that the majority of intermediate errors in parallel agentic reasoning produce detectable cross-agent factual conflicts. Leveraging the iterative structure of agentic workflows, ExComm periodically audits agent belief states to detect such conflicts, resolves them through a dedicated tool-based verification loop, and returns concise, targeted feedback to the involved agents. Corrections are incorporated through soft belief updates, which append verified feedback rather than overwriting existing beliefs. Furthermore, to prevent collapsing trajectory diversity due to communication, ExComm further introduces a trajectory diversification module that redirects redundant trajectories toward orthogonal strategies. Experiments on AIME 2024, AIME 2025, and GAIA with Gemini-2.5-Flash-Lite and Qwen3.5-4B show that ExComm consistently outperforms strong test-time scaling baselines, achieving average performance gains of 5.7% and 5.0% over the best-performing baselines, respectively. Further analyses demonstrate improved error recovery, favorable scaling behavior, stronger diversity than adapted communication baselines, and the best performance-cost trade-off among the evaluated methods.

Inference-time scaling has emerged as a major approach for improving reasoning capabilities, and has been increasingly applied to diffusion models. However, existing inference-time scaling methods for diffusion models typically rely on external verifiers or reward models to rank and select samples, limiting their scalability to settings where such evaluators are available and reliable. Moreover, while recent diffusion models perform sequential inference with region-wise, mixed-noise conditioning, inference-time scaling tailored to this setting remains relatively underexplored. We propose Iterative Partial Refinement (IPR), an inference-time scaling method for sequential diffusion that requires no external verifier. Starting from an already-generated sample, IPR re-noises a subset of regions and regenerates them conditioned on the remaining regions, enabling the model to revise earlier decisions under a richer context than was available during the initial generation. This iterative partial refinement produces more globally consistent samples without external verification. On reasoning tasks requiring global constraint satisfaction, IPR consistently improves performance: on MNIST Sudoku, the valid solution rate increases from 55.8% to 75.0%. These results show that iterative partial refinement alone can serve as an effective inference-time scaling strategy for diffusion models in sequential, mixed-noise settings. Code is available at: https://github.com/ahn-ml/IPR

Length-dependent logit rescaling is widely used to stabilize long-context self-attention, but existing analyses and methods suggest conflicting inverse-temperature laws for the context length $n$, ranging from $(\log n)^{1/2}$ to $\log n$ and $(\log n)^2$. We provide a general theory showing that the desirable scale is determined by the gap-counting function $N_n$ of each attention row. Counting how many competitors lie within each gap from the maximum, we define an upper-tail accumulation scale and prove that it gives the critical inverse-temperature scale for softmax concentration: below this scale, the top competitors remain unseparated, whereas above it, the attention entropy collapses. This framework unifies prior scaling laws as different $N_n$ and yields a direct diagnostic for attention-score families, from idealized theoretical models to more practical transformers.

Large language models (LLMs) are trained and evaluated as though perfect reliability is achievable for any task given sufficient scale. We show that this assumption is information-theoretically unjustified. Every generative task has a reliability ceiling that no model can exceed, determined by how much output uncertainty is resolvable from observable context. The gap decomposes into a resolvable component closable with additional context and a subjective component inherent to task ambiguity. Autoregressive generation further degrades this ceiling at a rate governed by the task's dependency kernel, which quantifies inter-token correlations in the output. From these two primitives, we derive a first-principles scaling law where LLM performance is bottlenecked by the scarcer resource: training data or model capacity. This law recovers the Chinchilla scaling law as a special case and provides a structural account of when scaling improves reliability. Beyond scaling, our framework unifies diverse practical phenomena, such as the benefits of retrieval-augmentation and the spectral mechanics of catastrophic forgetting. Our work formalizes the resource-complexity tradeoffs that govern model performance across domains, offering a unified theory of performance limits in generative language models.

Vision Transformer (ViT) autoencoders have emerged as compelling tokenizers for images, offering improved reconstruction over convolutional tokenizers. However, existing ViT tokenizers cannot explore this landscape as performance degrades outside training resolutions, and reliance on adversarial losses prevents stable scaling. ViTok (Hansen-Estruch et al., 2025) found that the compression ratio r mediates a reconstruction-generation trade-off where lower r means better reconstructions but harder generations, so improving tokenizer reconstruction is key to more Pareto-optimal tokenizers. We introduce ViTok-v2, which addresses these limitations with native resolution support via NaFlex for generalization across resolutions and aspect ratios, and a novel DINOv3 perceptual loss that replaces both LPIPS and GAN objectives for stable training at any scale. ViTok-v2 is trained on about 2B images and scaled to 5B parameters, the largest image autoencoder to date. ViTok-v2 matches or exceeds state-of-the-art reconstruction at 256p and outperforms all baselines at 512p and above. In joint scaling experiments with flow matching generators, we show that scaling both the autoencoder and the generator advances the Pareto frontier of this trade-off.

Clinical risk prediction using longitudinal medical data supports individualized care. Self-supervised foundation models have emerged as a promising approach for leveraging large-scale unlabeled healthcare records. In natural language processing, scaling laws suggest that larger models achieve predictably lower pretraining losses, supporting the foundation model paradigm. However, for structured medical data, characterized by a limited vocabulary and sparse observations, whether increasing model size consistently improves downstream predictions is unclear, as most studies evaluate only a single model scale. In this study, we evaluated the relationship between model scale and downstream task performance for structured medical foundation models. Using a random sample (2.3 million patients, 32 hospitals) from a nationwide 519-hospital Japanese claims database, we pretrained encoder-only Transformers at five scales (2.2M-101M parameters) for disease incidence and medication prediction. Downstream performance saturated at task-dependent thresholds: disease prediction benefited from larger models (32M-101M), whereas medication prediction saturated at 11M, reducing pretraining time by 178 h. Across all tasks, the best-performing model consistently outperformed a Light Gradient Boosting Machine baseline in the area under the precision-recall curve. These findings indicate that, unlike the monotonically decreasing pretraining loss, the optimal model size varied depending on task characteristics. This task-dependent saturation provides practical guidance for balancing predictive performance and computational cost in structured medical foundation models.

Scaling data and artificial neural networks has transformed AI, driving breakthroughs in language and vision. Whether similar principles apply to modeling brain activity remains unclear. Here we leveraged a dataset of 3.1 million neurons from the visual cortex of 73 mice across 323 sessions, totaling more than 150 billion neural tokens recorded during natural movies, images and parametric stimuli, and behavior. We train multi-modal, multi-task models that support three regimes flexibly at test time: neural prediction, behavioral decoding, neural forecasting, or any combination of the three. OmniMouse achieves state-of-the-art performance, outperforming specialized baselines across nearly all evaluation regimes. We find that performance scales reliably with more data, but gains from increasing model size saturate. This inverts the standard AI scaling story: in language and computer vision, massive datasets make parameter scaling the primary driver of progress, whereas in brain modeling -- even in the mouse visual cortex, a relatively simple system -- models remain data-limited despite vast recordings. The observation of systematic scaling raises the possibility of phase transitions in neural modeling, where larger and richer datasets might unlock qualitatively new capabilities, paralleling the emergent properties seen in large language models. Code available at https://github.com/enigma-brain/omnimouse.

Large language models are increasingly deployed as complex agentic systems that scale with task complexity. While prior work has extensively explored model- and system-level scaling, algorithm- and task-level scaling remain largely unaddressed, constraining the full potential of agentic systems. At the algorithm level, allocating additional inference-time computation can enhance workflow capacity but introduces cross-path redundancy: overlapping computations across multiple reasoning branches. At the task level, complex tasks can be decomposed into subproblems and delegated across multiple agents for improved scalability and parallelism. However, existing infrastructures' scheduling is unaware of the existence of multiple agents, missing opportunities to optimize resource allocation. We propose Hive, a multi-agent infrastructure that enables algorithm- and task-level scaling. Hive features a description frontend that captures per-agent behavior and supports test-time scaling algorithms. Leveraging this specification, our backend introduces two key mechanisms: Logits Cache that reuses intermediate logits across redundant sampling paths to mitigate cross-path redundancy at the algorithm level, and Agent-Aware Scheduling that efficiently allocates compute and KV-cache resources according to agent contributions at the task level. Experiments show that Logits Cache achieves an average speedup of $1.11\times$-$1.76\times$ for re-sampling, and Agent-Aware Scheduling reduces the hotspot miss rate by $33\%$-$51\%$.

We inspect the deductive connection between the neural scaling law and Zipf's law -- two statements discussed in machine learning and quantitative linguistics. The neural scaling law describes how the cross entropy rate of a foundation model -- such as a large language model -- changes with respect to the amount of training tokens, parameters, and compute. By contrast, Zipf's law posits that the distribution of tokens exhibits a power law tail. Whereas similar claims have been made in more specific settings, we show that the neural scaling law is a consequence of Zipf's law under certain broad assumptions that we reveal systematically. The derivation steps are as follows: We derive Heaps' law on the vocabulary growth from Zipf's law, Hilberg's hypothesis on the entropy scaling from Heaps' law, and the neural scaling from Hilberg's hypothesis. We illustrate these inference steps by a toy example of the Santa Fe process that satisfies all four statistical laws.

In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of physical qubits. Nevertheless, there are significant outstanding challenges in quantum hardware, fabrication, software architecture, and algorithms on the path towards a full-stack scalable quantum computing technology. Here, we provide a comprehensive review of these scaling challenges. We show how to facilitate scaling by adopting existing semiconductor technology to build much higher-quality qubits, employing systems engineering approaches, and performing distributed heterogeneous quantum-classical computing. We provide a detailed resource and sensitivity analysis for quantum applications on surface-code error-corrected quantum computers given current, target, and desired hardware specifications based on superconducting qubits, accounting for a realistic distribution of errors. We provide comprehensive resource estimates for several utility-scale applications including quantum chemistry calculations, catalyst design, NMR spectroscopy, and Fermi-Hubbard simulation. We show that orders of magnitude enhancement in performance could be obtained by a combination of hardware improvements and tight quantum-HPC integration. Furthermore, we introduce high-performance architectures for quantum-probabilistic computing with custom-designed accelerators to tackle today's industry-scale classical optimization, machine learning, and quantum simulation tasks in a cost-effective manner.

Neural operator (NO) architectures learn nonlinear maps between infinite-dimensional function spaces and are widely used to accelerate simulation and enable data-driven model discovery. While universality results ensure expressivity, they do not address \emph{complexity}: for broad operator classes described only through regularity (e.g.\ uniform continuity or $C^r$-regularity), information-theoretic lower bounds imply that minimax-optimal NO approximation rates scale \emph{exponentially} in the reciprocal accuracy $1/\varepsilon$. This has shifted the focus of NO theory toward identifying additional problem-specific structure, beyond regularity, under which suitably tailored NO architectures can leverage to unlock polynomial scaling in $1/\varepsilon$. We exhibit the first polynomial-scaling regime for NO approximations of solution operators in stochastic analysis; by identifying structured families of \emph{non-Markovian} BSDEs with randomized terminal condition parameterized by the Sobolev-regular terminal condition and by Sobolev-regular additive nonlinear perturbations of the generator. We prove that their solution operator can be approximated (uniformly over the family) by a tailored NO whose number of trainable parameters grows \emph{polynomially} in $1/\varepsilon$. We unlock this polynomial scaling regime by \emph{informing the NO's inductive bias} by factoring out the singular part of the associated semilinear elliptic PDE Green's function and by incorporating the Doléans--Dade exponential of the BSDE's common non-Markovian factor into the NO's decoding layers. As a byproduct, we extend polynomial-scaling guarantees from families of linear elliptic PDEs on regular domains to the semilinear setting.

Labeling corpora constitutes a bottleneck to create models for new tasks or domains. Large language models mitigate the issue with automatic corpus labeling methods, particularly for categorical annotations. Some NLP tasks such as emotion intensity prediction, however, require text regression, but there is no work on automating annotations for continuous label assignments. Regression is considered more challenging than classification: The fact that humans perform worse when tasked to choose values from a rating scale lead to comparative annotation methods, including best-worst scaling. This raises the question if large language model-based annotation methods show similar patterns, namely that they perform worse on rating scale annotation tasks than on comparative annotation tasks. To study this, we automate emotion intensity predictions and compare direct rating scale predictions, pairwise comparisons and best-worst scaling. We find that the latter shows the highest reliability. A transformer regressor fine-tuned on these data performs nearly on par with a model trained on the original manual annotations.

Machine Learning (ML) has deeply changed some fields recently, like Language and Vision and we may expect it to be relevant also to the analysis of of complex systems. Here we want to tackle the question of how and to which extent can one regress scale-free processes, i.e. processes displaying power law behavior, like earthquakes or avalanches? We are interested in predicting the large ones, i.e. rare events in the training set which therefore require extrapolation capabilities of the model. For this we consider two paradigmatic problems that are statistically self-similar. The first one is a 2-dimensional fractional Gaussian field obeying linear dynamics, self-similar by construction and amenable to exact analysis. The second one is the Abelian sandpile model, exhibiting self-organized criticality. The emerging paradigm of Geometric Deep Learning shows that including known symmetries into the model's architecture is key to success. Here one may hope to extrapolate only by leveraging scale invariance. This is however a peculiar symmetry, as it involves possibly non-trivial coarse-graining operations and anomalous scaling. We perform experiments on various existing architectures like U-net, Riesz network (scale invariant by construction), or our own proposals: a wavelet-decomposition based Graph Neural Network (with discrete scale symmetry), a Fourier embedding layer and a Fourier-Mellin Neural Operator. Based on these experiments and a complete characterization of the linear case, we identify the main issues relative to spectral biases and coarse-grained representations, and discuss how to alleviate them with the relevant inductive biases.

Modern infrastructure asset management constitutes a complex sequential decision-making problem, characterized by long planning horizons and system-level interactions, such as spatial deterioration correlations and economies of scale. While deep reinforcement learning has shown promise in optimizing maintenance policies, scaling to real-world networks remains challenging. Centralized approaches become computationally intractable in large-scale systems, whereas decentralized approaches often fail to capture essential coordination mechanisms. To address these challenges, we propose a graph-based framework that integrates accurate environment modeling with scalable decision support. First, we employ a hierarchical Bayesian model leveraging a Gaussian Process on Graph kernel to infer a realistic, spatially correlated networked environment of railway maintenance planning from real-world data provided by the Swiss Federal Railways. Second, we introduce a topology-aware Multi-Agent Reinforcement Learning (MARL) framework by integrating graph neural networks and graph Transformers to optimize network-level policies. A central contribution of this work is the demonstration of scalability through zero-shot transfer learning: graph-based agents, trained only on small network portions, are successfully deployed in a zero-shot manner on large-scale unseen networks without any retraining. Numerical results indicate that the proposed method significantly outperforms optimized heuristics and standard MARL baselines, reducing computational training time while maintaining superior performance on large-scale networks.

Underwater 3D reconstruction is critical for marine exploration, ecological monitoring, and subsea infrastructure inspection, yet remains challenging at large scale due to light attenuation, scattering, and limited capture coverage. While 3D Gaussian Splatting (3DGS) enables high-quality real-time rendering, its application to large underwater scenes is constrained by high memory consumption and inefficient optimization over extensive areas. We propose OceanXL, a fast and scalable 3DGS-based framework for large-scale underwater reconstruction. OceanXL adopts a divide-and-conquer strategy, partitioning scenes into spatially coherent blocks to enable efficient optimization while preserving global geometric consistency. We further introduce an adaptive pruning scheme tailored to underwater conditions that removes redundant primitives, producing compact representations without sacrificing visual fidelity. Together, these components improve training efficiency and rendering performance for large scenes. We also introduce a large-scale underwater dataset covering diverse marine environments. Experiments on five large-scale scenes demonstrate favorable scalability, compactness, and efficiency--quality trade-offs over large-scene baselines. Controlled comparisons on the small-scale SeaThru-NeRF dataset further show competitive reconstruction quality with substantially smaller model sizes than underwater-specific methods.

Cryptocurrency forecasting presents a distinctive combination of extreme cross-asset scale heterogeneity, non-stationary dynamics, and structural dependencies among Open, High, Low, and Close (OHLC) variables. We present CryptoL, a unified framework designed to address these challenges within multivariate time-series forecasting. CryptoL evaluates forecasting error in context-normalized coordinates within the RevIN pipeline, preventing inverse normalization from introducing an additional squared-scale weighting into the MSE objective. We formally characterize this effect through the empirical risk and parameter-gradient geometry, establishing the conditions under which large-scale assets can disproportionately influence shared-model optimization. Beyond loss-space normalization, CryptoL examines channel-independent and channel-dependent normalization for OHLC data, showing that a shared channel-dependent affine transformation preserves candle-order relations that independent channel transformations need not preserve. The framework further incorporates scale-adaptive numerical stabilization to reduce distortions caused by a fixed normalization constant across assets spanning many orders of magnitude, together with a soft feasibility loss that penalizes violations of the defining OHLC inequalities. Experiments across heterogeneous cryptocurrency assets evaluate these components through controlled ablations and demonstrate improvements in forecasting accuracy, training stability, and the frequency of financially valid OHLC predictions relative to the considered baselines. CryptoL therefore provides an integrated approach to scale-balanced optimization, structure-preserving normalization, numerical stabilization, and constraint-aware cryptocurrency forecasting.

Visual Autoregressive Models (VAR) generate images through next-scale prediction, producing all tokens within each scale in parallel. We show that this parallel decoding constitutes a mean-field-style approximation that discards spatial dependencies among same-scale tokens, causing locally incoherent samples regardless of backbone capacity -- a limitation of the decoding rule. Addressing this limitation, we introduce the Logit Refiner, a lightweight autoregressive module that restores intra-scale dependencies by sequentially sampling tokens conditioned on frozen backbone features. Adding only ~10% parameters and less than 5% of the base model's training compute, it plugs into any pretrained VAR checkpoint without retraining. Controlled ablations isolate joint intra-scale sampling -- rather than additional capacity or training -- as the critical ingredient. Across backbones from 310M to 2B parameters on class-conditional ImageNet 256x256, the refiner consistently improves generation quality, enabling a 1.1B-parameter model to surpass one twice its size. The approach further generalizes to text-to-image generation, confirming that the mean-field bottleneck persists across VAR variants and is effectively alleviated by our method. Project page: https://compvis.github.io/logit-refiner/

Localized dimensionality reduction improves the scalability of operator learning for high-dimensional partial differential equations (PDEs), but independently decoded local patches can introduce block offsets, interface mismatches, and spurious high-wavenumber content. We introduce Two-Scale Localized PCA-Net, which decomposes the solution into a coarse-global component and local residual corrections. A compact global PCA basis captures domain-scale structure, while nonoverlapping local PCA bases represent the remaining fine-scale residual. A block-balanced latent objective couples the two representations, and optional interface-aware fine-tuning further promotes continuity through reconstruction and trace losses. On Poisson benchmarks, the two-scale representation substantially reduces reconstruction error and visible block artifacts relative to plain and overlap-based localized PCA-Net while approximately halving PCA fitting cost relative to overlap. On heterogeneous Darcy flow, it strongly reduces interface and discrete-residual errors, with more modest reconstruction gains. Ablations show that the primary improvement arises from the two-scale output representation, while interface-aware fine-tuning provides complementary continuity refinement. Overall, separating globally coherent structure from localized residual detail provides an efficient representation for artifact-reduced PDE operator learning.

As AI video generators achieve cinematic realism, reliable detection becomes essential for safeguarding digital trust. We identify cross-scale coupling mismatch as a new forensic signal, where scale refers to the level of abstraction (semantic dynamics vs. pixel-level residuals): in natural videos, macro-level temporal dynamics and micro-level residual patterns are intrinsically coupled by the unified imaging physics pipeline, whereas AI generators, whose training objectives do not explicitly preserve this joint distribution, systematically violate this coupling. Detecting such mismatch is challenging because it requires independently extracting information at both scales while simultaneously quantifying their cross-scale relationship. We propose RIFT (Representation Inconsistency Forensics on Trajectories), an orthogonal forensic framework that addresses this through three interlocking components: a macro stream that builds a dynamic baseline of expected temporal evolution via differential geometry and persistent homology on learned manifold trajectories, a micro stream that acts as a sensitive forensic probe via steganalytic filtering and temporal modeling, and a coupling divergence module that measures the conditional dependency between the two streams. Gram-Schmidt orthogonality guarantees the information-theoretic validity of this measurement. Experiments on two benchmarks (VidProM, 120K videos, 7 generators; GenVidBench, 68K videos, 4 generators) demonstrate that RIFT achieves 99.33% and 99.72% F1-score respectively, with 97.87% unseen-generator detection rate in leave-one-out evaluation, while exhibiting encoder agnosticism: scaling from ViT-S/14 (22M) to ViT-L/14 (300M) changes F1 by less than 0.1%, and switching to a different encoder family (DINOv1) reduces F1 by only 0.73 pp. Code is available at https://github.com/Litsay/RIFT

A score-driven filter multiplies its scaled log-likelihood score by a scale parameter. We call this coefficient the gain and learn it online. Given the current state and realised scaled score, each admissible gain selects a reachable next state and predictive density. A scalar gain moves along a line; diagonal gains control coordinatewise transmission and may change direction. We evaluate gain selection using a one-step predictive Kullback-Leibler objective. In the scalar unscaled case, the negative consecutive-score product is a stochastic gradient; the positive product used in accelerated recursions is a descent direction. Positive scalar score scaling changes only the effective learning rate. Strictly increasing, continuously differentiable gain links with positive derivative induce mirror-descent geometry, while persistence adds a Bregman pull towards a reference gain. Under convexity, compactness, integrability, and schedule conditions, projected and discounted mirror updates satisfy dynamic-regret bounds relative to time-varying, current-information comparators. Simulations isolate score scaling, link geometry, persistence, and coordinatewise gains. Across twelve equity indices, the bounded discounted-logistic gain records a lower out-of-sample mean negative log score than the constant gain in eleven markets, although market-level evidence is mixed. It also avoids the extreme transients of the numerically capped exponential-link benchmark.

Mixed emotions represent a clinically relevant but still underexplored target for automatic emotion recognition. EEG provides millisecond-level access to neural activity, yet most EEG pipelines analyze the signal through a single temporal window, thereby fixing the temporal structure available to the model. This study introduces a multi-scale temporal framework for EEG-based emotion recognition. The EEG waveform is decomposed into windows of one or several durations, processed by a shared attention-based encoder, and integrated through a dynamic fusion module that assigns sample-specific weights across temporal scales. The framework is evaluated under a subject-independent protocol in binary and three-class settings, with the three-class task including the mixed affective category. The best results are 65.22% for the two-class task and 45.43% for the three-class task. Both are obtained with three-scale dynamic-fusion configurations and remain substantially above the full-signal baseline. The best-performing temporal scales differ between the two tasks. Dynamic fusion outperforms concatenation in the highest-scoring two-class configuration and slightly exceeds it in the highest-scoring three-class configuration, although these multi-scale settings require substantially more computation than the full-signal baseline.

Industrial anomaly inspection faces a major challenge due to the lack of real-world anomaly samples. While generative models are used to create anomaly data, existing methods still struggle when handling small-scale anomalies. This failure occurs because extreme downsampling in diffusion models causes the information of small anomalies to be lost in the latent space. To address this, we introduce UniScale, a unified training and inference framework for high-fidelity industrial anomaly generation across arbitrary scales. During training, we introduce an Error-Suppressed Multi-Scale Training (EMT) strategy, which enables the model to learn the rich location-aware textures of anomalies, while suppressing upsampling-induced interpolation errors in texture acquisition, ensuring the model is capable of learning small-scale anomalies, while remaining effective for regular scale anomalies. For inference, we propose Generation-then-Fusion Denoising. It decouples anomaly generation from background integration, preventing small anomalies from being overwhelmed. Extensive experiments demonstrate that our method outperforms state-of-the-art competitors in both anomaly generation quality and downstream detection performance. It achieves a relative IS(a) improvement of 45.86% (from 1.81 to 2.64) on VisA and 37.70% (from 1.22 to 1.68) on MVTec AD 2, while also improving the downstream pixel-level IoU by 4.22% on VisA and AUROC by 6.55% on MVTec AD 2. Code is available at https://github.com/HUST-SLOW/UniScale.

Accuracy changes after language-model self-revision are usually interpreted as changes in reasoning. We show this can fail at the answer-extraction boundary, and test the failure causally rather than only observationally. Across Qwen3.5 (0.8B-9B), Gemma-4-12B, and two frontier models via API (Tencent Hy3, Nvidia Nemotron-3-Ultra-550B) in 29 primary cells plus a frontier arm, we decompose the always-revise accuracy shift into a content margin (both answers parseable) and format-recovery/loss margins (parseability changes). On 12 cells with meaningful unparseable-answer rates, format effects exceed content effects (Wilcoxon p=1.7e-3). To test this causally, we force already-generated reasoning through grammar-constrained decoding so every answer is parseable by construction: across 14 cells this closes a median 71% of the gap between the naive total effect and the content-margin estimate, with two cells converging exactly and a residual on the two largest-effect cells reported rather than dismissed. A clustered model confirms floor-scale (0.8B/2B) models have far higher odds of content-level change and harm than capable-scale models (p<1e-7). Replicating a cited confidence-gating protocol verbatim on Qwen3.5 does not reproduce its reported gain and shows the same near-zero content margin. A frontier check on much larger models shows format-dominance intensifying with scale: content margin is exactly zero in all 5 cells despite total effects up to +0.275, though this arm is lower-powered. The calibration-floor criterion on the content margin reveals a squeeze: floor-scale cells have headroom but insufficient signal, capable-scale cells have signal but little headroom; only one cell is marginally viable, with negligible sealed-holdout gain. Content is a minority share of what the field has measured as self-correction. We release the instrument, code, and derived results.

Detecting that a stream of high-dimensional embeddings has changed is usually framed as a choice of statistic. We give a scale law that constrains any moment-based choice and test it against topological alternatives. The law: certifying a feature of spatial scale eps carrying mass fraction f requires polynomial tests of degree N* >= log(1/f)/(2 eps), proved via the Chebyshev extremal problem; a Gauss-quadrature construction gives N* >= 4b-1 for a b-scale topology, so cost is set by feature fineness, not feature count. The law is one-sided: we exhibit an annulus whose mean, covariance and all fourth-order moments equal those of a filled disk, yet H_1 is nonzero. Its practical content is a calibration rule. The upper bound is attained by Gaussian test functions, the RKHS witness of an RBF kernel, so the law predicts which bandwidth an MMD test should use: the feature scale. On real embedding streams we measure sigma*/eps with median 1.12 (IQR 1.01-1.52, n=26) over three settings and three scales, and a data-driven bandwidth reaches AUC >= 0.95. Against an adversary optimised against the defender's statistics (mean, covariance, k-NN, kurtosis), only a bandwidth-matched kernel test still detects. For persistent homology the verdict is mixed and depends on choices usually left implicit. The summary matters more than the filtration: total persistence attains recall 0.75 at FPR 1% where the first persistence landscape attains 0.00. What survives is a cost gap, not a power gap: where persistence works it costs 116x kurtosis, which works at least as well. We conclude not that topological summaries are useless, but that on this task a kernel test whose bandwidth the law sets dominates them.

We develop a non-asymptotic approximation, sampling, and finite-iteration optimization theory for variational physics-informed approximation of uniformly monotone nonlinear multiscale elliptic equations. For boundary-compatible neural feature classes, the population error splits into approximation, empirical quadrature, and projected-gradient terms, with all non-approximation constants uniform in the microscopic scale $\varepsilon$. Assuming a quantitative corrected $H^1$-estimate, a two-scale state class yields $$\mathcal A_m^\varepsilon \le C\bigl(\varepsilon+Φ_{0,m_0}^2+Φ_{1,m_1}^2\bigr)$$ in arbitrary dimension. We further introduce a convex primal-dual physics loss whose population value is a computable upper certificate for the state error. With additional flux-corrector regularity, a divergence-compatible two-scale flux class gives a certified state-flux bound combining $O(\varepsilon)$ approximation, state and flux feature errors, empirical sampling error, and an $O(K^{-1})$ optimization term. In contrast, for general periodic nonlinear fluxes satisfying a natural nondegeneracy condition, the empirical Rademacher complexities of strong-residual and squared-residual classes are bounded below by constant multiples of $(\varepsilon\sqrt N)^{-1}$ and $(\varepsilon^2\sqrt N)^{-1}$, respectively. These optimizer-independent lower bounds hold in every spatial dimension. Numerical experiments confirm the predicted $\varepsilon$- and $N$-scalings for nonlinear fluxes in $d=1,2,3$, validate every computed primal-dual certificate, and show that corrector-enriched classes substantially reduce energy and $H^1$ errors as the microscopic scale is refined.