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The burgeoning field of LLM-based Multi-Agent Systems (MAS) promises to tackle complex tasks through collaborative intelligence, yet fundamental questions regarding their scaling behavior and intrinsic collective dynamics remain underexplored. This paper systematically investigates how the performance of a homogeneous MAS evolves as the number of agents increases, isolating the variable of collaboration from model or knowledge heterogeneity. We propose the Sequential Iterative Multi-Agent System (SIMAS) framework, a minimalist architecture centered on sequential inter-agent communication, to clearly observe scaling effects. Through extensive experiments across diverse tasks and model scales, we establish that MAS performance does not scale monotonically with agent count but follows a pattern of diminishing returns, governed by a trade-off between collaborative synergy and coordination overhead. Our findings reveal that effective MAS requires a sufficiently capable base LLM, that task type critically modulates the optimal agent count, and that collective intelligence is an emergent property contingent on strategic interaction design rather than a guaranteed outcome of agent plurality. The performance degradation stems coordination overhead rather than merely long-context failure, and the scaling tendency generalizes across interaction architectures like structured debate topologies. This work provides a foundational understanding of MAS scaling laws, offering practical guidance for designing efficient collaborative systems and challenging the prevailing assumption that more agents invariably lead to better performance.

Scaling conditional memory offers a promising way to increase language-model capacity, but existing methods such as Engram learn large memory tables from scratch during pre-training, making memory scaling expensive and sometimes ineffective. We propose Memory Grafting, a conditional memory scaling method that utilizes frozen hidden states from a grafting model as conditional n-gram memory. Given frequent local n-grams, we run the grafting model offline, store final-token hidden representations as memory values, and let the recipient model retrieve them through exact longest-match suffix lookup. Retrieved memories are adapted by lightweight projections and gates, while a hash-based Engram fallback preserves coverage for unmatched contexts. Since the grafting model is only run offline and exact lookup has expected O(1) complexity with respect to memory-bank size, Memory Grafting expands external latent capacity with limited training and inference overhead. Experiments under matched recipient architectures and pre-training budgets show that Memory Grafting improves over both MoE and vanilla Engram baselines. In the 2.8B-scale setting, it improves the average benchmark score from 51.95 for MoE and 52.43 for vanilla Engram to 53.86. In the 0.92B-scale setting, all grafting-model variants improve over the baselines, with Qwen3.5-35B-A3B giving the strongest gains. These results suggest that pretrained models can serve as reusable constructors of external latent memory, providing a practical step toward scaling future language models beyond trainable parameters alone.

We study the information-theoretic limits of learning a one-hidden-layer teacher network with hierarchical features from noisy queries, in the context of knowledge transfer to a smaller student model. We work in the high-dimensional regime where the teacher width $k$ scales linearly with the input dimension $d$ -- a setting that captures large-but-finite-width networks and has only recently become analytically tractable. Using a heuristic leave-one-out decoupling argument, validated numerically throughout, we derive asymptotically sharp characterizations of the Bayes-optimal generalization error and individual feature overlaps via a system of closed fixed-point equations. These equations reveal that feature learnability is governed by a sequence of sharp phase transitions: as data grows, teacher features become recoverable sequentially, each through a discontinuous jump in overlap. This sequential acquisition underlies a precise notion of \textit{effective width} $k_c$ -- the number of learnable features at a given data budget $n$ -- which unifies two distinct scaling regimes: a feature-learning regime in which the Bayes-optimal generalization error $\varepsilon^{\rm BO}$ scales as $n^{1/(2β)-1}$, and a refinement regime in which it scales as $n^{-1}$, where $β>1/2$ is the exponent of the power-law feature hierarchy. Both laws collapse to the single relation $\varepsilon^{\rm BO}=Θ(k_c d/n)$. We further show empirically that a student trained with \textsc{Adam} near the effective width $k_c$ achieves these optimal scaling laws (up to a small algorithmic gap), and provide an information-theoretic account of the associated scaling in model size.

Test-time scaling has become an effective paradigm for improving the reasoning ability of large language models by allocating additional computation during inference. Recent structured approaches have further advanced this paradigm by organizing inference across multiple trajectories, refinement rounds, and verification-based feedback. However, existing structured test-time scaling methods either weakly coordinate parallel reasoning trajectories or rely on noisy historical information without explicitly deciding what should be retained and reused, limiting their ability to balance exploration and exploitation. In this work, we propose TMAS, a framework for scaling test-time compute via multi-agent synergy. TMAS organizes inference as a collaborative process among specialized agents, enabling structured information flow across agents, trajectories, and refinement iterations. To support effective cross-trajectory collaboration, TMAS introduces hierarchical memories: the experience bank reuses low-level reliable intermediate conclusions and local feedback, while the guideline bank records previously explored high-level strategies to steer subsequent rollouts away from redundant reasoning patterns. Furthermore, we design a hybrid reward reinforcement learning scheme tailored to TMAS, which jointly preserves basic reasoning capability, enhances experience utilization, and encourages exploration beyond previously attempted solution strategies. Extensive experiments on challenging reasoning benchmarks show that TMAS achieves stronger iterative scaling than existing test-time scaling baselines, with hybrid reward training further improving scaling effectiveness and stability across iterations. Code and data are available at https://github.com/IQuestLab/tmas.

Existing approaches to LLM personalization focus on constructing better personalized models or inputs, while treating inference as a single-shot process. In this work, we study Test-Time Personalization (TTP) along an unexplored axis: scaling inference-time computation by sampling N candidates from a personalized policy model and selecting the best with a personalized reward model. We prove that oracle selection yields expected utility growing logarithmically with the number of sampled candidates, establishing a theoretical ceiling for test-time scaling. However, standard reward models fail to realize this potential. To diagnose why, we derive a unified scaling law that decomposes any reward model's Best-of-N curve into four measurable quantities and reveals two failure modes, user-level collapse (near-constant prediction for some users) and query-level reward hacking (negative correlation with true quality for some queries). Guided by this law, we propose a probabilistic personalized reward model whose learned variance effectively mitigates both failure modes. Experiments confirm both elements of our framework: TTP delivers consistent scaling across multiple policy models and personalized text generation tasks, and our scaling law closely matches observed scaling curves across reward-model variants.

Upweighting high-quality data in LLM pretraining often improves performance, but in datalimited regimes, especially under overtraining, stronger upweighting increases repetition and can degrade performance. However, standard scaling laws do not reliably extrapolate across mixture recipes or under repetitions, making the selection for optimal data recipes at scaling underdetermined. To solve this, we introduce InfoLaw (Information Scaling Laws), a data-aware scaling framework that predicts loss from consumed tokens, model size, data mixture weights, and repetition. The key idea is to model pretraining as information accumulation, where quality controls information density and repetition induces scaledependent diminishing returns. We first collect the model performance after training on datasets that vary in scale, quality distribution, and repetition level. Then we build up the modeling for information so that information accurately predicts those model performance. InfoLaw predicts performance on unseen data recipes and larger scale runs (up to 7B, 425B tokens) with 0.15% mean and 0.96% max absolute error in loss, and it extrapolates reliably across overtraining levels, enabling efficient data-recipe selection under varying compute budgets.

Test-time scaling has become a powerful way to improve large language models. However, existing methods are best suited to short, bounded outputs that can be directly compared, ranked or refined. Long-horizon coding agents violate this premise: each attempt produces an extended trajectory of actions, observations, errors, and partial progress taken by the agent. In this setting, the main challenge is no longer generating more attempts, but representing prior experience in a form that can be effectively selected from and reused. We propose a test-time scaling framework for agentic coding based on compact representations of rollout trajectories. Our framework converts each rollout into a structured summary that preserves its salient hypotheses, progress, and failure modes while discarding low-signal trace details. This representation enables two complementary forms of inference-time scaling. For parallel scaling, we introduce Recursive Tournament Voting (RTV), which recursively narrows a population of rollout summaries through small-group comparisons. For sequential scaling, we adapt Parallel-Distill-Refine (PDR) to the agentic setting by conditioning new rollouts on summaries distilled from prior attempts. Our method consistently improves the performance of frontier coding agents across SWE-Bench Verified and Terminal-Bench v2.0. For example, by using our method Claude-4.5-Opus improves from 70.9% to 77.6% on SWE-Bench Verified (mini-SWE-agent) and 46.9% to 59.1% on Terminal-Bench v2.0 (Terminus 1). Our results suggest that test-time scaling for long-horizon agents is fundamentally a problem of representation, selection, and reuse.

Emerging 6G visions, reflected in ongoing standardization efforts within 3GPP, IETF, ETSI, ITU-T, and the O-RAN Alliance, increasingly characterize networks as AI-native systems in which high-level semantic reasoning layers operate above standardized control and data-plane functions. Although frontier-scale large language models (LLMs) such as Qwen2.5-7B and Olmo-3-7B demonstrate strong reasoning capability, their computational footprint limits deployment in latency-sensitive, edge-native infrastructures. This paper presents a systematic empirical study of the scaling behavior and deployment efficiency of compact language models for network-level semantic reasoning in AI-native 6G systems. Using 6G-Bench, a standardization-aligned benchmark comprising 30 decision-making tasks across five capability domains, we evaluate models ranging from 135M (SmolLM2-135M) to 7B parameters (Qwen2.5-7B), including mid-scale architectures such as Llama-3.2-1B, Granite-1B, and Qwen2.5-3B. Deterministic accuracy (pass@1) increases from 0.224 at 135M to 0.707 at 7B, but scaling gains are highly non-uniform. A pronounced stability transition occurs in the 1 to 1.5B range, where accuracy rises from 0.373 (Llama-3.2-1B) to 0.531 (Qwen2.5-1.5B) and the instability gap Delta_5 contracts from 0.356 to 0.138. Beyond 3B parameters, improvements diminish (+0.064 from 3B to 7B). Through single-query inference profiling and an Edge Score metric that normalizes accuracy by latency and memory footprint, we show that semantic reliability per unit edge resource does not scale monotonically with parameter count. Instead, mid-scale models (approximately 1.5 to 3B) achieve the most favorable balance between deterministic stability and computational efficiency, providing deployment-relevant guidance for AI-native 6G architectures. All scripts and results are publicly available at https://github.com/maferrag/6G-Bench

Despite the fact that experimental neural scaling laws have substantially guided empirical progress in large-scale machine learning, no existing theory can quantitatively predict the exponents of these important laws for any modern LLM trained on any natural language dataset. We provide the first such theory in the case of data-limited scaling laws. We isolate two key statistical properties of language that alone can predict neural scaling exponents: (i) the decay of pairwise token correlations with time separation between token pairs, and (ii) the decay of the next-token conditional entropy with the length of the conditioning context. We further derive a simple formula in terms of these statistics that predicts data-limited neural scaling exponents from first principles without any free parameters or synthetic data models. Our theory exhibits a remarkable match with experimentally measured neural scaling laws obtained from training GPT-2 and LLaMA style models from scratch on two qualitatively different benchmarks, TinyStories and WikiText.

Training process reward models (PRMs) requires step-level correctness labels, obtained either through expensive human annotation or by relying on ground-truth answers, limiting the ability to scale process-level supervision. We propose ScalePRM, which scales verification compute as an alternative: given a problem and a candidate solution, we generate multiple independent verifications of each reasoning step and aggregate their judgments to produce synthetic step-level labels without ground truth. We explore two representative inference-time scaling strategies, parallel scaling through self-consistency and sequential scaling through meta-critique, and train generative PRMs on the resulting synthetic data. On ProcessBench, a benchmark for identifying erroneous steps in mathematical reasoning, PRMs trained on step-level self-consistency data achieve 67.5 F1, surpassing reference-guided training with ground-truth access (66.4 F1) and GPT-4o as a critic (61.9 F1). When deployed as reward signals in RL training with Qwen2.5-Math-7B, our best PRM achieves 47.4% average accuracy across six mathematical reasoning benchmarks, outperforming ground-truth-based RLVR (43.9%). We also identify and address reward exploitation patterns unique to generative PRM-based RL. Our results demonstrate that scaling verification compute is a viable alternative to ground-truth supervision for training process reward models.

Pixel count and geographical coverage are two key characteristics of remote sensing images. Existing remote sensing image segmentation methods typically focus on images with either a small pixel count or a large pixel count but limited geographical coverage. In this paper, we introduce a novel segmentation task targeting ultra-wide area (UWA) remote sensing images, characterized by both a large pixel count and extremely wide geographical coverage. The core challenges of UWA segmentation lie in simultaneously handling ground objects with significantly varying scales and maintaining long-range contextual semantic continuity. To address these challenges, we propose the Scale-Frustum Representation Network (SFR-Net). Inspired by the viewing frustums of remote sensing images captured from different altitudes, we construct scale-frustum representations, enabling unified modeling of ground objects and contextual features at different scales. Furthermore, we design a cascaded cross-scale fusion mechanism to effectively integrate these representations, enhancing local semantic understanding while ensuring long-range contextual continuity. Experimental results on GID and FBPS demonstrate that SFR-Net achieves state-of-the-art performance, improving mIoU by 1.72% and 4.29%, respectively, over the strongest competing methods. In addition, the proposed scale-frustum representations can be integrated into generic segmentation networks to improve both segmentation accuracy and convergence speed. The implementation code will be publicly available at https://github.com/ChuyuZhong/SFR-Net.

Skillful medium-range precipitation forecasting at kilometer scale remains challenging over complex terrain because precipitation arises from multiscale nonlinear processes that global models cannot explicitly resolve at affordable cost. Global AI weather models can produce skillful medium-range forecasts, but their native 0.25 degrees resolution limits direct use for local hazard applications. Statistical downscaling can help bridge this gap, yet existing approaches often struggle with state-dependent, and especially lead-time-dependent, biases in global forecasts. We introduce SwAIther-Precip, a lead-time-aware downscaling framework that converts coarse-resolution AIFS forecasts into probabilistic km-scale precipitation fields over Switzerland. First, a U-Net conditioned on lead time via feature-wise linear modulation deterministically corrects systematic biases at coarse resolution. This targeted correction enables a cheaper super-resolution stage conditioned only on corrected precipitation, allowing direct training on observations rather than on the full atmospheric state. A diffusion-based model then generates fine-scale spatial variability independently of lead time. Using AIFS forecasts and CombiPrecip radar-gauge observations, SwAIther-Precip reduces CRPS by 48% relative to raw AIFS. The generated fields reproduce observed spatial variability with spectral fidelity above 0.85 at large scales and 0.88 at small scales, corresponding to an effective resolution of approximately 4 km on a 1 km grid for lead times up to 5 days. Training across lead times further improves long-range performance, yielding a 13% CRPS reduction at 6 days relative to lead-time-specific models. These results show that explicitly correcting lead-time-dependent biases before generative super-resolution is key to efficient km-scale probabilistic downscaling of global AI precipitation forecasts.

Recent advancements in 3D Gaussian Splatting (3DGS) have extended its capabilities to multi-scale segmentation. Existing methods reconstruct a scene with Gaussian primitives and learn multi-scale segmentation features separately, which leaves the geometry unaware of semantic structure and the feature learning dependent on incomplete mask supervision. To address these limitations, we present PePESeg3D, a novel framework that injects perception priors into a multi-scale 3D Gaussian segmentation pipeline. To fully exploit perception priors, we integrate them not only into contrastive feature learning but also into the upstream geometry reconstruction. Specifically, PePE Reconstruction incorporates monocular depth and mask constraints to ensure semantically coherent object structures. Building on this aligned geometry, PePE Contrastive Learning leverages dense depth-color cues and view-consistent centroid supervision to compensate for the incompleteness of multi-scale masks obtained from a 2D foundation model. Extensive experiments on the SPIn-NeRF, LERF-Mask, and NVOS benchmarks demonstrate that PePESeg3D achieves state-of-the-art performance in both multi-scale segmentation and scene reconstruction, highlighting the importance of integrating perception priors into both geometry optimization and feature learning for accurate multi-scale 3D segmentation. Our code is available at https://github.com/BeCow5X5/PePESeg3D.

Point cloud completion aims to infer a complete 3D shape from a partial point cloud and serves as a fundamental building block for downstream tasks such as reconstruction, editing, and simulation. Despite the recent progress, existing learning-based methods often implicitly rely on access to the ground-truth shape scale (GT-scale) during both training- and testing-time normalization, assuming privileged information that is unavailable in real-world inference. This hidden assumption limits practical deployment and can lead to severe completion artifacts, e.g., over- or under-completion and nested shells, once the oracle GT-scale cue is removed. We observe that the recent foundation image generation models exhibit a strong capability of understanding objects and geometries, and producing multi-view consistent renderings, making them promising priors for GT-scale-free 3D completion. Motivated by this insight, we propose ScaleBlind, a novel framework that leverages foundation-model-based image completion to recover global scale directly from partial inputs and then faithfully produces the 3D completion. Specifically, ScaleBlind dreams out complete multi-view appearances from rendered partial views, lifts the inferred missing regions back into 3D to obtain a geometry-aware coarse completion, and further refines it via a powerful cross-modal fusion network with the original partial point cloud. By harnessing 2D foundation priors, our method eliminates the need for accessing GT-scale information at inference. Moreover, it provides a principled bridge between 2D generative priors and 3D point cloud completion. Extensive experiments demonstrate the superiority of our framework, making ScaleBlind the new state-of-the-art for the point cloud completion task.

Hyperspectral imaging is widely used in remote sensing and engineering. Therefore, research on its classification methods is crucial. While CNN and Transformer-based methods have advanced, they still face locality constraints and high computational complexity. To address these issues, we propose an innovative hyperspectral image classification model, MSCM-net. Specifically, first of all, a model architecture combining multi-scale CNN and Mamba is proposed. It consists of a multi-scale feature extraction module (MCSE) and multiple stacked Mamba blocks, which integrates the local feature extraction capability of multi-scale CNN and the long sequence modeling advantage of Mamba. Secondly, the proposed MCSE module consists of multi-scale convolution and SENet. Convolution kernels of different scales extract local information with different receptive fields, enhancing the fusion of spatial and spectral information. Meanwhile, the SENet enables the model to automatically learn the importance of each channel in the multi-scale features. Furthermore, we also propose a dual-branch feature aggregation module, which further effectively extracts and integrates the spectral information contained in the central pixel and the spatial information in the surrounding pixels. Our model has undergone numerous experiments on three widely used benchmark datasets. The experimental results show that MSCM-net can achieve advanced classification performance while reducing computational complexity.

The discovery of scaling laws has motivated training neural networks on ever increasing quantities of data. This is typically done with a constant decoupled weight decay which causes the network weights to shrink steadily over the course of training. Taking inspiration from the Robbins--Monro conditions, we propose to scale weight decay by the fraction of the peak learning rate $η/η_{\max}$. We prove that this scaled weight decay preserves the asymptotic stationarity guarantees of the corresponding unregularized methods for both stochastic gradient descent and the non-Euclidean spectral optimizer Muon, thereby avoiding the additional asymptotic bias introduced by constant decoupled weight decay. This retains the stability benefits of weight decay without changing the asymptotic optimization target. Using a steady-state analysis, we explain why under standard weight decay the weight norm shrinks steadily as training proceeds, whereas under scaled weight decay it settles to a roughly constant value. When applied to the training of mixture-of-experts models, Muon with scaled weight decay (Muon-SW) consistently outpaces Muon with identical hyperparameters, reaching the same validation loss $\mathbf{30\%}$ faster at our largest scale across models from $72 - 930$ million parameters trained at $\sim 600$ tokens per active parameter. If this trend continues to hold, the method promises to substantially accelerate the pre-training of frontier models while requiring only a few lines of code to implement.

Self-supervised foundation models have recently shown strong potential for electroencephalogram (EEG)-based analysis. However, existing approaches struggle to capture the inherently multi-scale temporal structure of EEG signals, where local neural patterns and long-range dependencies jointly encode task-relevant information. This limitation hampers cross-scale representation learning and generalization across diverse downstream tasks. To address this challenge, we propose MSBraM, a Multi-Scale self-supervised Brain foundation Model designed to learn hierarchical EEG representations. MSBraM follows a two-stage pretraining framework. First, a multi-scale neural tokenizer discretizes raw EEG signals into semantic codes at different temporal resolutions via vector-quantized reconstruction. Second, the model is pretrained to predict masked codes using a curriculum multi-scale masking strategy, progressively integrating fine-grained local patterns with global temporal context. We pretrain MSBraM on over 2,400 hours of EEG data and evaluate it across 10 downstream tasks on 12 public datasets. Extensive experiments show that MSBraM achieves superior performance on other state-of-the-art pretrained models, demonstrating strong generalization and transferability. These results indicate that explicitly modeling multi-scale temporal dynamics is critical for effective EEG foundation models.

Self-supervised DINO models provide strong transferable visual representations, yet applying them directly to image segmentation remains challenging. Existing approaches commonly rely on heavy decoders with complex upsampling, introducing substantial parameter and computational overhead. We observe that introducing scale into DINO features is far more critical than increasing decoder capacity. In this work, we present SegDINO, an efficient segmentation framework that integrates a DINOv3 backbone with lightweight scale modeling. SegDINO introduces Token Pyramid Adaptation (TPA) to reorganize intermediate DINO features into a pseudo multi-scale hierarchy, and Scale-Aware Decoding (SAD) for efficient intra-scale refinement and top-down multi-scale propagation. We further curate PanCT, a new CT dataset containing 284 patients with expert-annotated pancreatic tumors, to assess SegDINO's ability to handle difficult small-lesion cases. Extensive experiments on PanCT and three public benchmarks demonstrate that SegDINO achieves state-of-the-art results with high efficiency. The code is available at https://github.com/script-Yang/segdino_v2.

Classical spectral descriptors such as the Heat Kernel Signature and Wave Kernel Signature are widely used for non-rigid 3D shape retrieval, yet their failure modes remain poorly understood. We present a frequency-scale saliency framework that audits these descriptors by quantifying the retrieval-level contribution of each descriptor scale interval through ablation. We introduce class spectral fingerprints to characterize category-level scale dependence, and show that descriptor similarity between class pairs is substantially correlated with retrieval failure, with a Spearman correlation of 0.479. Experiments on SHREC'11 demonstrate that short scales dominate retrieval performance while long scales are harmful, that HKS and WKS exhibit distinct scale dependence patterns, and that saliency-weighted retrieval improves mAP on hard categories by 0.156, with cross-fold and random-weight controls confirming that the gain is stable and not due to arbitrary reweighting.

Agentic Large Language Model (LLM) systems decompose complex tasks into workflow Directed Acyclic Graphs (DAGs) whose primitives must be scheduled on heterogeneous clusters. Existing deep reinforcement learning (DRL) schedulers are tied to a fixed cluster size and require retraining whenever the number of servers changes. We propose SCALE (Scalable Cross-Attention Learning with Extrapolation), a DRL scheduler that generalizes to unseen cluster scales without fine-tuning. SCALE employs a cross-attention pointer network where task features query against server features, so the architecture accepts any number of servers by construction. We observe, however, that permutation-invariant architecture alone does not guarantee good performance at new scales - the attention feature undergoes distribution shift as the server count grows. To counter this, we introduce Structured Representation Regularization (SRR): a decorrelation loss combined with a KL penalty toward the standard normal, which keeps feature statistics stable regardless of input size. Trained on 16 nodes and tested directly on 32 and 48 nodes, SCALE reduces average response time by 8.9% at N=48 relative to the same architecture without SRR, confirming that explicit regularization is necessary to close the scale-generalization gap.

We introduce scale-selective Proper Orthogonal Decomposition (POD) for transformer attention fields, inspired by the use of POD for extracting energetically dominant modes from turbulent flow ensembles. The Morlet continuous wavelet transform identifies dominant temporal scales in the attention lag structure across a document ensemble; POD then extracts the energetically dominant modes at each scale from the ensemble of attention fields. The resulting modes reveal layer-dependent scale organisation, with early layers emphasising fine scales and later layers shifting toward coarser scales. We define a spectral concentration index from the POD eigenvalue decay rate and show empirically that it differentiates layers by their attention field complexity. By the classical POD optimality theorem, the extracted modes minimise the average L2 reconstruction error over the ensemble (Theorem 1), giving a data-driven effective rank for each layer. The method requires no architectural modification and no linguistic annotations: dominant attention patterns emerge from ensemble statistics alone. The turbulence analogy is structural rather than physical: we borrow ensemble covariance and modal analysis, not fluid dynamics itself.

Modern deep neural networks usually have large parameter scales and nonlinear hierarchical structures, and they have achieved strong performance in computer vision. However, the source of their generalization performance remains difficult to explain using traditional statistical learning theory. Among the factors that may affect visual generalization, data scale, model complexity, and input modalities are fundamental and controllable variables. This study empirically analyzes how these three factors influence model generalization performance. Specifically, in a preliminary experiment, we construct a one-dimensional nonlinear function and vary the number of training samples and the polynomial degree to observe the effects of data scale and model complexity on model performance. In the main experiments, we compare model performance on CIFAR-10 and CIFAR-100 under different training data scales, model architectures, and input modalities. The experimental results show that increasing the training data scale consistently improves generalization performance, whereas changes in model complexity do not provide stable gains. In addition, removing color information degrades model performance, while explicit prior features such as gradients, edges, and wavelets have inconsistent effects across different model architectures. Overall, this study provides an empirical analysis of the relationships among data scale, model complexity, input modalities, and visual generalization performance. Code and experimental logs are available at: https://github.com/YidiZhouluo/DeepLearning-Empirical-Studies/tree/main/Exp_01.

We investigate whether neuron populations within neural networks evolve predictably with scale, extending scaling laws beyond macroscopic observables such as loss. To probe this question, we study Rosetta Neurons, a previously characterized class of neurons whose activation patterns are similar across independently trained models (Dravid et al., 2023). In separate analyses of language models up to 30B parameters and vision models up to 5B parameters, we observe that the population of Rosetta Neurons follows a sublinear power law in model size, growing in absolute number but occupying a shrinking fraction of the total neuron count. We further observe a Neuron Polarization Effect: Rosetta Neurons become more selective and increasingly monosemantic with scale, separating from a growing non-Rosetta population that remains less selective. An analytical model balancing feature utility against limited neuron capacity explains the sublinear power-law scaling and this polarization effect. Finally, we find that Rosetta Neurons become more domain-specialized with scale and illustrate their selectivity through a targeted data-filtering case study for continued pretraining. Our results point to a scaling law for interpretable, shared neuron-level structure, linking model size to systematic changes in neuron universality, selectivity, and specialization.

Recent works have explored unifying SLAM with geometric foundation models (GFMs). However, directly using GFM predictions for tracking is highly sensitive to model capability and uncertainty, as geometric inaccuracies in the predictions can adversely affect pose estimation. To address this limitation, we propose a decoupled framework that integrates classical feature-based SLAM with GFMs, which achieves higher quality and more consistent dense reconstruction. In brief, we use classical visual SLAM for robust low-latency tracking and use GFMs exclusively for mapping. By anchoring mapping to poses produced by the SLAM module and optimizing across depth scales, the proposed design avoids propagating inaccuracies from GFM predictions into pose estimation while imposing geometric constraints on the reconstruction. The system builds submaps from multiple posed keyframes and enforces scale consistency via lightweight frame and submap scale optimization. It also performs projection-based point cloud fusion within each submap, and updates submaps online to reflect trajectory updates from the feature-based SLAM. To evaluate tracking and reconstruction of our method, we introduce a loop-rich, building-scale indoor dataset with accurate sensor trajectories and LiDAR ground-truth. Experiments show that our approach achieves superior trajectory accuracy while improving reconstruction precision by 10%-20% over existing methods, with about 2 cm reconstruction error per 10 m chunk on building-scale dataset. On large-scale outdoor datasets, it attains 10 cm error per 30 m chunk (w.r.t LiDAR ground-truth models). Code and dataset: https://github.com/ori-drs/ScaRF-SLAM

Solving high-frequency partial differential equations (PDEs) with neural networks is notoriously difficult due to the spectral bias of conventional architectures. We propose the Multi-Scale Separable Fourier Neural Network (MS-SFNN), a framework designed to overcome this limitation by explicitly encoding multi-scale Fourier features within a separable representation. The network factorizes the solution into $d$ single-coordinate subnetworks with fixed, randomly initialized weights; these subnetworks are combined via element-wise products to form a rich set of basis functions. This separable construction scales linearly with the problem dimension, thus inherently alleviating the curse of dimensionality. Crucially, each subnetwork is equipped with trainable scaling factors coupled with cosine activations, providing an adaptive mechanism for multi-scale frequency selection that endows the model with strong spectral approximation capability. The PDE solution is expressed as a linear combination of these learned basis functions, and the combination coefficients are determined by solving a large-scale least-squares system. To resolve the memory bottleneck in high-frequency or three-dimensional settings, we replace automatic differentiation (AD) with analytical derivatives of the basis functions and use a memory-efficient batched QR decomposition for solving the least-squares systems efficiently. Extensive numerical experiments demonstrate that MS-SFNN achieves superior accuracy and substantially outperforms state-of-the-art methods, including Physics-Informed Neural Network (PINN) and the Separated-Variable Spectral Neural Network (SV-SNN).

Diffusion models steer conditional generation with a tunable guidance scale to trade off prompt alignment and diversity. However, existing debiasing techniques are optimized for a single scale, degrading fairness when users adjust this parameter. We trace this behavior to a previously overlooked source by decomposing total bias into two components: a model bias and a guidance bias. While prior work primarily targets the former, we show that the guidance bias grows monotonically with the guidance scale, eventually dominating the high-guidance regimes users prefer. To address this, we extend Strong Demographic Parity to guidance and derive a condition under which the target distribution retains its group ratio across guidance scales. We propose StayFair, which leverages this condition to design fair guidance algorithms in both regimes. For classifier guidance, it equalizes the classifier's output distributions across groups; for classifier-free guidance, it shifts the null embedding by a prompt-dependent offset. Because StayFair modifies only the guidance step, it is orthogonal to model debiasing and can be layered onto existing fair diffusion models to extend their fairness across guidance scales. Across class-conditional and text-to-image generation, StayFair decouples fairness from the guidance scale without sacrificing image quality.

Sonar imaging is the primary modality for underwater target detection, yet small targets remain difficult to detect due to insufficient pixel coverage, low acoustic contrast, and scale ambiguity across imaging ranges. CNN-based detectors extract local features efficiently but cannot suppress noise-induced false alarms without global acoustic context. Transformer-based methods capture long-range dependencies at quadratic computational cost. Existing Mamba-based vision models offer efficient linear-cost scanning but lack multi-scale semantic alignment across pyramid levels, multi-receptive-field fusion, and small-target-aware training supervision needed for reliable sonar detection. This letter proposes Mamba Dilated-Scale Fusion (MambaDSF), a hybrid framework addressing these limitations through three contributions: a Mamba Enhanced Feature Pyramid (MambaEFP) backbone that jointly captures local echo cues and global acoustic context at linear complexity; a Dilate Fusion Mamba (DFMamba) encoder that enforces multi-scale feature alignment across pyramid levels; and Scale-Adaptive Weighted IoU (SA-WIoU) and Cross-Scale Coherence (CSC) losses that stabilize small-target training. MambaDSF achieves 91.5% mAP50 on the UATD forward-looking sonar benchmark with 28.7 million parameters, surpassing all compared detectors. On a small-target subset the gain reached +2.2 percentage points, and cross-domain evaluation on FLS and MD-FLS confirms the generalization of the proposed architecture. The codes are publicly available at https://github.com/IDontKnowAAA/MambaDSF.

Multimodal Large Language Models (MLLMs) have demonstrated strong capabilities across a wide range of vision language tasks. However, when applied to large scale image classification, their performance degrades significantly as the label space expands a phenomenon we define as Performance Collapse in Long Sequence Recognition. Through an information theoretic analysis, we reveal that this collapse stems from a fundamental conflict between the escalating information entropy and the prominent attention dilution and decay within attention mechanisms, which impairs the model's ability to maintain a sufficient signal-to-noise ratio when processing extremely long prompts. To mitigate this, we propose Divide-and-Conquer Inference (DCI), a novel test-time scaling strategy for visual recognition with MLLMs. DCI recursively decomposes complex global classification tasks into multiple simpler, localized subproblems and employs a dynamic pruning mechanism to compress the search space. This method effectively improves the local signal to noise ratio and model accuracy by mitigating the inherent weight dilution issues in long-sequence inference. Moreover, while traditional self-attention incurs a prohibitive quadratic computational complexity, DCI achieves more favorable scaling behavior and substantially accelerates inference in large scale classification scenarios. Extensive experiments on benchmarks such as ImageNet-1K and ImageNet-21K demonstrate that DCI consistently improves classification accuracy. This enables lightweight open-source models to rival or even surpass frontier closed-source giants without any additional training or fine-tuning. As a model-agnostic, plug-and-play paradigm, DCI offers an efficient approach for scaling the inferential precision of MLLMs in large-scale scenarios.

Monocular SLAM historically suffers from scale ambiguity and tracking failure in dynamic environments. While recent vision foundation models (VFMs) provide remarkable zero-shot depth priors, naively integrating these deterministic predictions ignores predictive uncertainty and frame-to-frame scale inconsistencies. We propose PRISM-SLAM, a real-time framework that rigorously integrates VFM priors into a structured Bayesian factor graph to achieve scale-aware, metric-consistent localization and mapping. Specifically, we introduce a Plücker Ray-Distance Factor to anchor monocular observations in absolute space within a globally consistent metric coordinate system, mathematically resolving scale drift by making the metric scale Fisher-identifiable. To handle environmental dynamics, we derive an epistemic uncertainty proxy from temporal depth consistency and formulate a Dynamic Scene Uncertainty Gating (DSUG) mechanism. This soft-gating approach probabilistically down-weights dynamic distractors without incurring the heavy computational overhead associated with traditional semantic segmentation masks. By employing a multi-process architecture that asynchronously processes VFM inference and geometric tracking, PRISM-SLAM provides verified metric output at 30 FPS using solely RGB input, bridging the gap between foundation models and real-world robotic applications. Evaluated on the TUM RGB-D and 7-Scenes benchmarks, PRISM-SLAM achieves a metric $SE(3)$ Absolute Trajectory Error (ATE) nearly identical to its oracle-aligned $Sim(3)$ error. This demonstrates that our system can produce deployment-ready metric trajectories by delivering robust metric SLAM solutions without any post-hoc scale correction. Project page: https://prismslam-cmd.github.io/prismslam_pr/

We study group decision-making in artificial societies where the rules of play are themselves subject to collective amendment. Using the self-amending game Nomic, we compare multiple scales across two LLM families and find that collective adaptation does not improve monotonically with model size. Instead, both families exhibit a narrow mid-scale regime that supports sustained rule adoption, diverse amendments, and balanced consensus. Smaller models tend to remain rule-inert, whereas larger models often converge on restrictive voting patterns, and heterogeneous mixed-size groups collapse into veto-driven gridlock. These cross-scale contrasts persist under temperature perturbations and under a shift from unanimity to majority voting, although latent-state structure varies by family and scale. Hidden-state divergence alone does not explain collective performance: high representational divergence can coincide with poor behavioural outcomes. Linear probes reveal regime-selective coupling between latent vote-predictive signals and collective behaviour, but decodability is necessary rather than sufficient for adaptive play. Overall, the recurring regularity is non-monotonicity, not the particular scale at which the optimum appears. Self-amending games therefore provide a controlled testbed for studying collective adaptation in artificial societies beyond raw model scale.