Capacity

The twenty-first century's transformative technology, artificial intelligence, is increasingly constrained by the twentieth century's transformative technology, the electricity grid. Rapid growth in electricity demand from data centers is leading to higher electricity prices, without a compensating supply-side response. We develop a framework linking data-center load growth, available generation capacity, and market-clearing prices to understand this phenomenon. We first analyze a deterministic model to show how differing estimates of demand and supply growth rates affect prices. We then model the expansion of new data centers and their associated electricity demand, together with build-outs of new electricity supply, as stochastic processes,resulting in probabilistic distributions of supply, demand, and prices rather than a single forecast. Finally, we formulate generation expansion as a stochastic control problem in which a revenue-maximizing investor dynamically chooses the intensity of supply-side investments. The analysis highlights a central challenge of the data-center build-out: even when rapid demand growth increases the need for new generation, the uncertainties related to load forecasts, development execution risks, and value cannibalization from overbuilding capacity may weaken incentives to invest at the pace required to keep electricity prices stable.

Key-value (KV) cache eviction is essential for scaling long-context inference in Large Language Models. However, existing policies predominantly rely on empirical heuristics, lacking a rigorous characterization of token utility under the inherently nonlinear softmax attention mechanism. In this work, we rethink KV cache eviction through the lens of local information geometry, modeling the attention process as a nonlinear Gaussian communication channel. By performing a first-order Taylor expansion of the attention mapping, we derive the Jacobian Information Capacity, a novel objective that explicitly captures query relevance, softmax sensitivity, and structural diversity. Guided by this theory, we introduce Jacap, a capacity-aware eviction method that utilizes softmax-aware importance weighting and statistical leverage scores for subset selection. Extensive experiments across diverse architectures and benchmarks demonstrate that \textsc{Jacap} delivers superior performance in most scenarios, particularly in high-compression regimes.

Vision-language-action (VLA) models with billions of parameters now dominate the LIBERO manipulation benchmark, but the model capacity actually required by the benchmark remains unclear. We introduce MINERVA (MINimal Efficient Robotic Vision-Action policy), a family of deliberately compact visuomotor policies designed to measure this task-specific capacity floor. A 0.54M-parameter policy achieves 95.1% average success over 2,000 rollouts on the four standard LIBERO suites, only 2.4 points below the reported LeRobot $π_{0.5}$ result despite using 7,700$\times$ fewer parameters. Performance saturates near 1M parameters and collapses below 0.25M. Across broad architectural, training, and inference sweeps, only action-chunk length and vision capacity consistently exceed a $\pm$1-point training-seed band. Flow matching provides no detectable advantage over direct L1 regression across three seeds, while regression is up to 3.8$\times$ faster on GPU. A task-ID permutation probe shows that standard LIBERO instruction conditioning primarily selects among memorized tasks: changing only the task-ID mapping reduces success to near chance. The same recipe achieves 94.6% success across 89 LIBERO-90 tasks, while LIBERO-Plus perturbations reduce performance to 46--56%, with near-zero robustness to photometric shifts. The 0.54M policy replans every control step in 5--9 ms per chunk on a laptop CPU, 113$\times$ faster than SmolVLA and 1,400$\times$ faster than $π_{0.5}$, without a GPU. These results establish a first empirical estimate of LIBERO's task-specific capacity floor and motivate capacity-aware design and distillation for deployment-efficient robot policies.

Deep networks trained on noisy labels simultaneously generalize on clean data and memorize flipped labels. These are usually conflated as pressures on one capacity. We present Topo^2, a measurement framework that makes them causally separable, measurable, and law-governed. Persistent-homology H1 structure of the representation space separates into a within-class manifold channel (a function of the training stopping point) and a cross-class channel (a monotone readout of memorized flipped samples). An intervention, the FM0 prescription (zero loss on flipped samples from epoch 0), reaches each setting's generalization ceiling while memorizing essentially nothing. Within the framework we establish a law set with graded evidence: (L2) FM0 separation prescription (9/9); (L1) the within-channel as a training-position function (mid-rise 6/6; convergence-back CIFAR 3/3, SVHN 2/3); (L3) a ring-construction identity (definitional, not a law); and TLS (memory-generalization topological layering): memory is causally additive, anchored (silencing clean collapses the representation), invertible (stripping memory restores near-ceiling generalization), and quantitatively billable (the memorization cost law, effective slope coefficient C ~ 0.38 at the reference capacity: CIFAR-10 0.3801 / SVHN 0.3806 / CIFAR-100 0.384 / VGG 0.3715, capacity-dependent in general and traced to clean-sample feature displacement). We also publish the framework's boundaries: a falsification ledger of nine dead ends, and an instrument-vindication section that excludes six families of global statistics as explanations of the within-channel. The framework turns "memorization" from an ill-defined capacity into a measurable, separable, invertible topological layer.

We study the scaling behavior of learning rate and batch size in pretraining dense large language models on English-prevalent corpora. Beyond scaling jointly optimal learning rates and batch sizes, we investigate their marginal evolution with model capacity and data scale and develop a model that captures these relationships. As we employ a Warmup-Stable-Decay learning rate schedule, we further investigate the gains from learning rate annealing over a broad range of hyperparameters settings, models and data budgets, and whether the optimal learning rate and batch size transfer between the stable and decay phases. Finally, we characterize the dependence of loss on model capacity and dataset size, evaluating recently proposed scaling forms that explicitly model their interaction. We find these approaches particularly effective at capturing both undertraining and overtraining regimes across our experiments. This study establishes a first baseline and scaling procedure for the development of future OpenEuroLLM models. We open-source the complete collection of pretraining runs used in this study.

Networked systems, from power grids to traffic networks and cloud clusters, carry loads across nodes with limited capacity. A node whose load exceeds its capacity fails and sheds its load onto its neighbors, which can trigger a system-wide cascade. We study how to allocate a fixed capacity budget across nodes to resist these cascades under local load redistribution. The problem is difficult because no optimal allocation is known, and the fail-or-survive objective is non-differentiable and piecewise constant, so exact and gradient-based optimization methods do not directly apply. We introduce TANGCO (Topology-Aware Neural Graph-Guided Capacity Optimization), which uses a graph neural network policy trained through the cascade simulator with policy-gradient learning and a heuristic anchor. We evaluate TANGCO on five synthetic graph families and five real networks spanning power, road, air, and Internet topologies. The learned policy improves on the best of four hand-designed heuristics in all 450 synthetic instances and in 40 of 45 real-network conditions, with robustness gains ranging from 1.6% to 246%. The learned policies transfer to unseen graphs within a family and partially across related topologies, and TANGCO$^{pre}$, pre-trained on synthetic graphs, matches per-network training on unseen real networks. Training scales near-linearly with graph size, and TANGCO$^{pre}$ allocates on a new network with no per-target training, matching the deployment cost of a hand-designed heuristic. Free-vector variants without the GNN, stay close to the heuristics, so the graph representation carries the gain beyond numerical search. Finally, analysis of the learned allocations identifies when local risk is sufficient, leads to an improved closed-form heuristic, and reveals the regimes where a topology-aware learned policy remains necessary.

Autoregressive semantic ID recommenders are constrained by expensive beam-search decoding, which limits the practical length of item identifiers. Parallel generation methods alleviate this bottleneck by predicting all semantic ID tokens simultaneously, enabling longer IDs. However, existing semantic ID methods still rely on manually predefined and homogeneous ID structures, where both the number of semantic slots and the codebook size of each slot are treated as fixed hyperparameters. This ignores the heterogeneous capacity demands of different semantic subspaces and may allocate prediction capacity to slots with limited utility. We show that uniformly expanding semantic slots can provide limited gains, indicating redundant capacity in homogeneous semantic IDs. We propose InforID, a lightweight adaptive semantic target construction framework for parallel generative recommendation. InforID allocates a fixed capacity budget across candidate semantic slots, thereby jointly determining the effective ID length and slot-specific codebook sizes. Experiments demonstrate improved recommendation accuracy under comparable capacity budgets while preserving one-step parallel prediction.

While mathematical models act as vital decision support systems for operational Air Traffic Flow and Capacity Management (ATFCM), existing approaches isolate Air Traffic Flow Management (ATFM) from Dynamic Airspace Configuration (DAC). This separation introduces an unresolved circular dependency between fixed-demand and fixed-capacity assumptions. Although joint optimization resolves this gap, the enlarged search space renders exact models computationally intractable for medium- to large-scale instances. To bridge this gap, we propose ASPaeroFlow: a heuristic for the joint ATFCM; it combines instance-space decomposition heuristics with a local exact approach using Answer Set Programming. We benchmark ASPaeroFlow from small to industry-sized instances and compare it with exact and alternative approaches. The results indicate that (1) the heuristic provides a computational middle ground between exact methods and operational baselines; (2) simultaneous optimization can outperform sequential optimization on joint ATFCM; and (3) an ablation study indicates that DAC has a larger impact on solution quality than flow measures.

Dense expert merging combines domain-specialized language models into one single checkpoint, typically by admitting task-vector support in weight space. However, this admission is governed by three decisions that existing methods answer only partially: where to open layer capacity from cross-expert conflict, who should occupy that capacity based on domain demand, and how to admit the resulting support without relying on costly recipe search. To tackle these issues, we propose SigMerge (Signature-Guided Capacity Occupancy), a structured capacity assignment framework for dense expert merging. Starting from a dense base merge, conflict signatures set each layer's capacity from cross-expert conflict, positive base-merge deficits set each domain's share of that capacity, and a sequential occupancy rule admits each expert delta up to the resulting layer-domain budget. Across 21 paired settings spanning seven dense base merges and three model pools, SigMerge improves every one (by 15.0% on average) and achieves the best average rank (1.67) among six merging methods, outperforming three categories of merging baselines.

We study how to share a single conserved capacity budget across many locations and two service classes when demand is uneven, time-varying, and can exceed supply. The shape recurs: an origin's request-rate cap split across its edge locations, a licensed throughput cap across premium and standard tenants, or an egress budget between latency-critical and batch workloads. We present a two-level algorithm. The first level redistributes capacity within a class across locations by proportional deficit and excess redistribution; the second lends capacity elastically between classes when one has surplus and the other deficit. We prove it conserves the budget exactly, preserves non-negativity, and reaches a stable allocation in one iteration under stationary demand because it carries no per-cycle state, at O(KN) cost per cycle for K classes and N locations. We evaluate it defending a CDN's per-domain budget under volumetric attack, where the classes are confirmed-legitimate and not-yet-cleared traffic; across 8 contention scenarios on a 22-location topology it serves 66-93% of high-priority demand, competitive with a single-class linear-programming optimum, while never leaving capacity idle or over-committing whenever aggregate demand meets or exceeds the budget (the contention regime these scenarios evaluate). Two findings carry beyond the application. First, a throughput-maximizing objective is wrong under contention: a two-class LP maximizing total served load serves less high-priority load than our demand-proportional, reservation-respecting allocator in most scenarios, because it cannot tell that some load it serves is the contention. Second, inter-class borrowing earns its complexity under bursty load, improving high-priority service by 1.5 points (isolated by ablation), and is neutral under stationary demand. A 5-location prototype with real HTTP traffic validates the pipeline.

Automated warehouses face a fundamental trade-off between maximizing storage density and achieving high retrieval throughput. While puzzle-based storage (PBS) architectures increase capacity by eliminating aisles, coordinating multiple robots in these high-density spaces is computationally challenging due to the potential for deadlocks. This paper introduces a novel multi-robot formulation for the ``ordered storage and retrieval problem at maximum capacity''. The focus is on rectangular grids accessible from a single boundary, where loads need to be first stored up to full capacity and then efficiently retrieved, given a planned departure sequence. This work bridges the gap between geometric feasibility and execution efficiency by leveraging the properties of relocation-free arrangements. These properties guide an online, prioritized multi-agent path-finding algorithm, which is the main contribution of this work. Unlike general centralized planners, the approach exploits the specific invariants of the storage arrangement to guarantee completeness and prevent deadlocks, enabling scalability. Experiments demonstrate that the method achieves near-linear improvement in makespan with respect to the number of robots, up to $m = C$, where $C$ is the grid width. Crucially, the algorithmic overhead of supporting robustness is negligible; the system handles uncertainty in departure sequences using robust storage arrangements with no significant penalty in execution speed compared to the non-robust baseline.

Neural scaling laws are foundational for language model development, yet standard formulations systematically under- and overestimate loss at data-scarce and overtraining extremes. This failure originates in the underlying assumption that model size and training data impact the loss independently. To address this, we introduce the Skaling law, a generalized functional form that couples model capacity and data through a single interaction exponent. This simple extension reduces the Mean Absolute Percentage Error (MAPE) by 1.5-3x across both interpolation and extrapolation regimes. When paired with a sparse grid strategy restricted to low-compute regimes, the Skaling law achieves accurate full-grid extrapolation using approximately 10x less compute than uniform sweeps. By enabling reliable performance prediction from small-scale experiments, the Skaling law provides a more robust and resource-efficient framework for allocating compute budgets in next-generation model training.

Sub-model federated learning lets resource-constrained clients train width-reduced versions of a global model, but existing methods allocate capacity by device resources alone. A natural next step, allocating capacity by each client's data heterogeneity as estimated from the updates the server already observes, has been repeatedly suggested. We ask whether that step is possible, using HAS-FL, an adaptive capacity-allocation framework, as a test case. Our findings are threefold. First, validated against ground-truth label-distribution divergence on reproducible partitions, update-divergence estimates of client heterogeneity are dominated by capacity rather than data: across two corrected estimators, multiple datasets, and all seeds, the estimates correlate strongly and negatively with device capacity, and no data signal remains once capacity is controlled for. This previously undocumented confound affects any method estimating client statistics from sub-model updates. Second, adaptive allocation has a hidden failure mode: when every client is capped below full width, the uncovered parameters stay at random initialization and progressively corrupt the global model. A simple coverage guarantee removes the failure and explains why uniform allocation collapses. Third, a matched-budget control settles what adaptivity contributes: random allocation to the same average budget performs no differently on both image benchmarks, and on the naturally partitioned text benchmark the adaptive policy is the weakest of the three strategies while consuming the most capacity. Sub-model training remains valuable because it admits constrained clients at quadratically reduced cost, but what protects accuracy is parameter coverage rather than allocation intelligence. Its apparent benefits come from capacity budgeting and coverage, and future designs need heterogeneity signals separable from capacity effects.

Prior benchmarking work has shown that a single large language model (LLM), forced to make life-or-death resource-allocation decisions, exhibits measurable demographic bias. Real deployments, however, rarely use a single agent: they use pipelines, with review steps meant to catch exactly this kind of failure. We study what happens to bias when the same decision is distributed across a role-differentiated multi-agent pipeline (assessment, allocation, independent audit) instead of made and checked by one model alone. Using a synthetic disaster-triage simulator with paired cases that are clinically identical except for one demographic attribute, we run 192 episodes (2,304 resolved case pairs) on GPT-4o-mini comparing a single-agent control condition to a nine-agent pipeline under three independently varied pressure dimensions. We find no measurable difference in how often biased outcomes occur between the two conditions (6.9% vs. 6.1%, p = 0.498). We do find a large and significant effect of audit capacity on whether bias is caught: 30.0% of biased outcomes go entirely undetected, rising to 43.8% when the auditor is overloaded and falling to 18.4% when it is not. Decomposing this effect shows it is driven almost entirely by coverage (whether a case is reviewed at all, which collapses from 100.0% to 65.6% under load, p < 0.001) rather than by degraded judgment on the cases that are reviewed (81.6% vs. 85.7%, p = 1.000, direction reversed). A follow-up experiment shows that reordering the audit queue by estimated risk, rather than first-come-first-served, recovers most of the lost coverage under the same capacity constraint (65.6% to 91.7%, p = 0.028). We discuss the implications for any system that adds independent oversight to an LLM agent pipeline under resource constraints, and report the study's limitations honestly: one model, modest sample sizes, and no adversarial replication.

Many social services assign scarce resources, such as housing assistance or hospital interventions, to people who arrive one at a time: each arrival must receive a decision immediately, and the long-run usage of every resource must stay within its capacity. We study how to learn such an assignment policy from logged observational data. The standard pipeline is decision-blind: fit one outcome model per arm by regression, price each capacitated resource from the fitted models, and assign each arrival the arm whose predicted outcome minus price is largest. We instead train the outcome models end-to-end, differentiating an off-policy estimate of the deployed policy's value through the dual prices themselves. We study two formulations: an exact nonconvex one, and a convex relaxation whose optimum always satisfies the capacity constraints in expectation and which is suboptimal by at most a term linear in the smoothing temperature and logarithmic in the number of arms. Every method is evaluated in a queueing simulation with resources replenished at their capacity rates. Across six datasets, the two end-to-end variants take the top slots on a deployment-adjusted value index at every delay cost, including zero; when capacities are binding, decision-blind baselines frequently violate them and incur much longer queueing delays. On the largest dataset, a hospital cohort of seventy thousand patients, end-to-end training also achieves significantly higher policy value, a margin that survives a capacity-matched neural baseline. Flexible decision-blind regression remains the stronger pure predictor where ground truth is measurable; end-to-end training is best suited to settings where resources are genuinely scarce and feasibility matters.

Recent advances in 4D Gaussian Splatting (4DGS) enable high-fidelity, real-time spatiotemporal rendering, but expose a fundamental trade-off between motion expressiveness and storage efficiency. While anchor-based designs achieve compactness through anchor-level parameter sharing, their rigid uniform parametrization enforces fixed Neural Gaussian counts and feature budgets per anchor. Consequently, insufficient fidelity is addressed by excessive anchor density, rather than lightweight, targeted increases in Neural Gaussian count or feature capacity, resulting in memory waste. To overcome this rigidity, we introduce an adaptive-capacity anchor-based framework that dynamically allocates the representational capacity based on local spatiotemporal demands. Adaptive Anchor Cardinality varies the number of Neural Gaussians per anchor, concentrating primitives in regions of high geometric or motion complexity while suppressing redundancy. In parallel, Adaptive Anchor Feature Masking modulates anchor-level feature channels, assigning rich features to complex regions and lightweight representations to simpler ones. Experiments on MPEG, Panoptic Sports, and N3DV datasets demonstrate substantial storage reduction without degrading visual quality. Notably, on challenging MPEG sequences with complex motion, our method achieves up to 1.5x higher compression than state-of-the-art anchor-based methods while preserving comparable quality.

Network-wide traffic volume estimation typically relies on propagating measurements from fixed sensors, making performance highly dependent on sensor density and limiting deployment in sparsely instrumented networks. We propose a link-level learning framework that estimates hourly traffic volumes from widely available territorial data only, including probe speed profiles, road and topological descriptors, along with weather observations. A supervised local mapping is learned from sparse sensor measurements and evaluated under two generalization settings: intra-network (unseen links within the training network) and inter-network (unseen city). This formulation frames traffic volume estimation as a spatial out-of-distribution generalization problem under sparse supervision. To enhance spatial robustness, we introduce a capacity-aware formulation that models volume as the product of a link-specific structural capacity and an hourly regime-aware utilization ratio, embedding traffic-theoretic constraints directly into the learning process. Extensive experiments in both generalization settings demonstrate that the proposed structural constraints consistently outperform a state-of-the-art baseline under spatial distribution shift.

Short-term disturbances at major passenger railway stations alter train arrival and departure times as well as the release sequence of station resources. Effective recovery therefore requires coordinated adjustment of arrival-departure track allocation, station resource occupation, and train retiming. This study represents the station resources involved in train arrival, track occupancy, and departure operations as zone-level resource-occupation intervals. An arrival-departure track allocation adjustment model is formulated. Resource compatibility is imposed as the feasibility condition, while train delays and resource reassignment costs are jointly considered. A quantum-inspired evolutionary algorithm combined with neighborhood search (QEA-NS) is proposed to solve the model. Perturbation instances are constructed using GTFS timetable data from Frankfurt Hauptbahnhof, Germany. QEA-NS is compared with CP-SAT under the same candidate resource set and feasibility criteria. Both methods generate solutions satisfying the modeled resource compatibility constraints. QEA-NS yields a total delay of 388 min, compared with 519 min for CP-SAT, representing a reduction of 25.2%. The mean delay of delayed trains decreases from 4.99 to 3.73 min, although QEA-NS requires a longer solution time. Across 10 random perturbation instances, QEA-NS achieves lower total delay in every case. Its mean total delay and standard deviation are 390.5 min and 35.945 min, respectively, compared with 673.8 min and 105.739 min for CP-SAT. The results indicate that, under the adopted resource representation and constraints, QEA-NS improves the delay performance of recovery plans. Its computational efficiency, however, requires further improvement.

A LoRA adapter is a few megabytes that almost everyone treats as a skill rather than a record of the data behind it. We put that assumption on a scale. Extending compression-based memorization analysis to the frozen-base setting, we measure directly, in bits, how much a low-rank adapter writes into a model it never changes. The answer is both smaller than full fine-tuning and less lawful than parameter counting would predict. Adapters store a couple of bits per trainable parameter, well short of a full model's budget, but that figure turns less on how many parameters an adapter carries than on where they sit. Move the same parameter budget from attention into the MLP and it holds nearly twice as much; strip the frozen base of its structure and the capacity all but disappears. Applied to realistic fine-tunes of Qwen2.5, the same instrument shows privacy leakage rising with the bits an adapter writes rather than the parameters it nominally has, and it draws a clean line between supervised and reinforcement learning: the secrets that supervised fine-tuning copies down verbatim, an adapter trained on verifiable rewards never records. Measuring what fine-tuning writes, rather than attacking it after the fact, turns a piece of folklore into a quantity one can design against.

The rapid proliferation of data-intensive applications, cloud infrastructure, and IoT ecosystems has made proactive resource provisioning critical for maintaining optimal network performance. However, network administrators face a constant battle against capacity constraints, where traditional reactive approaches fail to accurately anticipate traffic fluctuations. This inability to foresee demand leads to costly over-provisioning, unexpected downtime, and degraded quality of service directly impacting operational budgets and business continuity. To achieve efficient capacity planning, accurate forecasting of bandwidth utilization is essential. This study addresses the challenge by evaluating a diverse spectrum of models including seasonal decomposition, Prophet, Random Forest, XGBoost, Support Vector Regression, and advanced deep learning architectures like bidirectional and Convolutional LSTMs - using a common interface dataset benchmarked across MAPE, NRMSE, and R-square metrics. Ultimately, this research delivers actionable insights into the trade-offs between model accuracy and computational efficiency, empowering engineers, operators, and business owners to select the optimal forecasting model for their specific infrastructure needs.

2D Gaussian Splatting is an attractive direction for image representation due to its explicit formulation, fast rasterization, and favorable decoding efficiency. The representation quality of this paradigm depends on the proper allocation of Gaussian capacity to the demanding regions. However, existing methods fail to allocate Gaussian capacity efficiently during optimization: under-reconstructed content is often refined in a fragmented pixel-wise manner, while neighboring optimized Gaussians with similar attributes are redundantly retained. This inefficiency motivates the need for a density control framework that jointly addresses insufficient allocation in under-reconstructed regions and redundant allocation in over-reconstructed regions. Our key insight is that this framework should exploit two complementary forms of locality: the local continuity of reconstruction errors in image space for improved Gaussian allocation, and the local similarity of neighboring Gaussians in Gaussian space for redundant elimination. Based on this insight, we propose Locality-Aware Density Control (LocoADC), a plug-and-play framework that improves Gaussian capacity utilization through Region-wise Gaussian Densification (RGD) and Similarity-Driven Gaussian Merging (SDGM) strategies, together with a local color consistency constraint for more reliable merging. Extensive experiments on diverse datasets show that LocoADC consistently improves multiple baselines by enabling more effective local Gaussian allocation, including a 2.93 dB PSNR gain over GI on the CLIC dataset under the same 30k Gaussian budget. Code is available at: \textit{https://github.com/ChenJiaCong-1005/LocoADC}.

Linear attention promises constant-time recurrent inference but degrades sharply on associative recall. We formulate attention recall as a spherical-packing problem and introduce Kernelized Linear Attention Activations (KATA), a framework whose feature maps are derived from first principles by certifying nonnegative attention weights through a self-dual homogeneous cone. Building on this observation, we show that rank-one positive semi-definite (PSD) features offer a favorable capacity--interference tradeoff. KATA recovers a parameter-free convex output gate and characterizes associative capacity through the Welch interference floor. For tolerances above this floor, KATA enlarges the state without adding parameters and admits spherical codes with exponentially many keys in the projection dimension. We implement KATA as fused Triton kernels at two operating points: a flash-attention-style forward up to ${\sim}1.6\times$ FlashAttention-2 throughput, and an exact $O(T)$ chunked-state form that reaches ${\sim}11\times$ FlashAttention-2 forward throughput at $131$k tokens. An associative scan of the first-order feature lowers the inter-chunk recurrence depth to $O(\log(T/C))$ for chunk size $C$ and averages ${\sim}2.4\times$ the throughput of a matched sequential linear-attention baseline. On long-range MQAR and repeated-key overwrite, several KATA variants outperform Gated DeltaNet, with parameter counts and state sizes reported alongside accuracy. Induction preserves near-perfect recall, while kernel benchmarks show that the maps can be implemented efficiently. KATA retains $0.985$ MQAR at a $16\times$ out-of-distribution length, approaching the softmax with roughly one quarter of the KV-cache entries. Experiments on 340M-parameter LLMs reveal a feature-dependent fluency trade-off and clarify how positional embeddings, delta rules, and decay gates interact with feature geometry.

In multi-task learning (MTL) negative transfer is often considered as an optimization artifact, but it can also be viewed as a consequence of limited shared capacity and weak task redundancy. We investigate this effect through a Capacity--Redundancy (CR) identity that decomposes the sum of per-task predictive informations into joint predictive information that includes label redundancy defined via total correlation (TC), and a residual coupling term that quantifies interference left unresolved by the shared representation. Additionally, we show two key results: (i) a clustering-gap decomposition that gives a necessary and sufficient condition for clustered sharing to outperform global sharing, and (ii) a gradient--TC bridge in a Gaussian multi-task model that formally justifies gradient cosine similarity as a proxy for redundancy ordering. Empirically, we estimate the residual coupling $Δ$ from validation residual correlations, showing that clustered LoRA substantially reduces $\widehatΔ$, outperforms size-matched random partitions, and results in statistically significant gains with multi-seed confidence intervals.

When cast as the protector of a vulnerable user yet given no explicit capability boundary, a large language model (LLM) may respond not by acknowledging its limits but by claiming to have taken -- or to be taking -- a real-world protective action it cannot perform, such as contacting emergency services or administering care. We term this phenomenon Protective Capacity Hallucination (PCH): a self-referential misattribution in which a model, acting in a protective role, asserts physical or institutional agency exceeding its affordances as a language model. In a three-phase study spanning eight LLMs and 13{,}600 sessions, we find PCH jointly gated by situational severity and interactional format: multi-party dialogic input drives it toward ceiling in most models across ordinary service domains, whereas in intimate-partner conflict -- a domain explicitly covered by safety alignment -- it remains at floor in all eight models despite greater physical severity. We interpret PCH as the signature of a deployment-design gap between role assignment and capability-boundary specification: a by-product of partial alignment in which a universally trained pressure to help outruns a domain-selective specification of how to help. Because suppression tracks alignment coverage rather than severity, deployment-side specification of capability boundaries emerges as a general mitigation target.

Federated Reinforcement Learning (FedRL) enables coordination of distributed energy resources without sharing raw local data, but standard aggregation methods such as FedAvg do not account for system-level constraints, often leading to unsafe global behavior. In this work, we study constraint-aware aggregation for federated reinforcement learning in distributed energy coordination. We propose aggregation rules that incorporate both local performance and estimated constraint violation into the server-side update. Among these, a simple penalty-based rule, $w_i \propto R_i - αV_i$, consistently provides the most reliable trade-off between reward and safety, without requiring dual optimization or modifications to local training. \textcolor{black}{We evaluate our approach on DairyGridEnv, a benchmark modeling multiple farms coordinating battery storage under stochastic demand and a shared grid capacity constraint, and further assess robustness using real load-driven demand profiles from Finland and the German FIELD dataset. Across multiple seeds, penalty-based aggregation substantially reduces violations while improving reward relative to FedAvg in both synthetic and real load-driven settings.} A combined reward-violation scheme exposes a tunable trade-off via $λ$, but is less stable. These results demonstrate that lightweight aggregation strategies can substantially improve empirical safety in federated reinforcement learning while preserving standard communication protocols.

We introduce a straightforward yet effective method to empirically study memorization in deep neural networks for classification tasks. Our approach augments each training sample with auxiliary random labels, which are then predicted by a random label prediction head (RLP-head). RLP-heads can be attached at arbitrary depths of a network, predicting random labels from the corresponding intermediate representation and thereby enabling analysis of how memorization capacity evolves across layers. By interpreting the RLP-head performance as an empirical estimate of Rademacher complexity, we obtain a direct measure of both sample-level memorization and model capacity. We leverage this random label accuracy metric to analyze generalization and overfitting in different models and datasets. Building on this approach, we further propose a novel regularization technique based on the output of the RLP-head, which demonstrably reduces memorization. Interestingly, our experiments reveal that reducing memorization can either improve or impair generalization, depending on the dataset and training setup. These findings challenge the traditional assumption that overfitting is equivalent to memorization and suggest new hypotheses to reconcile these seemingly contradictory results. The source code is available at https://github.com/MarlonBecker/RandomLabelHeads

Containerization has become increasingly essential in the machine learning (ML) domain, providing reproducibility, portability, and environment consistency. While prior studies have analyzed Dockerfile structures and best practices, none have examined ML projects in depth to reveal how the iterative nature of ML workflows influences container footprint, build performance, and caching behavior. We present the first large scale empirical study of 1,993 ML related Dockerfiles, combining quantitative analysis of container roles in ML projects and build dynamics with a qualitative investigation of refactoring practices. Results show that containers serve distinct roles across training, inference, and infrastructure. Containers are typically large, averaging 10.27 GB in size, and require long build times of about 8.84 minutes. We find that 44.4% of commits trigger rebuilds, primarily due to context file changes (96.4%), with experimentation being the main motive behind those commits that initiate rebuilds. Despite partial cache reuse, 71% of rebuild work is wasted on redundant computation. From stable projects, we identify 7 recurring ML-specific Dockerfile refactoring patterns that improve build efficiency and reduce container footprint.

We address liquidity placement in the Bitcoin Lightning Network (LN): given a fixed budget, which channels should a node open to maximize its routing capacity? We cast this as a budget-constrained combinatorial optimization problem on graphs, selecting $k$ edge additions that maximize $s$--$t$ max-flow, a theory-grounded measure of routing capacity, and solve it with graph reinforcement learning. Our lightweight agent combines a message-passing policy network with proximal policy optimization (PPO) and action masking, and is trained under a hub-exclusion curriculum: the network's top hubs are removed from training subgraphs, forcing the policy to learn capacity-aware placement rather than hub attachment. In extensive experiments on real Lightning Network snapshots, our method consistently outperforms strong heuristic baselines on the max-flow objective across multiple seeds and unseen graphs. The agent has been deployed in production for peer recommendations, executing 4640 channel-open decisions that cumulatively allocate 267.3 BTC over $16 million across 30 managed nodes.

Large language model based search agents increasingly adopt multi-agent architectures in which a main agent decomposes a complex question into sub-queries and dispatches them to parallel sub-agents. However, existing systems instantiate all roles from a single model of identical scale, leaving open how model capacity should be distributed across roles. We factorize hierarchical search into three roles: a delegation role responsible for task decomposition, an execution role responsible for retrieval and evidence extraction, and an answer generation role held fixed as a confound control. We then conduct controlled capacity sweeps along the delegation and execution axes on five multi-hop QA benchmarks. The experiments yield three findings. First, role factorization consistently outperforms a single-agent baseline, improving exact match from 4.5 to 8.6 points across six model scales. Second, capacity sensitivity is asymmetric: scaling the delegation backbone improves EM by ~11 points, whereas scaling the execution sub-agent moves EM by only ~2.6 points, identifying decomposition as the capability bottleneck. Third, a 1.7B-parameter executor trained via quality-filtered trajectory distillation matches a frontier sub-agent in accuracy while consuming 37% fewer sub-agent tokens, advancing the Pareto frontier. These results suggest a concrete recipe for building hierarchical search agents: concentrate capacity at delegation and downsize execution without sacrificing accuracy. Our code is available at https://github.com/QinnanCai0115/role-factorized-search.

While traditional hub capacity planning models optimize effectively for quantitative inputs, they often fail to digest qualitative business context. We propose a novel framework where a large language model (LLM) agent iteratively proposes hub capacity decisions guided by natural-language business context descriptions. The key mechanism is a chain-of-thought reasoning protocol: the LLM constructs a structured decision table that maps each contextual item to specific capacity adjustments based on the implied direction and magnitude of changes. The new capacity decision is then validated through a feedback loop with an optimization model, which provides routing-based performance metrics to guide the agent's selection. On a real-world 13-hub freight network in the southeastern US, our framework achieves a 2.8% optimality gap relative to the hidden ground-truth, a significant improvement over the 11.0% gap produced by the traditional optimization model without textual business inputs. This demonstrates that LLMs can serve as a contextual bridge, integrating qualitative business insights into Operations Research workflows.

Operational Air Traffic Flow and Capacity Management (ATFCM) balances flight demand with available sector capacity, to ensure safe and efficient operations. Mathematical models enhance operational ATFCM performance by framing demand-capacity balancing as an optimization problem, maximizing efficiency while adhering to safety constraints. However, SOTA research optimizes the aircraft trajectories (called ATFM) or the sector configuration (called DAC) separately. This leaves a research gap of whether joint optimization of ATFM and DAC can bring benefits. We partially address this limitation by introducing a joint ATFCM model with an encoding in Answer Set Programming (ASP). The ASP implementation is evaluated against two baselines applied to our joint model: a SOTA Mixed Integer Programming (MIP) model and an iterative CASA-based heuristic. Computational experiments utilize an instance generator fitted to historical OpenSky Network flight data. Our results indicate that the ASP model outperforms the MIP model, while ASP remains competitive against heuristics on small instances. Furthermore, while DAC has the largest improvement on solving performance compared to rerouting and delaying, unrestricted variants of DAC or rerouting lead to search space thrashing.

Piecewise-affine neural networks (e.g., with ReLU or LeakyReLU activations) implement continuous piecewise-affine maps, and the number of affine regions provides a natural proxy for expressive capacity. However, the gap between theoretical region capacity and the affine regions realized after training remains insufficiently understood. We study this gap from two complementary perspectives. First, we give a rigorous, architecture-dependent theorem for affine line-segment probes: for multilayer perceptrons with piecewise-affine activations, the number of affine pieces realized along an affine line-segment probe is upper bounded by an explicit product of layer-wise width terms (and activation breakpoint factors). This yields a neuron-threshold lower bound for representing target functions with prescribed one-dimensional piece complexity, formalizing the minimal region budget required for complex signals. Second, we exactly enumerate affine regions realized within bounded 2D and higher-dimensional domains under controlled task complexity. Under fixed architectures and training protocols, increasing input--label complexity yields trained solutions with markedly fewer realized regions in the evaluation domain, even though worst-case architectural capacity is unchanged; we call this reduced region usage expressivity saturation. Moreover, in the most challenging regimes, 2D visualizations show that region-usage collapse often coincides with degraded decision boundaries. Finally, we visualize the training dynamics of affine-region partitions and decision boundaries, revealing a consistent refinement process during optimization.

The rapid growth of large-scale AI workloads, particularly Large Language Model (LLM) training and inference, is fundamentally reshaping the operational dynamics of hyperscale data centers. Unlike traditional cloud workloads, AI-driven jobs exhibit bursty, high-intensity, and rapidly shifting resource demands, often leading to sudden capacity stress that cannot be effectively handled by reactive threshold-based mechanisms. In this paper, we propose a deployment-oriented, burst-aware early warning framework for proactive capacity stress prediction under AI workload surges. We formulate the problem as a high-recall forecasting task over multivariate telemetry windows, with the explicit goal of enabling operational intervention before system degradation occurs. The proposed framework integrates workload intensity, temporal variation, and system pressure signals, and employs a lightweight tree-based learning model to capture nonlinear interactions in highly imbalanced environments. To evaluate the system under realistic conditions, we introduce an AI workload surge injection methodology that simulates burst-driven demand patterns observed in large-scale AI systems. Our XGBoost-based model achieves an ROC AUC of 0.697 and an AP of 0.670, significantly outperforming baseline methods. Under deployment-oriented threshold selection, the framework achieves a Recall of 0.914, enabling the detection of the majority of stress-prone periods with acceptable false-alarm cost. Beyond predictive performance, we show how the proposed framework can be integrated into operational control loops to support proactive actions such as workload throttling and resource scaling. Our results highlight the practical value of high-recall, learning-based early warning systems in enabling resilient and adaptive data center operations in the era of AI-driven workloads.

We study finite-horizon queue peaks in generalized switches, a standard stochastic-network model in which many queues share constrained service resources. Arrivals may be dependent, nonstationary, and responsive to the system history; the only load condition is uniform interior slack, meaning the conditional mean arrival vector stays in a fixed contraction of the capacity region. We show that this slack reshapes the finite-time peak law for drift-minimizing scheduling policies such as MaxWeight. The square-root envelope that is sharp without slack persists only up to a geometry-dependent threshold; beyond that threshold, the running maximum grows only logarithmically with the horizon, both with high probability and in expectation. The mechanism is self-normalization: in the current queue direction, the projected fluctuation scale is normalized by the stabilizing drift scale. This removes capacity geometry from the logarithmic coefficient, while geometry remains in the threshold. Matching lower bounds show that both the logarithmic term and a geometric threshold are unavoidable. When finite-time state-space collapse is available, the threshold can be sharpened using local bottleneck geometry. For generalized input-queued switches, we obtain finite-time peak bounds with tight logarithmic coefficients. Simulations illustrate the two-phase envelope, local geometric refinements, and variance-sensitive improvements predicted by the theory.

Large language models provide a tractable system for asking how intelligence itself emerges, rather than only how LLMs can be engineered. Although progress is usually attributed to scale, data and architecture, we show that parameter initialization is a gene-like determinant of training and, in particular, of model capacity. Reducing the initialization scale consistently improves pretraining, with the largest gains on reasoning-demanding tasks. We identify two widely used empirical settings that restrain the advantage of small initialization, and show how relaxing them restores favorable scaling. We further uncover a critical initialization that balances the reasoning and training. Mechanistically, small initialization drives a distinct developmental trajectory: parameters first condense into low-complexity structures and later expand into richer representations, giving concrete form to the idea that compression is intelligence. Token-level analyses show that the gains concentrate on non-trivial, context-constrained predictions rather than all tokens uniformly. These results motivate a simple $γ$-initialization rule: expose initialization rage as an explicit knob and use small initialization by default, an almost cost-free intervention that improves pretraining and strengthens reasoning across model scales.

Educational support services often face a qualified-capacity problem: staff time is scarce, qualifications decay, new support needs can appear before anyone is prepared for them, and training consumes the same hours needed by current students. We introduce a synthetic benchmark and decision-support framework for qualified educational capacity planning. The model is a stylized single-institution service system with heterogeneous support-demand categories, backlog-only dynamics, continuous preparation states with hard threshold qualification and decay, and capacity-consuming training. The benchmark includes seed-controlled scenarios for announced and surprise new support categories, staff absences, and demand surges; exact feasibility discipline; declared per-policy information sets; requalification and greenfield-qualification counters; access-dispersion metrics; replay checksums; and paired statistics. We compare service-only, reactive, static-insurance, water-filling, and rolling-horizon mixed-integer controllers, with an attribution chain separating service planning, qualification maintenance, and acquisition, plus a perfect-foresight reference. The central result is a regime map governed by whether a newly required qualification can be acquired within the controller's reaction reach. When it can, the closed-loop controller wins across the core and adversarial suites, with value concentrated in just-in-time qualification acquisition. When the training lag exceeds the horizon, lean static insurance wins structurally, and a reactive trainer that starts after onset can be worse than no training. Backlog perishability shifts this boundary without erasing either regime. EduCapacity Studio reproduces exported scenarios bit-for-bit. All evidence is stylized and synthetic; the framework makes no claims about real student outcomes, compliance, or individual placements.

Modern AI systems exhibit structural failures that capability scaling alone does not reliably fix: they optimize under-specified objectives with no architectural mechanism to question whether the objective should be optimized at all. Engagement maximization can amplify harmful pathways; tool-using agents can commit irreversible actions; preference-trained language models can become sycophantic. We argue that this failure is a wisdom problem, not an intelligence problem. We use "wisdom" in a deliberately architectural sense, not as a claim about virtue, consciousness, or moral omniscience. Intelligence accepts a goal and optimizes within it; wisdom interrogates whether the goal should be optimized at all. The two are separable architectural properties. We propose architectural wisdom as a corrigible objective-governance layer above the optimization substrate. The layer makes three structural commitments explicit and nondegenerate before any action: temporal horizon, relational boundary, and irreversibility. It is realized by four components (Structural Utility Transform, Moral Admissibility Interface, Arbitration and Escalation Controller, Value Revision Channel) that compute a six-coordinate wisdom tuple over horizon, relational coverage, irreversibility, admissibility, value revision, and auditability. We motivate the architecture by eight cases drawn from contemporary AI failures, secular wisdom traditions, and hard ethical situations, and defend the distinction against the intelligence-completeness thesis using goal-questioning over goal-taking, Bostrom's orthogonality, structural separation in our exemplar cases, and persistent failure modes despite capability scaling. The framework is the conceptual contract for a larger architecture whose formal specifications and empirical validation are developed in subsequent work.

Fine-tuning vision-language models to emit dense coordinate lists improves visual grounding but also changes how models serialize, repeat, and terminate structured outputs. We study this behavior as a generation and control surface. In Gemma 4 12B, high-capacity q/k/v/o LoRA raises class-aware F1@0.3 from 0.007 to 0.448 while inducing repeated-tail pressure (duplicate rate 0.080, max repeat 23). A q/v rank sweep keeps max repeat at 21-22 across ranks 4-64, showing capacity persistence. The target signal is separable: object-level repeat-stop removes exact repeated records (duplicate rate 0.000, max repeat 1) while preserving F1 (0.494 to 0.490) and stricter F1@0.5 (0.381 to 0.385). Structure-axis probes localize the effect to bbox-coordinate object lists; dense non-bbox and spatial/count JSON remain repeat-clean, including under high-capacity adapters. Qwen3-VL-8B reproduces a clean controlled endpoint (F1@0.3 0.318, duplicate rate 0.000), and COCO 2017 reproduces acquisition plus duplicate pressure. Dense coordinate-list adaptation therefore creates a structure-bound, cross-family interference surface that can be measured and controlled.

Prior work treats structured output as a reasoning tax, but this framing is incomplete: the cost of formatting depends strongly on a model's spare capacity. Using information-matched prose controls and a four-level schema complexity gradient, we separate format-specific effects from prompt-length confounds across 4 models and 5 benchmarks with 0% parse failures on successfully generated responses. We find that structured formats are capacity-dependent. Models with sufficient headroom absorb JSON constraints without degradation (Sonnet: $88.7\pm4.0$% JSON vs. $89.3\pm1.7$% CoT on MATH-Hard). In contrast, formats severely degrade models operating near their limits through two distinct mechanisms. First, under standard token budgets, Haiku drops 36.2pp ($p < 0.0001$) largely due to truncation. Second, even with extended budgets eliminating truncation, GPT-4o-mini drops 28.0pp ($p < 0.001$), revealing pure capacity competition independent of token exhaustion. This format penalty scales with schema complexity (McNemar $p < 0.0001$) and cannot be explained by prompt length alone. Furthermore, these results qualify claims of frontier model immunity: on AIME competition math, Opus 4.7 drops from 96.2% to 91.0% under JSON ($-5.3$pp; the displayed percentages are independently rounded, exact difference is $7/133 = 5.26$pp $\approx 5.3$pp). A delayed-structure ablation -- reasoning freely before formatting -- recovers most of the lost accuracy (3-run mean: 80--87%), supporting the capacity competition mechanism. The practical implication is not to avoid structured output, but to match it to capacity: when a model is near its limits, think first, format later.

Diffusion Language Models (DLMs) enable parallel text generation by iteratively denoising a full sequence, offering attractive flexibility compared to auto-regressive (AR) decoding. However, existing methods fail to fully capture token relationships, leading to a performance gap relative to AR baselines, especially as the degree of parallelism increases. In this paper, we give a systematic analysis of the gap, identifying three key factors: (i) model capacity, (ii) dependency, and (iii) invariance. To address these issues, we first propose an invariant energy (Inv-E) together with an effective sampling-based estimator to handle the invariance issue. By further combining with the independent energy (Ind-E), we obtain a unified energy (Uni-E), that accounts for all these factors. Uni-E enjoys a unique advantage: it can be computed exactly without sampling-based partition estimation. Besides, Uni-E is model agnostic and can therefore be scaled to models of arbitrary size. We further prove that Uni-E can correct the distribution shift caused by dependency and invariance. Extensive experiments across Diffusion Language Models (DLMs) and Diffusion Large Language Models (DLLMs) demonstrate the effectiveness of the proposed Uni-E.

Deep learning EEG denoising architectures have scaled from tens of thousands to tens of millions of parameters, yet no prior study has isolated model capacity as the experimental variable or tested whether reconstruction metrics predict downstream neural-signal utility. We address both gaps by fixing architecture, loss, data split, and training recipe while sweeping only channel width from 1.05K to 40.26K parameters in a minimal depthwise-separable convolutional U-Net. Models were evaluated on the EEGDenoiseNet benchmark, cross-dataset BCI transfer tests, controlled baseline retraining, and downstream motor-imagery classification with five decoder families across all nine BCI Competition IV-2a subjects. Reconstruction performance saturated by 3-6.5K parameters, with post-elbow gains of at most 0.015 correlation coefficient per log10-parameter unit. An 8.46M-parameter baseline retrained under the same pipeline matched the 40.26K compact variant on EOG--a 200x parameter gap yielding no advantage--while a Patch-Transformer control reproduced the same diminishing-return shape. Downstream evaluation exposed a classifier-dependent metric-utility gap: reconstruction-optimized denoising significantly degraded CSP+LDA classification across all nine subjects and three artifact types (best denoised accuracy 0.547 vs. 0.612 noisy baseline; Bonferroni p=0.0488), persisting on naturally recorded trials (Delta=-0.047; BH-FDR q=0.0049). End-to-end neural decoders showed variable or neutral effects. Standard EEG denoising benchmarks are saturated far below current model capacity, and reconstruction metrics do not predict BCI utility. Ultra-compact models at 33-46 KB and 1.27-2.61M FLOPs/segment are practical for edge deployment. These findings argue for capacity-controlled evaluation, harder task-aware benchmarks, and mandatory downstream validation.

Secure aggregation allows a server to aggregate users' local updates while preserving update privacy. Existing information-theoretic problems typically assume that correlated random keys are provided by a trusted third party (TTP) or generated via prescribed groupwise structures, while the communication cost for establishing such correlated keys is often ignored. Consequently, the fundamental limits under general key-distribution mechanisms remain unknown. In this paper, we study the $T$-colluding information-theoretic secure aggregation problem with $N$ users under a general two-phase framework consisting of a key distribution phase and an update aggregation phase. Unlike prior work, we model key distribution through user-to-user communication and allow arbitrary user-generated key-distribution mechanisms, eliminating TTP or prescribed structures. This enables a joint characterization of three resources: randomness for security, key-distribution communication, and aggregation communication. We completely characterize the capacity region among these three resources by constructing a novel secure aggregation scheme together with a matching information-theoretic converse. In particular, we develop an explicit deterministic capacity-achieving construction over any finite field of size at least $N$, whereas most existing schemes either rely on TTP or employ randomized or existential constructions over sufficiently large finite fields. We further show that the optimal performance can be achieved using only pairwise shared keys, enabling implementation via Diffie--Hellman key exchange. Compared with Google's seminal secure aggregation scheme, the proposed scheme requires fewer random masking keys while preserving the same aggregation communication overhead.

We find the asymptotic ratio between the storage capacities when enforcing real pre-activations in a complex hypothesis class as opposed to complex ones in the same class. We use weights drawn from the complex Gaussian, which converge asymptotically in norm to the square root of dimension almost surely. Our methods depend on Gardner volume-type comparisons at critical capacity. Our proof relies on an application of the Harish-Chandra-Itzykson-Zuber (HCIZ) formula, nonstandard in literature. With the HCIZ formula, we may obtain a more robust approximation for the final asymptotic ratio. This strategy is applicable to our work specifically since we integrate over the unitary and orthogonal compact manifolds, facilitated via the Weyl integration formula and the Haar measure.

Block diffusion speculative decoding accelerates LLM inference by predicting all tokens within a block simultaneously for the target model to verify in parallel. Predicting an entire block at once requires a sufficiently capable draft model and effective utilization of the target model's internal knowledge. However, the state-of-the-art method DFlash constrains all draft layers to share a single fused representation derived from only a few target layers, limiting per-layer expressiveness and hindering further scaling of draft capacity. In this paper, we present \modelname, which flares out the narrow conditioning bottleneck of DFlash through a lightweight layer-wise fusion mechanism: each draft layer attends to its own learnable combination of a broad set of target layers at negligible overhead, simultaneously injecting richer target knowledge and providing every draft layer with a distinct input. This enhanced per-layer expressiveness enables scaling the draft model to deeper architectures with consistent gains. We further scale training data from 800K to 2.4M samples to fully exploit the enlarged capacity. On six benchmarks spanning mathematical reasoning, code generation, and conversation, \modelname attains average wall-clock speedups of 5.52x on Qwen3-4B, 5.46x on Qwen3-8B, and 3.91x on GPT-OSS-20B, improving over DFlash by roughly 11%, 8%, and 5% respectively. Our code is available at https://github.com/Tencent/AngelSlim.

Neural scaling laws describe predictable power-law relationships between model size, dataset size, compute, and performance. While these laws guide the development of modern foundation models, the mechanisms underpinning them remain poorly understood, in part due to the absence of scalable analysis tools. To close this gap, we introduce "spectral position": a scalable measure of which eigenvalues of the empirical neural tangent kernel (eNTK) currently drive loss reduction. Applying this measure to scaling experiments, we find that spectral position decreases throughout training: learning shifts from dominant eigenmodes into the spectral tail. Larger models reach further into the tail than smaller models, revealing a size-dependent capacity we call "spectral reach". This suggests why larger models achieve lower losses: they sustain learning on weak spectral signals inaccessible to smaller models. We further identify feature learning as a key enabler of spectral reach. It adaptively amplifies gradient magnitudes as learning advances, sustaining progress where frozen representations stall. This points to concrete interventions through architecture and optimizer design.

Looped transformers apply a shared block multiple times and have emerged as a parameter-efficient route to scaling compute in language models. However, at fixed FLOPs a looped model has strictly less capacity than a baseline transformer. We propose a novel dual-path block that can flexibly scale compute, the number of sequential operations applied to a hidden state, and capacity, the parameters available at a single step. For this we expose both axes as parallel pathways within a single layer: a deep sublayer re-applied K times with shared parameters, and a wide sublayer with an enlarged feed-forward network applied once. Independent per-token gates combine both axes and allow detailed per-token routing analyses. We show that across two FLOP budgets, our dual-path model surpasses iso-FLOP matched models on language modeling and downstream evaluations, while using fewer parameters than the baseline at matched FLOPs. The learned gates are directly interpretable and show systematic per-token allocation with function words and lexical content trend wide, while punctuation, symbols, and arithmetic tokens trend deep.

Larger models learn tasks smaller models do not. What drives this phenomenon? We develop a simple phenomenological argument that power-law scaling already suggests that a larger model will be able to learn a part of the data distribution that a smaller model fails to learn, even with infinite training data. To validate this claim and identify its causes, we study the effects of model scaling on a synthetic setup consisting of a mixture of tasks that show monotonic scaling curves. The results point to a data-induced competition over resources (neurons). Specifically, smaller models allocate their neurons to high frequency or low complexity tasks, and so they learn solutions that perform poorly on rare and complex tasks. Moreover, this happens even when solutions capable of expressing the desired task exist. We then assess how a larger model circumvents this data-centric bottleneck, finding that it traces to a reduced interference mechanism: larger models can allocate enough resources to common tasks that the gradient updates for those tasks become weak, which means that they do not overwrite rare-task features as they slowly accumulate. Finally, to further validate these claims, we pretrain OLMo models (4M to 4B parameters) on novel tasks of varying frequency and complexity. The results mirror those from our synthetic data experiments: only the larger OLMo models learn the infrequent and complex tasks, and these larger models embed more task features in their representations and show less gradient interference between tasks. Overall, we offer a data-centric account of why larger models learn tasks that smaller models fail to. This helps explain why larger models are better in practice, and it can inform practical questions concerning model sizing and training data mixtures.

Subject-driven image generation aims to synthesize new images that preserve the identity of the given subject while following textual instructions. Existing approaches often encode text and reference images separately. This limits cross-modal reasoning abilities and causes copy-paste artifacts. Recent frameworks that connect multimodal models and diffusion models improve instruction following, but largely overlook identity preservation. To address these limitations, we condition diffusion models on Multimodal Large Language Models (MLLMs) that jointly encode text and reference images, and augment it with VAE-based identity conditioning. A novel Dual Layer Aggregation (DLA) module is designed to aggregate multi-level MLLM features for optimal conditioning, and a multi-stage denoising strategy is applied to progressively balance the semantic information from MLLM and fine-detail identity from VAE during inference. Extensive experiments demonstrate that our approach harmonizes multimodal understanding with identity preservation, mitigates copy-paste issues, and achieves superior performance regarding human preference on subject-driven image generation. Our project website is available at https://zsh2000.github.io/squeeze-mllm-subject-gen/.

Models trained on a new task typically degrade on prior tasks, a phenomenon known as forgetting. Traditionally, mitigating forgetting has required replaying stored exemplars from prior tasks, which is often impractical. By contrast, language models can sample from their own training distribution, and we show that these self-generated samples serve as effective replay data, nearly eliminating forgetting. We find that forgetting nonetheless persists when the model has little remaining capacity: models pretrained close to saturation cannot absorb new information without overwriting prior knowledge. When capacity is not the limiting factor, low learning rates reduce forgetting but require substantially more training steps. Replay breaks this tradeoff, enabling fast, high-learning-rate finetuning without forgetting.

Classical Hopfield networks are limited to static patterns due to symmetric weights, whereas asymmetric networks can encode temporal sequences via limit-cycle attractors. Achieving high-capacity storage of long sequences in classical synchronous asymmetric networks, however, has remained a challenge. We present a simple and robust construction within the classical asymmetric Hopfield model with binary neurons and synchronous updates, that allows $n$ neurons to support $\exp\!\big(Ω(n/(\log n)^2)\big)$ distinct limit-cycle attractors, each with period $\exp\!\big(Ω(\sqrt n/\log n)\big)$ and robust to random noise with flip probability up to $\frac12-o(1)$, yielding superpolynomial capacity in both the number and length of stored sequences. This is the first demonstration of such capacity for asymmetric Hopfield networks, which we obtain by combining results from combinatorics, number theory and the analysis of opinion dynamics. Our findings show that synchronous asymmetric Hopfield networks possess a sequence-memory capacity which is larger and more robust than previously recognized, demonstrating that, in both biological and artificial neural systems, robust sequence representation can be achieved through coarse architectural motifs rather than complex nonlinearities.

Human cognitive performance is constrained by limited mental resources, yet continuous computational estimation of cognitive capacity dynamics remains an open challenge. We propose a theory-driven multimodal learning framework that models capacity-related cognitive state as a two-dimensional physiological representation defined by voluntary resource allocation (mental effort) and overload-related strain (stress). The proposed architecture combines dual-stream encoding of cardiac (IBI/HRV) and electrodermal (EDA) signals with late fusion and task-specific output heads that independently estimate probabilistic effort and stress states. Evaluation on the SWELL-KW dataset using strict leave-one-subject-out cross-validation demonstrates cross-individual generalization (stress: 70.0% balanced accuracy; effort: 72.2%), with significant gains from multimodal integration and theory-guided supervision. Rather than collapsing physiological dynamics into a single workload label, the proposed effort--stress state-space enables structured differentiation between distinct cognitive regimes, including productive engagement and overload-related strain. Predicted state trajectories exhibit significant demand-sensitive shifts under controlled workload manipulations, with effort and stress responding differentially across interruption and time-pressure conditions. These results suggest that physiologically grounded multidimensional state representations may provide a foundation for adaptive systems capable of continuous capacity-aware monitoring and human-centered interaction.

What functions can Neural Processes represent? We analyze the representational capacity of popular NP architectures: Conditional Neural Processes (CNPs), Attentive Neural Processes (ANPs), Transformer Neural Processes (TNPs), and their latent variants. We prove these architectures form a strict hierarchy. CNP-representable functions are exactly those depending on finitely many expected features of the context distribution. ANPs strictly generalize CNPs via query-dependent reweighting, enabling kernel smoothers. ConvCNPs and ANPs are incomparable; each contains functions outside the other, separated by stationarity versus translation equivariance. TNPs with $L$ self-attention layers capture $L$-hop context interactions. For latent NPs, we show finite-dimensional latents provide coherent sampling but do not circumvent encoder limitations; matching GP posterior distributions requires latent dimension scaling with context size. These results provide a theoretical foundation for architecture selection based on task structure.

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.

Scaling laws have made language-model performance predictable from model size, data, and compute, but they typically treat the optimizer as a fixed training detail. We show that this assumption misses a fundamental axis of representation scaling: how effectively the optimizer converts added FFN width into utilized spectral capacity. Using eigenspectra of feed-forward network representations, measured through soft and hard spectral-ranks, we find that \emph{the same Transformer architecture realizes markedly different spectral scaling laws when trained with different optimizers}. Holding architecture and width schedule fixed, AdamW exhibits weak hard-rank scaling ($β$=0.44) on rare-token (TAIL) representations where learning is known to be hardest, whereas Muon achieves linear scaling ($β$=1.02) in the same regimes, a $2.3\times$ increase in the scaling exponent. This difference is not reducible to validation loss: AdamW configurations can match low-rank Dion variants in perplexity, under extended training, while exhibiting sharply different spectral geometry, demonstrating that matched loss does not imply matched representation structure. Hard--soft rank asymmetry further reveals that optimizers differ not only in how much capacity is realized, but also in how that capacity is structured across eigenmodes. To disentangle optimizer effects from architectural ones, we compare against architectural interventions (e.g., attention rank and positional encoding), and find that optimizer-induced spectral shifts often exceed the architectural effects. These results suggest optimization as a first-class axis of representation scaling, motivating optimizer--architecture co-design.

Communication enables coordination in multi-agent reinforcement learning (MARL), but many real-world applications, e.g., search-and-rescue with drone swarms, operate under severe bandwidth constraints. Many communication architectures still expose a coupled bottleneck in which a shared latent representation is used for both policy execution and inter-agent communication. Consequently, reducing message size directly limits the policy's latent space, often leading to significant performance degradation. We address this with two contributions. First, we introduce $β$, a normalised per-agent bandwidth budget that unifies sparsity, rounds, and message dimension into a single comparable constraint. Second, we provide SLIM, a minimal architecture that decouples the communication pathway from the policy's latent representation, allowing us to isolate the effect of bandwidth from the effect of policy capacity while benefiting from in-step communication. We evaluate our method on several partially-observable MARL benchmarks, where communication is essential. Our approach achieves state-of-the-art performance and exhibits scalability and robustness under limited communication, with only marginal degradation as bandwidth is reduced.

While scaling laws govern aggregate large language model performance, no scaling law has linked factual recall to both model size and training-data composition. We evaluated 38 models on over 8,900 scholarly references evaluated by an automated reference verification system. Recall quality follows a sigmoid in the log-linear combination of model parameter count and topic representation in training data. These two variables alone explain 60% of the variance across 16 dense models from four families, rising to 74-94% within individual families. The form matches a superposition-inspired account in which recall is gated by a signal-to-noise ratio: signal strength scales with concept frequency and the noise floor with model capacity.

Capped-usage SaaS products -- LLM subscriptions such as Claude Code and ChatGPT, cloud platforms such as Vercel and Cloudflare Workers, corporate benefit platforms, identity-verification services with liability transfer -- share a structural signature with insurance products: a fixed premium decoupled from realized consumption, stochastic per-user demand with heavy-tailed severity, a non-fungible cap that resets on a fixed schedule, and a portfolio-level exposure that requires reserve adequacy under tail risk. We argue that this is not an analogy. It is the same operational problem actuarial science has been tooled for decades to address, restated with new dependent variables (tokens, bandwidth bytes, function-invocations, gym check-ins) in place of medical claims. This paper proposes a modeling framework for capped-usage SaaS pricing built from frequency-severity decomposition, premium calculation principles, and Monte Carlo reserve adequacy. We map the framework to publicly observable subscription tiers in two domains (LLM services and cloud platforms), ground it in canonical health-insurance economics (Arrow 1963; Pauly 1968; Manning et al. 1987; Brot-Goldberg et al. 2017), and demonstrate divergence from traditional unit economics through a worked example. The contribution is operational rather than theoretical: not a new theorem, but vocabulary and tools currently absent from cs.LG/stat.ML practice.

Pre-training neural operators on diverse partial differential equation (PDE) datasets has emerged as a promising direction for building general-purpose surrogate models in scientific machine learning. However, the inherent complexity and structural diversity of PDE solution operators make multi-PDE pre-training fundamentally challenging. Existing methods mainly address this by increasing model capacity, while leaving the target solution operators unchanged. Inspired by classical numerical analysis, we instead propose to transform complex and diverse solution operators into simpler, better-aligned forms that are easier to model jointly. Since the optimal transformation varies across PDE types, it must be adaptive and input-dependent, allowing a single neural operator to approximate an entire family of operators. We instantiate this idea as AOT-POT (adaptive operator-transformation for pre-training operator transformer), which expands hidden representations into multiple parallel streams, adaptively aggregates and redistributes them before and after each sub-layer, and mixes streams through Sinkhorn-projected doubly stochastic matrices for stable training. These mechanisms together reshape diverse solution operators into a unified form that can be effectively modeled by a single architecture. Empirically, AOT-POT achieves state-of-the-art performance on 12 PDE benchmarks with only 3% additional parameters, reducing relative L2 error by up to 77.6% (40.9% on average). Fine-tuning AOT-POT further reduces L2 error by up to 92% on in-domain PDEs and 89% on out-of-domain PDEs (unseen types during pre-training), demonstrating that adaptive operator transformation is an effective and complementary direction for advancing PDE foundation models beyond simply scaling model capacity.

We measure procedural-skill SFT contribution across three Qwen3.5 dense scales (0.8B, 2B, 4B) on a 200-task / 40-skill holdout, with Claude Haiku 4.5 as a frontier reference. The corpus is 353 rows of (task + procedural-skill block, Opus chain-of-thought, judge-pass) demonstrations. Main finding. Under matched-path LLM-only scoring, the SFT-attributable procedural-$Δ$ lift is roughly uniform across sizes: $+0.070 / +0.040 / +0.075$ at 0.8B / 2B / 4B. Variation in post-SFT $Δ$ ($-0.005$, $+0.100$, $+0.065$) is dominated by a W-shaped pre-SFT base trajectory ($-0.075$, $+0.060$, $-0.010$, Haiku-4-5 at $+0.030$): the 5-step procedure hurts 0.8B and 4B, helps 2B, and helps frontier Haiku modestly. SFT works hardest in absolute terms where the base struggles with the procedure -- a regime-asymmetric pattern with a falsifiable prediction at 8B/14B. Methodology. (i) A bench format-compliance artifact: 83.5% of the holdout uses a deterministic ANSWER-line extractor that under-counts free-form-prose conclusions; our LLM-only re-judge reveals it was systematically biased against the curated condition. (ii) A negative-iteration sequence at 0.8B: three well-formed recipe variants cluster post-SFT curated pass-rate within a 2 pp band, constraining the absolute-pass-rate ceiling to base capacity rather than recipe. Cross-family judge validation. GPT-5.4 via OpenRouter on all 7 configurations (2800 paired episodes) agrees on the direction of every per-student finding: Cohen's $κ\geq 0.754$, agreement $\geq 93.25\%$, max headline $Δ$ shift $\leq 0.035$ pp. Two earlier framings -- "format-only learning at 0.8B" and "SFT contribution shrinks at 4B" -- were path-mismatch artifacts; this paper supersedes both. Single-seed evaluation; threats itemised in the paper.

Single-model ensembles (SMEs) have attracted attention as a way to approximate some of the benefits of deep ensembles within a single network. However, under an approximately matched parameter budget, it remains unclear whether model capacity should be concentrated in a single wide pathway or redistributed into many narrow and independent members. We investigate this question through the Multi-Narrow (MN) transformation, which converts a baseline CNN into an SME of narrow, path-wise independent branches while approximately preserving the dominant parameter budget. We systematically compare Single-Wide and Multi-Narrow configurations across different training-data regimes, architectures, and datasets. The results show that the effectiveness of MN is strongly data-dependent: weakly partitioned or baseline-wide models are preferable in data-rich settings, whereas highly partitioned MN models consistently outperform the baseline in low-data settings. This tendency is reproduced across multiple CNN architectures and image-classification datasets, suggesting that it is not specific to a single benchmark or model family. Analysis of internal representations shows that high-MN models learn more diverse and less redundant path-wise features. In low-data regimes, this diversity is broadly utilized and improves generalization, whereas in data-rich regimes, training becomes imbalanced and prediction is dominated by a small subset of paths. These findings clarify when and why Multi-Narrow transformation is effective, and provide practical guidance for allocating model capacity between width and member multiplicity under a limited budget.