Growth

Scaling laws predict how loss decreases with increases in computation. We show, contrary to conventional wisdom, that architectural interventions can modify scaling exponents in pre-training, leading to power-law improvements in performance as computation increases. As an anchoring point, we consider the architectural formulation of looped transformers. Although not typically used in this way, looping, also known as recursive depth, provides a mechanism for model growth, by increasing the number of loops during training. Model growth, with and without shared weights, provides the biggest changes to the scaling exponents. In particular, a 7.4B model growth architecture matches GPT-3 13B on CORE with roughly $20\times$ less compute, and has compute efficiency gains that increase with scale. Moreover, simply using a boundary operator in a vanilla transformer, which normalizes and injects an earlier block, also provides an exponent increase, although to a lesser extent. In the data-constrained, multi-epoch setting, standard looping has a useful regularizing effect, where we find it is compute-optimal to increase the number of loops with scale. These results can be understood through the lens of computational depth: for a given computational budget, we wish to increase the usable depth of the transformer, which can lead to efficiency gains that increase with scale.

Vine robots navigate cluttered environments by extending from their tip. Although their ability to operate in such environments has been extensively demonstrated, little work has addressed growth planning, i.e., finding optimal growth paths. Moreover, existing planners do not account for the growth pressure necessary to follow a given path, which can cause the robot to burst when it is too high. In this paper, we address the problem of finding minimum-pressure paths for vine robots growing around polytopic obstacles. We propose an efficient algorithm that is guaranteed to find globally optimal solutions in 2D and approximate solutions in 3D, with an error that vanishes as a discretization parameter approaches zero. First, we derive a growth pressure equation for vine robots of arbitrary shape, which we use to show that there always exists a minimum-pressure path that is piecewise-linear and can bend only at specific points on the obstacles. We then leverage this observation to reduce the growth-planning problem to a shortest-path problem with time-dependent weights, which we efficiently solve using a modified Dijkstra's algorithm. We demonstrate the speed and scalability of our approach through numerical simulations. We also validate our algorithm with hardware experiments and provide an open-source and high-performance implementation in the Python package, VinePlanner: https://github.com/Ahsoka/VinePlanner.

AI is changing what leaders must judge, explain, learn, and coordinate, yet existing measures do not capture these behaviors at the level needed to study leadership in AI-enabled work. We develop the AI Leadership Battery, which organizes 36 behaviorally specific subdimensions into 11 theory-specified content families. Following established scale-development procedures, the research used deductive item generation; content validation of definitional correspondence and definitional distinctiveness; exploratory factor analysis and item reduction; confirmatory factor analysis in independent samples; and tests of internal consistency reliability, convergent validity, discriminant validity, and criterion-related and incremental validity. Across the development and validation studies, the analyses provided evidence for the Battery's content, multidimensional structure, reliability, and distinction from selected orbiting constructs. The Battery also contributed additional information beyond orbiting constructs across organizational growth, decision speed, customer/stakeholder response capability, AI-enabled team performance, AI-enabled work experience, AI security and risk management, and AI adoption and integration. The resulting measure provides researchers with a behavioral framework for examining how leaders in AI-enabled work regulate judgment, learning, adaptation, transparency, and accountability.

AI agents increasingly act through agent skills, i.e., natural-language instructions, that direct a host agent toward shell, network, credential, file, and process actions, and public registries distribute them at scale. In the first half of 2026, the OpenClaw AI agent went viral, and its public skill registry boomed: the observable stock nearly doubled in 91 days, and a majority of the listings visible in June were created in just two months. By the end of our study window, the wave had crested, and monthly listing creation and core-repository activity were falling from their spring peaks. This paper measures what the boom left behind, drawing on the OpenClaw Git history, its GitHub issues and pull requests, and three ClawHub registry snapshots. Attention is concentrated: the top 10% of skills received 46.93% of all downloads. No simple skill features (like size or download counts) remained a stable predictor of continued listing once creation cohort and skill age were controlled. Human scrutiny did not stay: 77.86% have zero stars and zero comments, while 85.06% of the readable skills carry privilege evidence. And automated cleanup is not ready: the three security scanners disagreed on 23,702 of the 61,990 skills they all cover. After human adjudication, weighted scanner sensitivity against the reference standard ranged from 21.67% to 61.06%. Governing fast-growing agent-skill registries cannot rely on simple metadata or single scanner scores; it requires robust, transparent measurement and independent validation.

Post-training quantization compresses large language models (LLMs) by storing their weights at reduced precision, and each quantized weight introduces an error into the hidden states. Naively, these errors should accumulate with depth and corrupt next-token prediction; randomly initialized models accumulate these discrepancies rapidly, whereas quantized pretrained models accumulate much less hidden-state error and largely maintain downstream task performance, even though they were never trained with quantization noise. This raises the question we address: why does post-training quantization work? Comparing full-precision and quantized forward passes, we identify two mechanisms that characterize pretrained quantization robustness. First, the error a layer newly introduces tends to oppose the error it inherits from the layer's input. The two cancel partially such that the discrepancy between full-precision and quantized passes grows slowly. This counteracting residual interaction develops during pretraining. Our quantitative analysis identifies it as a major factor slowing hidden-error growth. Second, LM-head geometry preferentially preserves the scores and probabilities of high-ranked tokens, which typically represent the model's most confident predictions. Together, these mechanisms explain why quantization error that passes through numerous layers can still produce only small output changes, and we verify the findings across models and quantization settings.

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.

Long-output reasoning has made the key--value (KV) cache a critical memory bottleneck for efficient LLM serving. Existing KV compression methods usually rely on a predefined per-request budget and adjust only which KV states are retained, leaving the total capacity fixed throughout decoding. However, reasoning workloads exhibit substantial demand variation: different requests require different KV capacities, and the attention demand of an individual request evolves during generation. We introduce \textbf{GrowPage}, an on-demand KV budgeting framework that treats KV capacity as a runtime resource. GrowPage maintains lightweight dual-timescale query summaries to capture recent and long-term attention behaviors, and uses their relative attention working sets to estimate demand evolution. At each capacity boundary, GrowPage either compresses KV states within the current allocation or acquires an additional physical page when broader demand emerges. By integrating with PagedAttention's page-level memory abstraction, GrowPage preserves continuous batching and prefix caching. Experiments on reasoning benchmarks across multiple models show that GrowPage achieves a superior performance--throughput trade-off over existing approaches.

The research explores the pioneering integration of Physics-Informed Neural Networks (PINNs) into the domain of Ground-Penetrating Radar (GPR) data prediction. This research presents a detailed development framework for a specialized PINN model, proficient at interpreting and forecasting GPR data, much like how medical imaging models predict tumor behavior. By harnessing the synergy between deep learning algorithms and the physical laws governing subsurface structures or in medical terms, human tissues the model effectively embeds the physics of electromagnetic wave propagation into its architecture. This ensures that predictions not only align with fundamental physical principles but also mirror the precision needed in medical diagnostics for detecting and monitoring tumors. The suggested deep learning structure comprises three components: a CNN, a spatial feature channel attention (SFCA) mechanism, and ConvLSTM, along with temporal feature frame attention (TFFA) modules. The attention mechanism computes channel attention and temporal attention weights using self-adaptation, thereby fine tuning the visual and temporal feature responses to extract the most pertinent and significant visual and temporal features. By integrating physics directly into the neural network, our model has shown enhanced accuracy in forecasting GPR data. This improvement is vital for conducting effective assessments of bridge deck conditions and other evaluations related to civil infrastructure. The use of Physics Informed Neural Networks (PINNs) has demonstrated the potential to transform the field of Non-Destructive Evaluation (NDE) by enhancing the precision of infrastructure deterioration predictions. Moreover, it offers a deeper insight into the fundamental mechanisms of deterioration, viewed through the prism of physics-based models.

We study masking diffusion for discrete sampling and introduce a path-resolved measure of data geometry called the \emph{unmasking growth complexity} ({\textsf{UGC}\xspace}). Its local increments directly control Kullback--Leibler (KL) discretization error, yielding a unified analysis of Bernoulli-subset and fixed-cardinality unmasking schemes. In log-reveal-odds coordinates, this structure yields optimized single-block and multi-block schedules, and quantifies the gains from adapting computational effort to data geometry. Crucially, we show how {\textsf{UGC}\xspace} increments can be estimated from samples via KL increments along coupled reveal trajectories. This leads to \emph{certified-optimal} samplers that achieve a prescribed KL error with high probability and iteration complexity within a constant factor of the corresponding oracle procedure. Collapsing the \ugc path yields the aggregate {\textsf{UGC}\xspace} mass, which connects to classical multivariate dependence measures and complexity measures from previous analyses of discrete diffusion. In the fine-partition limit, the squared integral of the square-root {\textsf{UGC}\xspace} density determines the sharp leading-order optimal Euler discretization error. Examples exhibit substantial dimension-dependent gains over coarse schedules, including $\widetildeΩ(\sqrt{d})$ improvements achievable with a constant number of adaptively placed blocks.

We develop the Sparse Orthogonal Regression Technique (SORT), a sparse spectral framework for learning orthonormal-basis expansions from noisy and irregularly sampled data. SORT estimates expansion coefficients directly from observations using L1-regularized regression, avoiding explicit quadrature or analytic inner-product evaluation. The central application is data-driven discovery of ordinary differential equations: vector fields are represented in chosen orthogonal bases and learned as sparse coefficient expansions. This provides a complementary route to symbolic regression, grammar-based discovery, and SINDy-style sparse identification by first recovering a compact spectral representation, which can later guide searches for simpler analytic forms. Across the dynamical-system experiments, SORT matches or improves upon library-based sparse-regression baselines when the basis is well adapted to the problem, and shows more stable degradation under sparse sampling, noisy derivative estimates, and representation mismatch. Specific examples illustrate why this representation is useful: if a finite library misses the problem-specific nonlinearity, the resulting model can fail. SORT is not immune to mismatch, but it shifts the problem away from brittle selection among generic terms to basis design adapted to the problem domain. The experiments also show that dominant low-order coefficients persist as model order increases, supporting order-consistent model growth. Beyond equation discovery, the same learned expansion supports nonlinear approximation and estimation of complex, high-dimensional integrals by coefficient readout. Overall, SORT provides a reusable intermediate representation for system identification, approximation, and integration, while making basis design an explicit part of the scientific modeling problem.

Evolutionary multitasking allows several related problems to be solved in a single run of an algorithm. In this paper, we investigate integrating evolutionary multitasking with Edge Assembly Crossover (MT-EAX) to solve the classical Travelling Salesperson Problem (TSP). To fairly compare MT-EAX against standard EAX under strict compute budgets, we evaluate three scaling methods: generation scaling, population scaling, and balanced scaling. Our results show that generationally scaled MT-EAX is highly effective compute-wise in the early stages of the search, saving $60\%$ to $90\%$ of compute for equal or better solution quality. We observe that instance geometry has a significant impact, with clustered, normally distributed instances securing larger improvements than uniformly distributed ones. However, when scaling by population or utilising explicit solution transfer, the results are negative due to population starvation and incompatible cross-instance parent selection. We demonstrate that the advantage of MT-EAX derives from increased diversity through parallel search in early generations, which can be successfully preserved using a decoupled configuration to often strictly outperform or match standard EAX performance at final convergence.

Recurrent context compression controls context growth in long-horizon agents, but its behavioral effects remain poorly understood. In this preliminary empirical study, we show that compression can weaken the influence of recent interactions, increasing blocked actions, repeated exploration, and instability across runs. Motivated by these observations, we introduce TRACE, a verifier-guided framework that evaluates individual compaction events through paired closed-loop continuations from the same environment state and uses summary preferences to optimize a natural-language compression prompt while keeping all models frozen. Initial results on AppWorld show improvements over existing compression baselines in task performance, multi-run reliability, and context--execution efficiency. These findings provide early evidence for boundary-local evaluation as a promising direction for reliable agent context compression.

We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex. We introduce the Subgradient Tamed Unadjusted Langevin Algorithm (SG-TULA), a discretisation of the Langevin diffusion that operates directly on subgradients, without relying on computationally demanding smoothing procedures. To handle the superlinear regime, taming techniques are employed to produce a stable, explicit scheme. We derive non-asymptotic convergence bounds in Wasserstein-2 distance, with all constants tracked explicitly in terms of dimension and inverse temperature, improving upon the currently known rates for subgradient-based Langevin algorithms. We further provide excess risk estimates for the associated optimisation problem. We verify the assumptions, with explicit constants, for the regularized pretraining potential of a LLM in the GPT-2 lineage and the boosted coordinate-wise variant of SG-TULA pretrains the former competitively against finetuned AdamW and Muon, for which no comparable non-asymptotic guarantees are presently available.

Spatial mapping of lung adenocarcinoma (LUAD) growth patterns across whole slide images (WSIs) requires resolving architectural context at the region level, yet existing methods operate at the individual tile level and produce generic morphological clusters rather than clinically defined pattern maps. We propose a weakly supervised Bag-of-Visual-Words (BoVW) pipeline that learns a visual vocabulary from frozen foundation model embeddings extracted from a small set of annotated regions of interest (ROIs). Pattern prototypes are constructed as mean BoVW histograms of same-label ROIs and used for nearest-prototype classification of sliding-window regions under Jensen--Shannon divergence. The resulting predictions are projected onto the WSI tile grid to produce interpretable spatial pattern maps. We evaluate the method on 87 CPTAC-LUAD patients using three foundation model encoders and multiple vocabulary sizes on two clinically motivated tasks. For tumour/healthy classification, the best configuration achieves a balanced accuracy of $0.974$ with H-Optimus-1, approaching the $0.987$ obtained by a supervised SVM trained on mean-pooled WSI embeddings. For binary histologic grade classification, the BoVW pipeline achieves higher balanced accuracy than the supervised baseline for all encoders, suggesting that ROI-level pattern decomposition preserves grade-relevant heterogeneity that is attenuated by global mean pooling.

Reinforcement learning for flow-matching text-to-speech is complicated by deterministic ODE sampling: trajectory-level policy-gradient methods typically convert the ODE into an SDE and track per-step likelihood ratios, introducing stochastic perturbations and substantial overhead. We propose GROW, a group-relative advantage-weighted on-policy RL method that acts directly on the standard flow-matching objective. For each prompt, GROW samples a group of on-policy utterances, separately standardizes intelligibility and speaker-similarity rewards within the group, and combines them to reweight flow-matching regression. A Wasserstein-2 velocity penalty anchors the updated model to a frozen pretrained reference. A group-mean reward baseline is introduced to convert reward weighting into advantage weighting. For strong pretrained TTS models with concentrated rewards, positive exponential weighting is dominated by reward-agnostic self-imitation, whereas a zero-mean signed advantage preserves effective within-group credit assignment. Instantiated on DiTAR and evaluated on LibriSpeech and Seed-TTS EN/ZH, GROW reduces average WER from 2.016 to 1.558 and raises speaker similarity from 0.676 to 0.715 while keeping UTMOS. With 10-NFE training rollouts and 32-NFE evaluation, GROW retains comparable performance while training 2.9x faster than 32-NFE DiTAR-GRPO. We will open-source complete GROW codes, faithful DiTAR reproduction, and all model checkpoints.

Two central challenges in diffusion-based sampling are the theoretical one of understanding their remarkable effectiveness even in high-dimensional settings, and the practical one of designing algorithms with certified performance guarantees. We show that these questions are intimately connected via the \emph{denoising growth complexity} ($\mathsf{DGC}$). It is a geometric measure defined by a log-time weighted integral of the derivative of the denoising mean-squared error along the Gaussian heat flow. We show how the $\mathsf{DGC}$ increments lead to a simple and explicit bound on the KL error of an Euler scheme applied to the stochastic innovations representation. The bound is local along the path: each step is controlled by the corresponding $\mathsf{DGC}$ increment and its relative stepsize. This structure allows us to derive KL sampling guarantees for optimized stepsize schedules, both in a simpler single-block setting and in a more refined $K$-block setting. The $\mathsf{DGC}$ function has a natural martingale structure, which we exploit to develop fully data-certified versions of these algorithms. It also admits information-theoretic upper bounds in terms of covariance, rate distortion, metric entropy, and the Poincar'e constant, thereby recovering and sharpening a range of existing diffusion-sampling guarantees, as well as giving new results. In log heat-time, the fine partition limit is governed by an integral involving the square root of the $\mathsf{DGC}$ density, whereas a single-block schedule depends on its ordinary integral. This comparison precisely characterizes when adaptation to data geometry yields substantial computational gains, including logarithmic-to-constant separations for simple Gaussian mixture models.

We introduce RELTA-SGLD, a taming scheme that stabilizes superlinear stochastic-gradient updates while reducing unnecessary suppression of the original learning drift. A threshold determines where the taming turns on, while a relative-growth principle derived from the one-step Lyapunov stability condition determines the required taming strength. Together, they produce a lighter $λ$-scale denominator and preserve a nonvanishing far-tail return. As a consequence, we prove polynomial moment stability and first-order stationary accuracy in both $W_1$ and $W_2$ for nonconvex SGLD with superlinearly growing stochastic-gradient oracles, improving the corresponding half-order and quarter-order bounds for comparable stochastic-gradient tamed schemes. On Fashion-MNIST under active stabilization pressure, RELTA improves the mean learning metrics over both untamed SGLD and TUSLA and remains competitive with a tuned AdamW reference. In an ordinary-training regime, its lighter localized denominator reduces unnecessary perturbation of the original update and maintains nearly untamed learning dynamics.

We introduce \emph{gate-zero growth}, a function-preserving (FP) operator for continual learning that adds new residual blocks through a zero-initialised gate. Under a transversality condition, gate-zero growth induces \emph{rank separation} in the functional Jacobian: old directions are unchanged, new-weight directions are exactly flat at the growth point, and new gate directions are the only first-order source of new functional variation. As gates open during continual learning, function drift is $O(\|\boldsymbolα\|^2)$ and Jacobian leakage $O(\|\boldsymbolα\|_\infty)$, giving a controlled departure from the FP locus. On a $300\mathrm{M}\to857\mathrm{M}$ Transformer adapted from WikiText-103 to BookCorpus, gate-zero growth reaches near-zero old-domain forgetting ($Δ_A < 0.1$) under both exact-preservation (Isolation) and joint-frontier (Freeze-Nothing) operating points, while a non-FP control ($G_{\text{stack}}$) suffers an order-of-magnitude larger forgetting under the same recipe. The same geometric analysis covers LoRA, ReZero, and zero-init adapter constructions, establishing gate-zero growth as the canonical instance of a shared local geometry that governs safe capacity activation in CL.

Key-value (KV) cache growth is a major bottleneck in autoregressive decoding, as memory and bandwidth scale linearly with context length. Existing KV eviction methods often rely on static heuristics or proxy scores, which poorly track future token utility and cause brittle eviction as relevance shifts. To address this, we introduce KVpop, which learns a fixed-budget KV eviction policy by directly supervising the keep-or-drop decision. The scorer is trained against a novel future-attention target, computed efficiently without materializing dense attention maps. We further introduce a delayed memory-based scorer that, uniquely among learned eviction methods, defers scoring for a fixed number of steps to exploit near-future context. On AIME and HMMT mathematical reasoning, KVpop retains 98% of full-attention performance on Qwen3-4B at 75% KV cache compression and 97% at 88% compression, consistently outperforming established eviction baselines. Qwen3-8B shows even stronger results, reaching near-full teacher performance. These results show that supervising eviction with future-attention signals cuts memory costs while maintaining quality.

Can the robot use a plate to cut a cake if no knife is available? Tool use greatly expands robot capabilities, but to use tools creatively beyond their intended functions, the robot faces the challenge of $\textit{open-world affordance grounding}$: select an open-category object to act as a tool and localize its specific region of action. To this end, we introduce GROW$^2$ (GROunding Which and Where), which leverages object parts as a natural abstraction to split the grounding process hierarchically into semantic and geometric levels, thus bypassing the need for data-heavy, end-to-end training. Semantically, GROW$^2$ harnesses the commonsense reasoning of Vision-Language Models (VLMs) to parse a natural-language task instruction, select a suitable object as the tool, and identify task-relevant parts on the tool and the target object. Geometrically, vision foundation models then ground the selected parts into precise 3D regions from a single RGB-D image. Experiments on established benchmarks show that GROW$^2$ outperforms state-of-the-art baselines on affordance prediction benchmarks. Further, it achieves zero-shot generalization over open-category objects and outperforms baselines in both simulated and real-world robot tool use experiments.

AI coding agents dramatically accelerate implementation speed but introduce two structural failure modes that existing spec-driven approaches do not fully solve: (1) context explosion -- the agent must reason over an entire repository at once, degrading output quality as the context window fills; and (2) silent spec-code drift -- code evolves, the specification does not, and the divergence becomes invisible until it is costly to repair. We present the Spec Growth Engine, a lightweight framework that addresses both failure modes through a machine-readable spec graph whose nodes carry explicit contract/design separation, a Spine context assembler that scopes agent context to an ownership path, a vertical-slice growth protocol that enforces hardest-first ordering, and a drift gate that makes spec-code divergence a blocking merge condition. The design synthesises well-established software engineering principles (Parnas information hiding, C4, ADRs, Walking Skeleton, Reflexion Models, Fitness Functions) into a lean, code-coupled, machine-enforced whole -- without the overhead of heavy-weight frameworks such as RUP or MDA.

Social-physical human-robot interaction (spHRI) has grown rapidly across robotics, human-computer interaction, human-robot interaction, and haptics. Yet, fragmented terminology and inconsistent methodologies make systematic synthesis difficult. To support scalable review practices, we evaluated the extent to which small language models (SLMs; < 1.5B parameters) can assist with title and abstract screening for a large spHRI systematic review. While no SLMs matched human reviewers' performance, the models operated locally and screened papers orders of magnitude faster. The combined SLM ensemble identified 39 papers reviewers missed, representing 10.29% of the final relevant dataset. These results demonstrate that SLMs can augment, rather than replace, expert reviewers and make large-scale literature reviews accessible and sustainable.

Diffusion models have become a promising alternative to autoregressive models. Among these, uniform diffusion language models (UDLMs) permit any token to be updated at any step, in principle enabling more flexible generation. However, no UDLM has yet been pretrained from scratch at both large parameter scale and large token budget. Both autoregressive modeling and masked diffusion modeling already have capable models at scale that the community can study and build on; uniform diffusion has none. A scratch-pretrained UDLM at scale would provide a clean reference point for studying scaling behavior, generation dynamics, controllability, and trade-offs against established autoregressive and masked diffusion models. To this end, we introduce Sumi ("ink" in Japanese), a fully open 7B uniform diffusion language model pretrained from scratch on 1.5T tokens. Sumi performs competitively with autoregressive models trained at comparable token budgets on knowledge, reasoning, and coding benchmarks, while under-performing on commonsense benchmarks, where our education-heavy data mixture is a likely contributor. We release our model weights, checkpoints, and full training recipe, including a complete specification of the data mixture over publicly available corpora. We hope this release enables the community to study native uniform diffusion at scale and catalyzes work on its as-yet poorly understood aspects.

We introduce a new simple model to study the fitness progress of Evolution Strategies (ES) in generic problems. In this model, we bypass the underlying fitness landscape and assume that the mutation of any individual produces an offspring whose fitness relative to the parent is given by an invariant distribution $Z$, such as a mean-shifted Gaussian. This serves as a prototypical model for the optimisation landscape when an evolution algorithm operates far from the global optimum. This simple model can be used to approximate the optimisation process for problems where it is intractable to model the exact fitness function, including tasks such as hyperparameter tuning in machine learning models. We rigorously analyse the expected growth rate $\mathcal{R}_μ$ of the continuous steady-state $(μ+1)$-ES in this model. Unlike comma-selection strategies, the steady-state $(μ+1)$-ES maintains overlapping generations, introducing complex mathematical dependencies among surviving parents that make it harder to analyse. We give a general technique to analyse the the $(μ+ 1)$-ES by constructing modified processes whose growth rates provably sandwich that of the original process. These modified processes are then easier to analyse but still close enough to the true process to give a tight bound on the expected growth rate. When $Z = \mathcal{N}(-δ, 1)$ and $μ\le e^δ$, we show that $\mathcal{R}_μ = \frac{\log^{1 + o(1)} μ}μ \mathcal{R}_1$.

We propose that value -- the quantity goal-directed agents create, destroy, and exchange -- is a lawful structural quantity in the same category as information. Following Shannon's method, we make one ruthless abstraction: value is the rate at which an agent converts a resource into goal-progress, relative to a frame fixed by its goal. A scale-invariance axiom forces a logarithmic measure, $V=\sum_i k_i\ln e_i$; compounding of a reinvested resource forces the same form via the ergodicity argument of Peters (2019) -- kin routes, a consistency check, not an over-determination. We derive a coding theorem of value, $ΔG \le I(X;Y)$; realized value decomposes as $G=D(q\|r)-D(q\|p)$. For populations, value is frame-relative while price is frame-independent; a fleet that pools its resource and fuses its perception inherits the ceiling $G_{\rm fleet}\le I(X;Y_{1:m})\le H(X)$ (a corollary; an earlier sum-form claim was wrong and is corrected in v5). A dynamical layer yields an is/ought asymmetry from which alignment emerges as a control-stability condition. We test the single-frame laws on live language models, pre-registered: perception mutual information tracks realized capability (Spearman $ρ=0.977$ over 30 model$\times$domain points); out-of-sample $ΔG$ tracks $I(X;Y)$, shape-invariant across four task shapes ($n=42$, slope $0.953$); over-confidence is measurable dissipation. The stated continuation gate has since been run (pre-registered, frontier-model population): the coupled capacity-region prediction -- growth-gap law, coalition submodularity with an XOR synergy control, joint ceiling, Kelly selection -- is confirmed within its frozen bands on real agents; the mean-field residual law $\|Vg\|/γ$ found no domain (populations hold no goal dispersion) and is retired to its mathematical scope. The contribution is the unification and the governance mapping that follows.

Precision agriculture requires the estimation of plant growth stages in real-time. When the plant growth stage is known, the wastage of resources in cultivation, such as nutrients and water, is reduced as only the required resources need to be supplied. Plants at different growth stages, however, have similar morphological features, which can make autonomous growth stage estimation difficult. This paper presents two feature extraction methods for growth stage estimation: one that uses a bank of Gabor filters and morphological operations, and the other that uses pre-trained convolutional neural networks (CNNs) and transfer learning. We test these methods on a publicly available plant growth stage dataset (bccr-segset) for two species, canola and radish, grown and captured under indoor conditions. The two proposed feature extraction methods are compared, using support vector machines and boosted trees as classifiers. We find that both methods are suitable for real-time applications, and that CNN features outperform the hand-crafted features, both with regard to speed and accuracy. The best system (VGG-19 features, classified with a radial basis function support vector machine) obtained an accuracy of 98.4% for both species, processing an image in 0.08 seconds.

The spatiotemporal evolution of many physical, chemical, and biological systems is described by nonlinear partial differential equations (PDEs). Recently, deep neural network-based surrogate models have emerged as efficient alternatives to computationally expensive numerical PDE solvers. In this work, we propose a physics-constrained deep neural network as a surrogate model to learn the microstructural evolution of a binary mixture, in which conservation of the order parameter is imposed directly on the network output as a hard constraint. We train the model to accurately predict the time-evolution of phase separation in binary mixtures governed by the Cahn-Hilliard equation. We show that predictions from our trained surrogate model remain stable and accurate over long-time rollouts for both critical and off-critical mixtures and preserve the mixture composition throughout evolution. In contrast, a variant in which conservation is enforced only via a penalty term in the loss function drifts away from the initial composition and significantly loses predictive accuracy over the same rollout. This establishes that the hard constraint is essential for long-time stability and order parameter conservation. We also show that our model accurately captures the growth of domain size and is consistent with the Lifshitz-Slyozov domain-growth law. These results demonstrate the effectiveness of the proposed framework for modeling systems with conserved kinetics, and the construction extends directly to other systems with conserved quantities.

Large language model (LLM) "answer engines" such as ChatGPT now send measurable referral traffic to the open web, and a practice analogous to search engine optimization, here called Answer Engine Optimization (AEO), has emerged. Public AEO success stories typically quote large raw growth multiples, but raw referral growth is confounded by the rapid platform-level growth of the answer engines themselves. We report a longitudinal field study on a single high-traffic domain (glasp.co) whose corpus of hundreds of thousands of YouTube question-and-answer pages received a defined bundle of AEO interventions in January 2026 (detailed in Section 4). Because the interventions were concentrated on one subset of the site, the untreated remainder of the same domain acts as a contemporaneous control that absorbs the platform tailwind. Using first-party analytics and server logs rather than probabilistic third-party estimators, we find: (1) raw growth is dominated by the platform tailwind: on monthly aggregates total ChatGPT referrals grew 5.7x while untreated pages on the same domain grew 3.5x over the same window; (2) an interrupted time-series model on the weekly treated/control ratio estimates a discrete, intervention-aligned level increase of 1.82x (95% CI 1.31-2.54, HAC p=0.001), robust across engagement-filtered traffic (2.27x) and alternative specifications; (3) however, a conservative placebo-in-time permutation test yields p=0.16, so the effect is suggestive, not conclusive, given a short and noisy pre-period; and (4) Google organic clicks to treated pages did not fall beyond the ambient site-wide trend and indexation was preserved, consistent with the SEO-protection rule. The methodological message, separating treatment from platform tailwind with an on-domain control, matters more than any single multiple, and implies that headline AEO multiples substantially overstate causal effect.

The parameter counts of the most widely used large language models (LLMs) are often withheld by their developers, leaving model size -- a primary reference point for interpreting capabilities and costs -- largely undisclosed. We propose a black-box method to infer conservative lower bounds on LLM size from generated text outputs alone, requiring nothing beyond the ability to submit text fragments and observe next-token predictions. Our approach is grounded in a key observation: popular, widely-circulated texts -- such as classical literature, religious texts, and foundational documents -- are present in virtually every large-scale pretraining corpus, and how accurately a model predicts the next word across text fragments of varying length is a reliable signal of how much it has memorized them, which in turn is fundamentally limited by its total parameter count. We aggregate this memorization signal across a diverse corpus of texts and fragment lengths into a single accuracy profile vector per model, and build two complementary inference methods on top of it: a pairwise statistical test that determines which of two models is larger, and a scaling-law estimator that extracts a one-dimensional latent index from these vectors via Principal Component Analysis (PCA) to map the aggregated signal to a parameter count. Validated on a broad set of open-weight models, both methods produce accurate and reliable lower bounds. When applied to popular closed-weight models, our framework recovers internal product hierarchies and reveals a clear divergence in industry scaling strategies: while some developers yield significantly higher bounds indicative of large generational parameter growth, others operate under strict parameter ceilings, demonstrating that hidden design choices can be systematically probed even under strict API limitations.

The fastest-growing data in production today is unstructured text: agent traces, chat logs, reasoning chains, model outputs. People want to analyze it, and the questions worth asking ("show me where the agent got confused") cannot be answered by SQL alone, since text is not queryable without a model in the query path. The natural place this analysis is happening is the new class of AI applications (Claude Code, Cursor, Claude Desktop, in-browser agents) that run client-side and host both a human user and an LLM agent in the same process. These applications increasingly want to work with data, but the lakehouse read path has been hard to use from a JS runtime: Spark, Trino, and managed warehouses do not fit there. To build this new kind of AI data application, three properties of the engine become first-order: a JS-native distribution that drops into the runtime the application already runs in, a bundle small enough to ship inside a cold tab or per-turn agent sandbox, and a way to interleave analytic operators with model-based interpretation of text. We present Hyperparam, three open-source JavaScript libraries (Hyparquet, Squirreling, Icebird) totaling under 70 KB, that read Parquet and Apache Iceberg directly from object storage and meet the third property with per-cell, async-native SQL execution, so expensive cells fire only when downstream operators demand them. Squirreling runs LLM-shaped async UDFs over 300x faster than DuckDB-WASM on filter-bounded queries (and 192x on sort-bounded queries) and completes a ten-task agent analyst suite at two-thirds lower cost. We argue that data engineering as a discipline needs to update for the AI-native client applications now in production and the agents that work alongside their users.

We study the sample complexity of policy gradient for log-growth control -- the problem of learning, from observed state transitions, a feedback gain that optimally stabilizes a scalar linear system driven through a multiplicative-noise actuation channel. The objective $J(K) = \mathbb{E}[\log|1+BK|]$ is the top Lyapunov exponent of the closed loop. This problem carries a structural difficulty we call the cusp obstruction: the optimal gain $K^*$ always places the noise singularity $b_{\rm sing}(K) = -1/K$ in the interior of the support. At this singular optimum the policy gradient exists only as a Cauchy principal value, not as a Lebesgue integral, and the natural single-sample gradient estimator has infinite variance. Standard first-order stochastic-optimization analysis is thus inapplicable at the optimum, and merely smoothing the objective does not resolve the difficulty. The obstruction, however, has an exploitable symmetry: the Cauchy kernel is an odd function of the displacement from the moving pole, so pairing each observation with its reflection through the pole cancels the divergent part. This one cancellation simultaneously controls the population curvature, the gradient-estimator variance, and the bias incurred when the noise density is estimated. Combining these bounds with a closed-form single-transition gradient oracle, we prove that projected mini-batch policy gradient, initialized in any compact subset of the stabilizing region, attains total sample complexity $\tilde{O}(1/η)$ when the noise density is known and $\tilde{O}(η^{-(2s+1)/(2s)})$ when it must be estimated, for $C^s$ noise densities with $s \geq 2$.

We investigate growth dynamics in deterministic equational discovery substrates. Across three toy domains (arithmetic, boolean, higher-order list; n=592 trajectories), short-range substrate sizes fit a power-law N(t) proportional to t^b. Within each substrate b is architecture-sensitive (cross-validated R^2 approximately 0.82); the regression does not transfer across substrates (arith+bool to list yields R^2 approximately -0.84). A heuristic mean-field closure model predicts a saturating power-law dN/dt = K N^k exp(-mu N) of which the pure power-law is the short-range approximation. Three robustness checks: bootstrap intervals on (k, mu) are tight in 4/5 toy trajectories and degenerate in 1/5; out-of-sample forecasting on toy data (fit first 100 epochs, predict next 400) is won by pure power-law 5/5, indicating the toy trajectories do not reach saturation; on two real-world growth proxies the result splits. New Mathlib/*.lean file additions per month (mathlib4, 60 months, 9701 files) support the saturating form on OOS forecasting by approximately 7x over pure power-law; Coq mathcomp monthly commits (129 months, 3083 commits) favour pure power-law on both tests with mu collapsing to zero. The dynamics are substrate-conditional at two levels: within-substrate architecture-to-b regressions do not transfer, and the preferred functional family for N(t) itself (pure vs. saturating power-law) differs by substrate. We propose "saturating power-law growth with substrate-conditional (k, mu), observable when the substrate has reached its saturation regime" as a working framing.

Standard deep-learning pipelines usually choose the network architecture before training and keep it fixed throughout optimization. In contrast, a model can also be adapted by editing its structure during training, for example by pruning existing hidden-neuron units or growing new ones. Although growth is appealing for adaptive and continual systems, we show that it is not simply the inverse of pruning. Pruning selects among units that have participated in training from the start, whereas growth inserts new units into an already specialized optimization trajectory. We isolate this insertion problem and show that newborn units are often forward-active but backward-starved: they participate in the forward computation, yet receive much weaker gradient signal than incumbent units. This disadvantage is minor in small MLP benchmarks, but becomes clear in harder image-classification settings with a convolutional trunk. In these settings, \textsc{Grow} can achieve high final accuracy during the structural-editing procedure, while \textsc{Prune} is stronger when performance is averaged over the training trajectory or when the final sparse network is retrained from scratch. Interventions targeting optimizer state, insertion, selection, and trainability show that improving the integration of newborn units can improve adaptive performance, but does not automatically produce better final subnetworks. In continual-learning benchmarks stressing plasticity loss, \textsc{Grow} becomes competitive mainly when new units have enough time to integrate. Together, these results suggest that \textsc{Grow} should be evaluated not only as an architecture-search operator, but as a time-sensitive optimization process whose success depends on insertion stability.

Model growth from a given checkpoint aims to accelerate training of a larger model, offering potential resource savings. Despite recent interest, warmstarting has seen limited practical adoption in large-scale training. We attribute this to two underexplored factors: (1) an overemphasis on preserving the smaller model's performance at initialization, which constrains operator design for new architectures, and (2) insufficient analysis of how growth interacts with hyperparameters and scaling behavior, compounded by inconsistent growth factors across the literature. We show that preserving the base model's initial post-growth performance is not necessary for strong final performance, and that simple, architecture-agnostic growth strategies can outperform more complex warmstarting operators. Crucially, we empirically identify an upper bound on the growth factor $g$ beyond which training from scratch is more efficient. We observe this across multiple ablation setups. Notably, this limit is also present, but unreported, in prior published results. Across our experiments on dense MLPs and dense language models, we find that a $2\times$ growth factor is the most reliable in yielding convergence speedups, with gains most pronounced under 20 tokens/parameter budgets and diminishing as budget increases. We fit scaling laws over these observations to provide predictive guidance for practitioners deciding when and how much to grow. Together, our analysis provides practical guidelines and empirical limits for model growth.

We study the evolution of hidden-weight spectra in wide neural networks trained by (stochastic) gradient descent. We develop a two-level dynamical mean-field theory (DMFT) that jointly tracks bulk and outlier spectral dynamics for spiked ensembles whose spike directions remain statistically dependent on the random bulk. We apply this framework to two settings: (1) infinite-width nonlinear networks in mean-field/$μ$P scaling and (2) deep linear networks in the proportional high-dimensional limit, where width, input dimension, and sample size diverge with fixed ratios. Our theory predicts how outliers evolve with training time, width, output scale, and initialization variance. In deep linear networks, $μ$P yields width-consistent outlier dynamics and hyperparameter transfer, including width-stable growth of the leading NTK mode toward the edge of stability (EoS). In contrast, NTK parameterization exhibits strongly width-dependent outlier dynamics, despite converging to a stable large-width limit. We show that this bulk+outlier picture is descriptive of simple tasks with small output channels, but that tasks involving large numbers of outputs (ImageNet classification or GPT language modeling) are better described by a restructuring of the spectral bulk. We develop a toy model with extensive output channels that recapitulates this phenomenon and show that edge of the spectrum still converges for sufficiently wide networks.

Sign languages, of any geographical or accentual variation, understandably face continuous scrutiny under the ever present popularity of verbal dictation and audism. Through this, many potential problems arise with the current lack of accessible communication for those who rely on such sign languages for essential conversation. Such AI systems regularly take the form of recognition and interpretation models, designed to provide seamless and accurate translation. In reality these systems are built from biased data and created without any input from deaf communities. Such models are widely used and accepted by their hearing counterparts who remain ignorant to the inherent culture, semantics and colloquial language present in gestural language systems. This phenomenon is best analysed under the scope of The Technological System and Technological bluff by Ellul. Indeed, what is at play here is the standardization of language by technicians into what can be captured by technique: data, statistics, a mathematical language. For that AI technique to exist, sign language must be rationalized, in a search for profit that annihilates the conditions for communication and fails to capture the human experience of the deaf person. By that process, it presents normative effects, creating a model of Man, standardized, massified, and who has to adapt to the tool and technical milieu instead of the other way around, which we assume should have been the goal of such a technology. Technique thus reshapes what it means to be human, to submit deaf people to the goals of productivity and efficiency. In doing so, it exhibits clear counter productivity, alienating instead of emancipating, isolating instead of nourishing human relationships. Therefore this paper argues for the idea of AI as Ableist Intelligence, as such systems seek to emphasise the humiliated and marginalised nature of sign.

We present an efficient algorithm for uniformly sampling from an arbitrary compact body $\mathcal{X} \subset \mathbb{R}^n$ from a warm start under isoperimetry and a natural volume growth condition. Our result provides a substantial common generalization of known results for convex bodies and star-shaped bodies. The complexity of the algorithm is polynomial in the dimension, the Poincaré constant of the uniform distribution on $\mathcal{X}$ and the volume growth constant of the set $\mathcal{X}$.