Papers

Group relative policy optimization (GRPO) learns only from prompts whose sampled responses disagree: a group that is entirely correct or entirely incorrect has zero reward variance, contributes no gradient, and still consumes its rollouts. Prompt-selection methods reduce this waste by steering sampling toward intermediate pass rates, but they choose the target, its width, and the uncertainty model heuristically, in raw pass-rate or logit coordinates. We show that GRPO comes with a natural coordinate for pass rates: the arc length $\psi=\arcsin\sqrt{p}$ on the Bernoulli Fisher–Rao manifold. In arc length, the expected GRPO update is uniform up to two boundary ramps; the probability of a zero-variance group is bounded by two Gaussian boundary layers of width $1/\sqrt{2G}$; pass-rate evidence has constant noise; and the gradients of the pass@$k$ and pass$^k$ objectives are Gaussians whose center and width follow from $k$ in closed form. A prompt curriculum for GRPO is therefore a Gaussian in arc length, and choosing its center amounts to choosing the objective. We turn this observation into ARCUS, a drop-in sampler that tracks every prompt with a Kalman filter in arc length, scores prompts by an objective-matched Gaussian kernel times the predicted probability of an informative group, keeps only informative groups for the unchanged GRPO update, and paces the target toward the hardest objective whose predicted yield stays within a small slack of the best. Across six mathematical reasoning benchmarks and three backbones, ARCUS improves the average accuracy of GRPO by 2.8–2.9 points and that of dynamic sampling by 1.1–1.2 points, while generating 48–57% fewer rollouts than dynamic sampling.

Modern machine learning systems are trained on mixtures of data from different domains, and choosing the right mixture can substantially improve downstream performance. Despite an extensive literature on data mixing and reweighting, existing work is largely empirical and it remains unclear when auxiliary data genuinely improves scaling laws rather than merely providing more samples. To gain insight into this question, we study a high-dimensional mixed-data regression model with a shared regression function, heterogeneous covariances and noise levels, and dataset sizes that may grow at different rates. We establish the minimax risk under an ellipsoidal parameter constraint for the general covariance structure and derive deterministic equivalents for the test error of ridge regression under commutative covariances. We then specialize to a target domain and an auxiliary domain with aligned power-law covariance spectra, where the theory yields explicit scaling laws in terms of spectral decay, target regularity, and the relative growth of the two datasets. These laws identify regimes in which combining data mixtures provably yields a faster scaling rate than using either dataset alone. In particular, improving the scaling law requires a specific interplay between spectra and relative sample sizes of the domains. Our numerical experiments on language models exhibit the same qualitative phenomenon: appropriate data mixtures yield a faster decrease in target-domain test loss than training on either domain alone.

Time series anomaly detection (TSAD) plays a crucial role in healthcare, finance, industrial monitoring, and other sectors. Within and between these settings, anomalies span vastly different temporal scales, from sub-second point spikes to multi-hour drift patterns. However, most existing TSAD methods commit to a single temporal granularity, and multi-scale designs either analyze different scales in isolation or are constrained to a predefined coarse-to-fine hierarchy, both failing to sufficiently capture multi-scale interactions. To resolve this limitation, we propose Multi-Scale Autoencoder with Cross-Scale Attention for TSAD (MSCAD), a simple yet powerful semi-supervised TSAD framework founded on parallel autoencoder branches corresponding to different patch sizes. A stack of symmetric bidirectional cross-scale attention blocks enables every pair of scales to exchange information before reconstruction without allowing any single scale to be privileged. On the comprehensive TSB-AD benchmark (40 datasets, 530 series), MSCAD achieves large performance gains against 50 baselines across multiple metrics, with VUS-PR of 0.57(+9.6%) on the univariate split and 0.47(+9.3%) on the multivariate split compared to the state-of-the-art.

The classical information bottleneck (IB) measures the relevance of a representation $U$ of $X$ to a target $Y$ by $I(U;Y)$, which does not directly characterize the error of downstream decisions. For a binary hypothesis $Y$ inferred from many separately encoded observations, the optimal error exponent is the Chernoff information between the two conditional distributions of $U$ given $Y$. We study the mutual information constrained Chernoff bottleneck, which seeks an encoder that maximizes this Chernoff information subject to a rate constraint $I(U;X) \leq R$. We show that its optimal value $C(R)$ increases strictly up to $R = H(V)$, where $V$ merges the symbols of $X$ with equal likelihood ratio, remains at the uncompressed exponent beyond, and, unlike the IB curve, need not be concave. We further show that $k+1$ outputs suffice to attain $C(R)$, where $k$ is the cardinality of $V$. We propose an alternating algorithm that updates the encoder via a generalized Blahut–Arimoto algorithm and the Chernoff parameter $s$ via a nonlinear equation, and prove that its iterates remain feasible, with nondecreasing and convergent Chernoff information. Numerical experiments confirm the theory, and on real topic-detection data from the 20 Newsgroups corpus, compressing each word to only $17\%$ of its entropy retains $90\%$ of the error exponent and nearly the accuracy of the uncompressed classifier.

Tabular foundation models achieve strong zero-shot accuracy on structured data by pretraining on synthetic tables, but they ignore the column names, task descriptions, and auxiliary files that carry dataset semantics. Meanwhile, self-evolving machine learning engineering (MLE) agents train models from scratch on each dataset, yet jointly searching over features, architectures, and hyperparameters is noisy and prone to overfitting. We introduce TabFM-Auto, which pairs a tabular foundation model, TabFM, with a language model agent that evolves the data pipeline around it. Guided by dataset metadata and validation feedback, TabFM-Auto iteratively refines data cleaning, feature engineering, context selection, and post-processing to reduce TabFM's error. Across all 51 datasets of the TabArena benchmark, five TabFM-Auto configurations with different agents and language models take the top five overall positions, and the best raises TabFM from 1785 to 2013 Elo. The discovered pipelines also transfer to other frozen tabular foundation models (+69 to +143 Elo) with no further search. On the 8 tabular competitions of MLE-Bench, TabFM-Auto ranks first overall among MLE agents.

LLMs trained with Chain-of-thought excel in reasoning capability, but often come with excessive token cost. We find that the core of reasoning capacity lies in the Thinking model's weight component within the null space of a projection defined by the corresponding Non-thinking model's dominant singular directions, and removing the subspace component can largely improve reasoning efficiency without hurting the accuracy gained during thinking-mode post-training. Unlike existing efforts that mostly operate within the dominant subspace, we are the first to unveil the critical role of the null space and harness it for model optimization. Motivated by this finding, we propose Spectral Null-Space Swap ($S^3$), a training-free composition of paired Non-thinking and Thinking checkpoints. Our method keeps the Non-thinking model inside its own dominant subspace and takes the Thinking checkpoint outside it, improving reasoning efficiency while maintaining accuracy. We extensively evaluate $S^3$ on 2B-30B dense and mixture-of-experts (MoE) architectures spanning 28 evaluation environments across mathematical, multimodal, and audio reasoning domains. $S^3$ establishes new empirical Pareto Frontiers among training-free model composition strategies: across all settings, it reduces inference token overhead by an average of 27.4% compared to full Thinking models while simultaneously improving overall task accuracy by 1.0 percentage point (e.g., yielding +8.3% accuracy on HMMT25 alongside a 33.0% token speedup). We further use attention entropy for explanation and find that the retained component produces more concentrated attention, and we use a simplified analytical model about optimization to demonstrate why null-space can effectively reduce attention entropy, thereby improving the efficiency of reasoning.

Masked diffusion models (MDMs) generate text by unmasking several tokens per step, but they are trained and sampled under different conditions. The model is trained on randomly masked sequences, whereas inference follows a trajectory shaped by the model's own predictions. Additionally, each step has no access to what the previous one computed. Recent methods narrow these limitations from separate angles, leaving open how these choices interact. We introduce PUMBA, a unified framework for trajectory-aware training that trains the denoiser on consecutive steps of policy-induced trajectories, passes information between steps, and optimizes them jointly by backpropagation through time. A controlled study of this design space shows that i) exact train–inference alignment fails due to local overfitting, whereas a looser alignment still brings training masks closer to those seen at inference; ii) passing continuous information outperforms discrete gradient estimators through the commitment at each step; and iii) performance improves as backpropagation through time spans more steps, which we support theoretically. Combined, these components match the best checkpoint of a same-size autoregressive model. Building on these findings, we scale PUMBA to supervised fine-tuning of LLaDA-8B, where it improves the trade-off between performance and number of function evaluations (NFEs) in both full-canvas and block diffusion generation. At matched performance, it needs up to 22% fewer NFEs than standard fine-tuning with twice the budget in full-canvas generation, and up to 26% fewer than standard fine-tuning for the same number of steps in block diffusion.

As Graph Neural Networks (GNNs) are widely deployed as Machine Learning-as-a-Service (MLaaS) APIs, model stealing attacks have emerged as a critical security threat. By querying a victim model's black-box API, an adversary can construct a functionally equivalent surrogate model, compromising proprietary intellectual property and downstream security. Existing GNN stealing attacks, however, rely on overly permissive assumptions, such as soft-label outputs, large query budgets, full-graph query access, and prior knowledge of victim backbones that rarely hold in real-world deployments. In this work, we formalize a strictly constrained black-box, hard-label and backbone-agnostic threat model for GNN stealing attacks under a tight query budget. Given these realistic restrictions, we identify four fundamental challenges: sparse local structures and isolated nodes that degrade victim label quality, insufficient supervision signals, systematic imbalance with incomplete class coverage, and backbone mismatch. To address these interlocking barriers, we propose Dagger, a novel two-phase decoupling-based attack framework. Specifically, in Phase 1, Dagger pre-trains a surrogate using decoupled information propagation to preserve structural context over sparse local subgraphs while handling isolated nodes, combined with manifold-level node mixup to synthesize continuous supervision signals and smooth decision boundaries. In Phase 2, Dagger freezes the encoder and fine-tunes the classifier head via class-balanced sampling paired with logit adjustment to rectify severe query imbalance without requiring extra victim queries. Extensive experiments across four benchmark graphs and four GNN backbones demonstrate that Dagger consistently outperforms state-of-the-art GNN stealing attacks, achieving up to 18.16% higher fidelity while only utilizing 12.23$\times$ fewer queries than the strongest baseline.

Advances in the coding capabilities of LLM agents allow them to inspect and modify their own instructions, tools, and execution procedures. Existing approaches use this ability to search for improved agents through repeated downstream evaluation, which incurs substantial costs and ties the search to the evaluated tasks. We introduce SelfSearch, a reward-free search procedure in which agents modify themselves using records of previous self-improvement episodes. These records capture the reasoning, tool actions, and outcomes of earlier modification attempts, providing concrete experience for improving both task solving and self-modification. Without downstream reward signals during search, SelfSearch improves population-mean success over the initial agent in all six model–benchmark settings, with individual agents gaining up to 11.2 percentage points on Terminal-Bench 2.1. On SWE-bench Multilingual, an agent improves success by 5.0 percentage points while reducing execution cost by 38.5% on tasks solved by both the initial and evolved agents. SelfSearch achieves competitive task success with evaluation-guided search baselines at lower search cost. With only \$4.03 in search cost, it produces a harness that solves 82.0% of Terminal-Bench 2.1 tasks with DeepSeek V4 Flash under the settings of a public nine-harness comparison, matching the top-scoring harness, Codex. These results suggest that experience gained through self-modification can improve agents' downstream capabilities and efficiency.

Tabular machine learning typically relies on per-dataset workflows, fitting tree ensembles or running AutoML searches from scratch for every task. We present TabFM, a 400M-parameter tabular foundation model that formulates supervised tabular prediction as in-context learning. TabFM produces calibrated zero-shot predictions in a single forward pass without task-specific tuning. Trained entirely on synthetic tables generated from structural causal models, TabFM learns general tabular representations that transfer zero-shot to real-world tasks. Across all 51 benchmark datasets in TabArena (38 classification and 13 regression), zero-shot TabFM ranks first among default tabular foundation models and outperforms tuned AutoML pipelines. Two extensions over the same frozen weights improve performance further on both tracks: multi-view feature expansion with ensembling and post-hoc calibration (TabFM+), and LLM-guided, dataset-specific data processing and feature engineering (TabFM-Auto).

As the input dimension $n$ grows, rule-based machine learning, such as Learning Classifier Systems (LCSs), faces a fundamental scalability bottleneck for function approximation: both rule count and parameter count grow exponentially with $n$. Traditional LCSs partition the $n$-dimensional input space directly, requiring $\mathcal{O}(m^n)$ rules for adequate coverage, where $m$ is the per-variable resolution. This article breaks from this paradigm by reorganizing rules dimension-wise, guided by the Kolmogorov-Arnold representation theorem: any continuous $n$-dimensional function can be expressed as a finite superposition of one-dimensional functions. The proposed Kolmogorov-Arnold Classifier System (KACS) decomposes the target function into one-dimensional subproblems and assigns a dedicated ruleset to each, reducing the worst-case rule count from $\mathcal{O}(m^n)$ to $\mathcal{O}(mn^2)$ and replacing $n$-dimensional local models with one-dimensional models requiring only two parameters per rule, independent of $n$. We also provide the first constructive proof that an LCS, namely KACS, is a universal approximator for continuous functions on compact domains. Evaluated against a direct $n$-dimensional input space partitioning approach under otherwise identical conditions, KACS achieves competitive accuracy in many settings while using only 2% to 40% of the parameters. Our implementation is available at https://github.com/YNU-NakataLab/KACS.

Replacing a visible advertisement in a broadcast frame is geometrically straightforward but photometrically delicate. A pasted graphic can have the correct perspective and still appear detached when its brightness, shading, or shadow disagrees with the surface beneath it. This paper presents Ad-Relight, an inference-only procedure for transferring scene illumination to a supplied advertising graphic without collecting a banner-specific training set. The procedure first separates slowly varying shade from graphic structure, then probes a pretrained diffusion relighter with two nearly identical backgrounds to isolate the contribution of the target region. A final pass combines this residual with a smoothed luminance field and a soft attenuation mask. Across 560 generated placements, the approach improves structural similarity, perceptual distance, and illumination agreement over geometric compositing and direct relighting baselines. Human judgments and an automated preference study show the clearest gains on floor-mounted graphics with nonuniform lighting. The current study is image based; temporal stabilization remains an open extension.

A wide range of methods have been proposed, including physics-informed neural networks, which are powerful but do not guarantee identifiability of the dynamics, symbolic regression, which requires a set of precomputed operations, and causal discovery, which is more principled but usually relies on strong assumptions that physical systems may violate. In this work, we develop a theory-grounded method and prove that under a set of permissive assumptions, the structural drivers and drift of stochastic delayed differential equations are identifiable. Our method outperforms others on a benchmark for driver identifiability, and on a second benchmark to evaluate physical consistency of the learned dynamics.

This study provides a data-driven analysis of a novel dataset of single-cell Anion Exchange Membrane water electrolyzers (AEMWE), operated under constant current load across multiple heterogeneous experimental campaigns. We train and evaluate a range of machine learning models with different complexity, including linear baselines, LSTMs and CNNs, to perform medium-term forecasting of the cell voltage degradation curve. The models are assessed within a rigorous training and evaluation framework specifically designed for heterogeneous industrial data.

Deep Support Vector Data Description (Deep SVDD) has become a prominent framework for unsupervised anomaly detection by learning latent representations that compactly characterize normal data around a center. Despite its empirical success, anomaly decisions produced by Deep SVDD are typically made solely based on anomaly scores without rigorous statistical guarantees, thereby limiting their reliability in safety-critical and high-stakes applications where false positives must be strictly controlled. In this paper, we propose PADI (Post-Anomaly Detection Inference), a novel framework that equips a trained and frozen Deep SVDD detector with statistically valid inference by leveraging the Selective Inference framework. Specifically, PADI performs inference conditional on the event that a test instance is identified as anomalous by Deep SVDD, thereby enabling rigorous statistical assessment of anomaly decisions. Based on this formulation, we derive valid selective p-values that quantify the statistical significance of the detected anomaly. Using these p-values, we theoretically establish control of the false positive rate (FPR) at a user-specified significance level $\alpha$ (e.g., $\alpha=0.05$). Furthermore, we extend the proposed framework to Deep Semi-Supervised Anomaly Detection (Deep SAD), providing a principled approach for statistically reliable inference in semi-supervised anomaly detection settings. Extensive experiments on both synthetic and real-world benchmark datasets robustly support the theoretical findings. The results demonstrate that PADI consistently achieves proper FPR control while attaining superior true positive rates compared with existing approaches.

Systems operating in dynamic environments require timely updates to sustain performance. For resource-intensive systems such as machine learning models and digital twins, strategically timing updates is essential. Updating too frequently wastes resources, while updating too infrequently leads to costly performance degradation. The problem is particularly challenging when the system's degradation pattern is unknown a priori, as is common in new operating environments. We formalize this challenge as a novel timing bandit problem, where each arm represents a candidate update interval with a fixed update cost and an unknown, stochastic degradation cost. Three structural properties distinguish this setting from standard multi-armed bandits: selecting an interval commits the learner to multiple time slots before the next update; arm costs are composed of per-step degradation costs and a fixed update cost; and selecting a longer interval naturally reveals degradation at every intermediate step, providing consecutive feedback relevant to shorter intervals. By exploiting these structures, we develop Balanced Consecutive Arm Elimination (BCAE). BCAE achieves $\tilde{O}(\sqrt{T})$ regret, improving upon the $\tilde{\Omega}(K\sqrt{T})$ regret of standard bandit algorithms in this setting, where $K$ is the number of candidate update intervals. We further propose an Optimism-Enhanced variant (OE-BCAE) that integrates lower-confidence-bound principles to improve empirical adaptivity while preserving the same regret order. Moreover, the regret bound achieved by our algorithms matches the theoretical lower bound up to logarithmic factors. Simulation results demonstrate that our algorithms achieve low regret and remain stable as both the number of arms and the update cost vary.

Persistent textual memory allows language models to carry information across long interactions, but learning what to remember is fundamentally a credit-assignment problem. A memory rewrite may only become useful many steps later, while much of the observed utility may be inherited from information already stored before the rewrite. We introduce Memory Gain Policy Optimization (MGPO), which isolates the incremental value of each memory rewrite by crediting it for its marginal contribution to current and future downstream utility. This turns delayed memory utility into a direct learning signal for optimizing what information should persist. We study MGPO on document-level information extraction, where structured supervision makes the effects of individual memory updates directly measurable. MGPO improves extraction while reducing average memory length by nearly 80% relative to the initial memory policy before optimization. The learned memory policy also supports reuse and transfer across domains, downstream models without further training. These results show that effective memory learning depends not only on preserving useful information, but on identifying which memory updates create lasting incremental value.

Recent work on anchored diffusion language models improves denoising by shaping an intermediate latent space with supervised important-token targets. In this work, we introduce time-based (self-supervised) anchoring, which learns and reuses latent anchors without requiring such targets. Our key observation is that anchors encode persistent properties of the clean sequence, such as its semantic intent, global structure, or intermediate plan. Although their hidden representations become stale as the token canvas evolves, their semantic content remains useful across nearby diffusion times. This is implemented through a two-stage architecture consisting of a relatively expensive anchor network that generates the latent cache state and a lightweight denoising network that intelligently combines the cached latent state with the current state at each reverse step using a fusion module. This gives anchoring a latent-space caching interpretation: the anchor network is evaluated periodically, while its cached representation is reused across multiple reverse steps. We instantiate this framework as TADM:Post-train, which time-anchorizes pretrained DLMs, and TADM:Pretraining, which learns time-based anchors during pretraining. Applied to DiffusionGemma-26B, TADM:Post-train improves throughput by approximately 49% to 79% on several math, code, and STEM benchmarks (GSM8K, AIME26, GPQA-Diamond, LiveCodeBench-v6, HumanEval, MMLU-Pro). TADM:Pretraining reduces Transformer-layer computation by up to 38% relative to a standard single-stage DLM, achieves up to 73% higher measured throughput than ADLM.

What are the inductive biases of a Transformer architecture? Existing theory on how the forward pass shapes representations either considers whether Transformers escape from rank collapse or demonstrates that self-attention drives tokens toward cluster patterns. The latter view arises from an elegant dynamical systems perspective, but relies on simplified architectural assumptions, and does not explain the rich structures observed in practice. This leaves a major open question: when a full Transformer escapes rank collapse, how does it structure token representations? Using pattern-formation theory, we show that the dynamical view of Transformers can account for Positional Encoding, Multi-Head Attention, and Output-Value geometry. We demonstrate that a full Transformer architecture imposes an inductive prior by selectively amplifying a rich set of previously unreported patterns, including traveling or rotating waves among others. We characterize the role of each architectural component in controlling which pattern is amplified, which ones stabilize, compete, or coexist. Finally, we show that these structures can act as a controllable dynamical prior that facilitates learning. By choosing both task-aligned positional encoding and weight initialization, we demonstrate improved data efficiency and accelerated optimization on controlled sequence tasks and with ConViT on CIFAR-10.

Reasoning across videos requires aligning events, matching identities, comparing motion, and integrating partial observations. Evaluating these capabilities and testing how to improve them requires both reliable labels and targeted supervision. We introduce SYNCR, a simulator-grounded framework that connects these two needs through shared task generators. Built on Habitat, Kubric, and CLEVRER, SYNCR derives answers from environment state and provides 4,000 evaluation questions and 15,960 training questions over disjoint videos, spanning eight cross-video reasoning tasks. Visual ablations and human evaluation assess dependence on the supplied evidence and answer recoverability. Evaluation of 22 multimodal large language models reveals persistent difficulties in physical comparison and scene integration that increasing model size does not consistently resolve. Supervised fine-tuning raises Qwen3-VL-8B's average SYNCR accuracy from 32.6% to 61.6%, with gains extending to task configurations and video sources absent from training for those tasks. Transfer to real footage is most consistent for temporal ordering: accuracy improves by 9.0-20.5 percentage points on constructed Assembly101 and Panoptic ordering sets across three checkpoints spanning two model families and two model sizes, with additional gains on existing temporal reasoning benchmarks. These results establish SYNCR as a controlled setting for diagnosing cross-video reasoning failures, testing their learnability, and identifying where synthetic supervision transfers.

Projection pursuit searches for a direction along which the data look least Gaussian. When the observation space contains a large Gaussian complement, the empirical objective can be minimized by a direction that carries no signal, with empirical kurtosis as low as at the truth. Sample splitting exposes rather than repairs this failure. Appending coordinates independent of the latent regime degrades the search while leaving Bayes recoverability unchanged. Restricting the search to the column space of a known forward operator removes the failure exactly on the negative-kurtosis branch. Estimating a principal subspace from the data is the alternative. In a controlled two-component model, the leading sufficient scalings differ in the gain with which the operator transmits the discriminant: $\varsigma^{-4}$ for covariance-spike estimation and $\varsigma^{-8}$ for fourth-moment search. At fixed search dimension, the measured threshold ratio collapses onto $n/p^2$ with exponent $0.156$, close to the predicted $1/8$. This is an empirically supported scaling motivated by sufficient bounds, not a proved asymptotically tight law. When the search dimension is varied, the measured exponent is $0.325$, substantially larger than $1/8$, and the tested range does not identify its functional form. The crossing location also depends on calibration and model configuration. Under a downstream excess-error criterion, the scaling largely disappears.

On-policy self-distillation (OPSD) trains a student to match a privileged teacher distribution along its own sampled trajectory. Standard OPSD applies this supervision to unverified student rollouts while conditioning the teacher on privileged context, typically a reference solution. We separate these roles in a factorial analysis and find that scaffold correctness has a stronger effect on downstream accuracy than context correctness. Unverified scaffolds create an imitation gap because the teacher can use information unavailable to the student. This gap shrinks with model scale, yet OPSD continues to supervise mostly unverified trajectories. In contrast, verified scaffolds remain effective even when the teacher is conditioned on the student's own unsuccessful rollout. Based on this finding, we introduce OASIS, which retains the OPSD objective but supervises mostly verified by label on-policy trajectories and replaces written solutions with unverified model-generated attempts as the teacher context. OASIS therefore requires only final-answer labels. Across Qwen3-1.7B, 4B, and 8B on AIME 2024, AIME 2025, and HMMT 2025, OASIS improves over the base model by 3.2–3.8 points on average, while OPSD's gain falls from 3.05 points at 1.7B to 0.14 at 8B. At 8B, OASIS improves over OPSD by 3.05 points, showing that verified on-policy scaffolds preserve the effectiveness of self-distillation as models scale.

Click-Through Rate prediction, a core task in recommendation and advertising systems, relies on modeling interactions among sparse categorical features. Explicit cross networks are a central paradigm for CTR prediction, and recent progress has largely come from increasing the interaction capacity of a single predictor through deeper cross networks and more expressive cross operators. We revisit whether continually increasing interaction capacity remains the most effective way to improve predictive performance, and find that its benefits quickly exhibit diminishing returns even as capacity continues to grow. This motivates a complementary scaling direction that we call estimator scaling, where additional resources are used to incorporate multiple related estimators rather than only enlarging a single predictor. Through theoretical analysis, we show that the gains from estimator scaling are governed by the amount of non-shared predictive variation available across estimators. However, exploiting this variation naively can be expensive: independently trained models provide substantial estimator diversity but require deployment cost to grow with ensemble size. This motivates a parameter-efficient realization of estimator scaling that can incorporate diversity from multiple estimator sources without maintaining multiple full models. Building on this view, we introduce RECursive Averaged Predictor (RECAP), a parameter-efficient recursive CTR model that operationalizes estimator scaling at three levels: distillation across independently trained models, exponential moving averaging over training trajectories, and aggregation over inference-time routes within a weight-shared recursive backbone. Experiments across multiple benchmarks establish new state-of-the-art predictive performance on standard benchmarks, while placing the RECAP on a favorable performance-parameter Pareto frontier.

Zero-order optimization (ZO) trains without backpropagation, making it relevant to forward-only hardware and non-differentiable loss, but its gradient variance grows with perturbed dimension, inhibiting large-model training. Sharded Optimization Mixture of Assemblies (SOMA) trains LSTM experts independently on $N$ data clusters using simultaneous perturbation stochastic approximation (SPSA), without exchanging gradients, activations or optimizer state. Its separable loss removes cross-expert perturbation noise at the cost of jointly learned representations across domains. Using 80,000 estimated RTX 5090 GPU-hours, we show modest sharding improves training compute efficiency over all tested monolithic ZO controls. At 8.44M parameters and 150 aggregate GPU-hours, SOMA $N=2$ with 64 perturbations reaches 1.76 test nats/byte, versus 2.00–2.11 for monolithic SPSA at 64, 256 or 1,024 perturbations and 2.21 for EGGROLL. On WikiText-103, these frozen checkpoints reach 2.07, 2.25–2.36 and 2.49, respectively. On a fixed separable objective with equal-size blocks, we prove independent losses reduce relative gradient variance to approximately $1/N$ of a shared-loss estimator's. Holding starting weights, data, perturbations and compute fixed, independent rather than summed losses lower SOMA $N=4$ test loss by 0.035 nats/byte after 1,000 updates across three seeds. Larger ensembles offer a separate inference benefit: at similar model size with top-$k$ routing ($k=4$), SOMA $N=256$ achieves 2.36M tokens/s versus 257k for SOMA $N=8$ ($9.19\times$, including routing), at lower test loss (1.68 versus 1.71), albeit using $59.9\times$ as much aggregate training compute. We release all training and evaluation code and checkpoints.

Current pre-training datasets are derived from web crawls, with all their issues, and were not designed to support mid- and post-training pipelines–for instance, they contain little explicit reasoning. Thus, many frontier labs have begun to develop their own internal datasets, starting from state-of-the-art models, to augment their pre-training data mix, eg, with reasoning traces to address cold-start problems. While demonstratively effective, none of these datasets are public, and the effect of this so-called synthetic data on knowledge and skill acquisition of language models, including small ones, remains poorly understood. We present SYNTH, the first open-source synthetic corpus derived from 58,698 Wikipedia articles that collapses pre-, mid-, and post-training into a single training stage via structured amplification of curated encyclopedic seeds. We evaluate SYNTH by training a suite of models: a 56M tiny model (Monad), 0.3B-0.6B dense models (Baguettotron), and a 13B / 1B-active MoE. At iso-compute, SYNTH outperforms filtered web data, and our models remain competitive with similarly-sized open-weight baselines. Because SYNTH is back-translated from grounded passages, SYNTH-trained models achieve high factual precision despite 10-140x fewer training tokens, with memorization targeted by the seed corpus. These results show that synthetic datasets, including our SYNTH dataset, are capable of producing competitive generalist models from a fraction of the training data, enabling rapid iteration as the frontier advances. These findings open up possibilities for both generalist models with significantly increased data efficiency, as well as domain-specific models where no instruction or conversational data is available. Finally, we publicly release our SYNTH dataset and the suite of Baguettotron models under a permissive license, thus supporting open-source language model development.

Multimodal continual instruction tuning (MCIT) aims to enable multimodal large language models to acquire new capabilities from sequential tasks while preserving previously learned knowledge. Existing methods primarily mitigate catastrophic forgetting by constraining parameter updates or separating task-specific adaptations. However, continual adaptation can also benefit from external knowledge that provides domain-specific information and reusable reasoning patterns for solving diverse instructions. For example, to answer "How many red cubes are to the left of the sphere?", domain knowledge can provide relevant concepts about objects and spatial relations, while reasoning knowledge can specify ordered operations such as object recognition, spatial filtering, and counting. Despite this potential, how to leverage external knowledge for continual adaptation remains largely unexplored in existing MCIT methods. To this end, we propose ReCAP, a retrieval-guided framework that leverages external knowledge to guide capability reuse during continual adaptation. At each continual stage, ReCAP uses external search and an LLM to incrementally build a knowledge base of domain, reasoning, and format knowledge based on the current-stage training data. For each instruction, retrieved domain knowledge guides generation, while retrieved reasoning knowledge selects and orders capability modules to form an instance-specific capability path. As these capability modules are reused across stages, subsequent adaptation can overwrite previously learned parameters. To enable stable cross-stage reuse, ReCAP introduces adaptive subspace recycling, which parameterizes reusable capability modules with shared bases and stage-specific cores, protects historically important directions while recycling residual capacity. Extensive experiments on MCIT benchmarks show that ReCAP achieves SOTA performance.

Class-Incremental Learning (CIL) requires models to recognize new classes over time without forgetting previously learned ones. With the rise of vision-language pre-training, CLIP has become a strong foundation for CIL. A common design in CLIP-based CIL is to construct textual classifier weights by encoding class-name templates with the CLIP text encoder, and then classify visual features by image-text cosine similarity. This design is appealing: since CLIP aligns images and text in a shared embedding space, textual weights appear to provide an off-the-shelf classifier for incremental classes. However, we show that this seemingly natural design is not always beneficial, as a modality gap can still separate the two modalities and make textual classifier weights deviate from visual class distributions. Empirically, under identical task-wise CIL training, initializing the cosine classifier with visual class centers yields lower loss and better incremental accuracy than using CLIP textual features. Motivated by these observations, we propose VIS, a visual-only method for CLIP-based CIL that removes the deployed textual branch and constructs the incremental classifier entirely in the visual space. To obtain stronger task-adaptive visual representations, VIS uses only base-session data to enhance CLIP's final visual representation with informative visual-layer features. Built on the enhanced visual representation, VIS employs a simple kernelized incremental least-squares SVM, whose classifier weights are solved in closed form from additive sufficient statistics. When new classes arrive, VIS accumulates their sufficient statistics and recomputes the classifier weights for all seen classes, enabling efficient incremental updates while preserving historical class knowledge. Extensive experiments show that VIS achieves state-of-the-art performance without a textual branch.

Activation and key-value cache precision change what a quantized language model computes without altering its stored weights. Direct weight-code bounds, however, assign identical complexity to deployments that behave differently and charge separately for weight codes that behave identically. Behavioral Capacity Certificates (BCC) charge for behavior using the aggregate prior mass of complete implementations—weights, scales, activation and cache rules—that induce the same bounded loss. When quantization merges implementations, this shared mass lowers the complexity penalty, and a break-even law determines when the saving survives the cost of validating it. BCC supports a three-step deployment workflow, and our experiments verify each step. First, a forward-only screen shortlists per-layer bit-widths by how often candidate perturbations preserve the reference predictions, with quality comparable to Hessian-guided selection at lower preprocessing cost. Second, margin-certified cells identify weights that can be pruned or sign-flipped without changing the deployed behavior: every permitted combination preserves all declared predictions, and on OLMoE-1B-7B and SmolLM2-1.7B, independent probes bound the probability that any permitted combination changes a prediction on new text. Third, BCC bounds the population loss of the deployed model, nonvacuously for complete decoders and more tightly than the compressed-code route. At equal cache memory, giving keys higher precision than values yields lower NLL and higher prediction agreement on GPT-2, Qwen2.5, and SmolLM2, together with a tighter complexity bound in the GPT-2 audit.

Topological structures such as simplicial complexes, hypergraphs, and cell complexes extend standard graph models by modeling higher-order relationships. These structures appear in many modern datasets and require specialized methods for generating meaningful embeddings. In this paper, we introduce TopoEmbedX, a unified framework for embedding a wide range of topological domains into Euclidean spaces. The package brings together several existing topological embedding algorithms—DeepCell, Cell2Vec, CellDiff2Vec, HOLE, and HOGLEE—and introduces five new algorithms: ComplexNetMF, ComplexRep, ComplexRandNE, ComplexWalklets, and ComplexHeat. These algorithms extend well-known graph embedding techniques to higher-order settings using the augmented Hasse graph of a topological domain. TopoEmbedX provides a clear, consistent, and easy-to-use framework for topological representation learning. Experiments show that the embeddings generated by TopoEmbedX support tasks such as classification and regression across multidimensional data.

Every text classifier for an African language begins with a budgeting question: how many labelled examples are needed, and can labels from other African languages stand in for them? We answer both questions empirically for 28 language-task pairs, news topic classification in 16 languages (MasakhaNEWS) and tweet sentiment in 12 languages (AfriSenti), using a character n-gram linear model that trains in seconds on two CPU cores with no pretrained weights and no accelerator. Monolingual learning curves at budgets from 25 to several thousand labels show that topic classification reaches 90% of its full-data macro-F1 with about 400 labels in the median language, while sentiment is still improving at the full training size in 11 of 12 languages and needs thousands of labels. Pooling the full training data of the other languages in the benchmark is worth a great deal at small budgets and nothing at large ones: at 25 target labels it adds 0.20 macro-F1 on average for news (up to 0.43 for Lingala) and 0.08 for sentiment, the gain decays to zero by 800 labels, and at full size pooling hurts in 9 of 16 and 8 of 12 languages. Twenty-five target labels plus pooled data match what 100 to 400 monolingual labels achieve for most news languages. A complete zero-shot transfer matrix shows that transfer without any target labels recovers a median of only 13% (news) and 4% (sentiment) of the gap between a majority-class predictor and the in-language model, with the exceptions explained by shared script (Amharic and Tigrinya), shared lexicon (English and Nigerian Pidgin, the Arabic dialects), or a shared label prior rather than by language family. We release code that regenerates every number from the public benchmark files and translate the results into concrete annotation guidance for teams building African-language classifiers without GPUs.