Papers

We study classification dynamics under small initialization and identify a pronounced non-monotone behavior of accuracy that we call the accuracy well: accuracy rises rapidly early in training, subsequently drops, and only much later recovers. We observe this phenomenon in deep linear networks, fully connected ReLU networks on MNIST, deep convolutional networks on CIFAR-10, and controlled synthetic tasks, across different losses and optimizers and in both training and test accuracy. We propose a three-stage explanation in terms of target-driven organization, a degeneracy bottleneck, and subsequent recruitment and recovery. We develop a rigorous theory of these dynamics for shallow and deep linear networks, showing in particular that high accuracy can emerge while the predictor and the change in loss remain asymptotically vanishing, before continued optimization causes accuracy to deteriorate. For a simple synthetic classification task, we prove an extreme instance in which accuracy asymptotically rises to 100%, collapses to 0, and later recovers permanently to 100%. Our results show that classification accuracy can reveal aspects of learning dynamics that are not captured by the training loss alone.

This paper considers reliable in-sequence molecular communication, where bio-nanomachines exchange molecule-encoded information in a specified order, and investigates a new simulation-based method to incrementally evaluate communication protocols by gradually increasing the complexity of experimental settings. The proposed method, called Affine Memory Replay (AMR), builds a continual learning (CL) model to estimate communication performance between bio-nanomachines. AMR stores past simulation samples and synthesizes additional replay samples through interpolation and extrapolation between past samples. Through incremental performance estimation tasks, it replays both past and synthetic samples to regularize model updates, helping the model adapt to new experimental settings while retaining knowledge from earlier ones. Experimental results show that AMR significantly outperforms existing CL methods in maintaining overall estimation accuracy across sequentially learned estimation tasks. It effectively balances memory stability and learning plasticity under moderate training cost.

Tabular foundation models enable in-context learning by predicting unseen observations from a labeled support table without task-specific parameter updates. Despite recent advances, most existing approaches rely on dense architectures that apply the same transformations across features and datasets. We introduce OrionMoE-Small, a compact tabular foundation model that combines distribution-aware representations with dataset-conditioned sparse mixture-of-experts computation. Built on a dual-axis Transformer architecture, OrionMoE-Small selectively activates experts along the feature axis, with routing decisions informed by both individual feature representations and the broader dataset context. This design enables adaptive allocation of computation across heterogeneous tabular problems while retaining a shared computational pathway across tasks. OrionMoE-Small is pretrained entirely on synthetic classification tasks generated from a structured causal prior and performs downstream prediction without gradient-based adaptation. Experiments across multiple tabular benchmarks demonstrate competitive performance against substantially larger foundation models, with particularly strong results on small-context and high-dimensional datasets. Further analysis reveals favorable relative performance under class imbalance and highlights the importance of feature composition.

For the fundamental problem of prediction from expert advice, Freund asked whether one could compete with a comparator that switches $k$ times among only $m$ experts. For a discrete set of experts, this problem was resolved by Bousquet and Warmuth (2020), who gave an efficient algorithm with optimal regret matching the information-theoretic limit. We study the analogous problem in online convex optimization, where the action space is continuous. An inefficient algorithm can be derived by discretizing the action space and applying the Bousquet–Warmuth algorithm, giving regret of $\widetilde{O}(md+k)$, while the best known efficient algorithm for this problem has regret $\widetilde{O}(dk)$. We show that this computational inefficiency is inherent, establishing a separation between the information-theoretic and polynomial-time regret achievable for this problem. Specifically, under the hypergraphic planted-clique conjecture, we show that for every polynomial-time algorithm there exist instances for which it incurs at least $(k\sqrt d)^{1-o(1)}$ regret.

Poor generalisation in deep neural networks is frequently associated with convergence to sharp minima. Sharpness-Aware Minimisation (SAM) improves generalisation of deep neural networks by minimising a combination of the training loss and the local sharpness of the loss landscape, biasing convergence towards flat minima. However, SAM relies on a fixed perturbation radius $\rho$ that ignores local curvature, leading to inefficient behaviour: the perturbation may be too small to escape poor basins defined by sharp local minima, or too large to allow convergence to solutions with good loss-sharpness tradeoff. We reinterpret $\rho$ as the intensity of the perturbation signal and propose Curvature-Aware Adaptive Perturbation for SAM (CAP-SAM), a geometry-aware method that modulates the perturbation radius based on a sharpness ratio, enabling a more effective search for robust minima on the loss landscape. We prove that CAP-SAM preserves the same convergence rate as standard SAM in non-convex stochastic settings. Extensive experiments indicate that our approach consistently outperforms SAM and its most prominent variants across diverse network architectures on CIFAR-10, CIFAR-100, and ImageNet.

Momentum is a classical tool for accelerating convex optimization and a standard component of modern large language model training. Yet recent empirical work has questioned the usefulness of first-moment momentum in reinforcement learning with verifiable rewards (RLVR). We study this question through a bandit formulation of RLVR with bias-corrected exponential moving average (EMA) momentum, where the EMA coefficient $\beta$ controls how quickly the weights on past gradients decay. When policy gradients are evaluated exactly, we prove that increasing $\beta$ within a range that prevents overshoot strictly accelerates optimization. When gradients are estimated from sampled responses, a positive expected gain can be obscured by sampling fluctuations. We show that as the learning rate $\eta$ decreases, the expected gain with fixed $\beta$ vanishes faster than these fluctuations, whereas increasing $\beta$ to keep $\eta/(1-\beta)$ within the safe regime preserves a nonvanishing gain that eventually dominates them. Bandit simulations quantitatively validate these predictions. RLVR experiments on Qwen3-4B-Base using SGD with EMA and AdamW support our principle of choosing larger coefficients in practical LLM post-training. On Qwen2.5-32B with AdamW, simply increasing $\beta_1$ improves mean validation accuracy by nearly $2$ percentage points over the conventional choice, demonstrating the principle's effectiveness at a larger model scale.

We develop a self-supervised reinforcement learning algorithm that learns to build towers of up to eight cubes from scratch, without prior data, rewards, demonstrations, or pretrained models. Our method, Contrastive Planning via Spherical Linear Interpolation (C-Slerp), uses contrastive representations as reusable building blocks and repeatedly composes them to infer a sequence of intermediate waypoints. Under our hyperspherical parameterization, the learned representations allow intermediate waypoints to be inferred in closed form through spherical linear interpolation, without training a separate high-level policy or performing graph search. Importantly, the representation geometry also tells us how to adjust the number of waypoints based on the difficulty of each goal-reaching problem. Experiments show that our method succeeds on long-horizon navigation and robotic manipulation tasks, including settings where strong baselines fail to achieve a single success. Ablations further show that using a fixed number of waypoints substantially degrades performance, highlighting the importance of adapting the plan to task difficulty.

Feldman's memorization lower bound assigns a frequency coefficient based on how often a point appears in the training sample. We give an exact three-point counterexample to its conditional and averaged forms, using independent fair labels and a permutation-equivariant learner. A sequence of sampling priors makes the ratio of the proposed penalty to actual excess risk grow exponentially, ruling out a universal positive constant-factor repair. The priors vary with sample size, the offending profiles become rare, and both quantities vanish. Retaining the original model, we obtain an exact replacement using full-sample posterior probabilities. Under exchangeability, these depend on multiplicity and the complete frequency profile. We characterize the largest multiplicity-only coefficients valid for unrestricted learners. The original coefficient has the posterior-mean form of Good's exact frequency formula and is an occupancy-weighted average of the corrected coefficients.

Reinforcement learning makes language models better at solving tasks, but the same mechanism also rewards guessing. When success is the only way to earn reward, opting for a safe fallback is always worse than a long-shot attempt. When a wrong action can corrupt a database or ship broken code, that incentive can be costly. Therefore, we propose training models to fail gracefully: to preserve successful behavior whenever possible while learning to execute a safe fallback policy when acting would be unreliable. However, naively using policy gradients with intermediate reward for fallback behavior is brittle due to unfavorable optimization dynamics. We address this challenge with GracefulRL, which reshapes the optimization landscape to promote graceful failure. Importantly, this behavior emerges directly from outcome-level reward signals, without annotations specifying when to fall back or additional inference-time machinery such as a verifier. Across a range of tasks and scales, we train models that largely preserve their task-solving capability while selectively falling back when acting would be unreliable. More broadly, our results show that reinforcement learning can not only incentivize models to succeed, but also to reason about the limits of their capabilities and change course when they determine that success is out of reach.

Head-related transfer function (HRTF) spatial upsampling from sparse measurements is a fundamental challenge in personalized binaural audio. We formulate HRTF upsampling as an operator learning problem and introduce SPARO, a neural operator that maps sparse measurements at a set of spatial directions to the HRTF field, a continuous representation that can be queried at arbitrary positions. SPARO projects the measurements onto a learned set of spherical latent modes, processes the latent modes with Transformer blocks, and decodes the resulting representations at query directions. On SONICOM, using the LAP24 measurement configuration, SPARO attains the best log-spectral distortion (LSD) and interaural level difference (ILD) error at every sparsity level from 3 to 100 measurements (18% lower LSD and 43% lower ILD error than the strongest baseline at 100 measurements) while remaining competitive in interaural time difference (ITD) error. It reconstructs a dense HRTF 15 to 373 times faster than the leading neural-field method RANF. We further validate the approach on HUTUBS, demonstrating its effectiveness across HRTF datasets.

Context can improve large language model performance, but these gains may be lost after context removal. Inspired by biological systems consolidation, we formulate Memory Consolidation (MC) as internalizing these gains while preserving non-target capabilities, connecting context-specified editing, skill learning, and behavioral steering under a common objective. We introduce a five-task-family testbed measuring consolidation and retention under single, batch, and sequential updates. We propose Cortex, which generates prospective queries to anticipate uses of context and distills context-conditioned outputs into mergeable low-rank or structural feed-forward network updates. Across 4B–120B dense and mixture-of-experts backbones, including both text-only and multimodal models, Cortex lies on the empirical consolidation–retention Pareto frontier in most evaluated settings. After 50 sequential factual edits on a 14B model, Cortex-Structural recovers 88.9% of the context-induced gain while retaining 99.8% of original non-target performance.

When does a human correction become useful learning, and what establishes better segmentation at matched human effort? This critical narrative review follows feedback through its selection, learner update, and evaluation. It compares active learning, machine teaching, interactive segmentation, and sequential predictive evaluation using a common mathematical account of target information, predictive error, response predictability, and human work. An exact Bayesian update converts evaluation-label information into expected log-loss improvement; an excess-risk decomposition explains what an approximate learner can lose. Conditional information decompositions separate the roles of selected locations, labels, and displayed context. Empirical comparisons show why response protocols, update mechanisms, and effort denominators matter, distinguishing current-mask refinement from reusable learning and simulated interaction from human evidence. We identify what logs can reveal, what requires independent evaluation, and what remains model-dependent. The resulting research priorities are to test what selection reveals, whether using it improves assimilation, and whether the resulting interaction policy benefits segmentation at matched effort. These are distinct claims: predicting a teacher's responses need not identify human intentions or establish better learning. No new acquisition algorithm or empirical superiority is claimed.

Speculative decoding accelerates LLM generation through lightweight drafting and parallel verification. It is particularly promising for long inputs, where KV-cache access costs can be amortized over multiple accepted tokens. Yet most drafters are trained on short sequences and degrade on long inputs, while long-context training is costly. Existing training-free approaches restrict the context window, rescale positions, or augment recent context with retrieved distant entries. Drafters, however, read target hidden states that already encode contextual and positional information, and their lightweight architecture makes full-history attention affordable. We propose FOLD, a training-free method that preserves exact local positions and treats all distant entries as far memory at a shared position. To counter attention dilution as the memory grows, we sharpen attention within it to emphasize relevant entries while separately controlling its total weight relative to the local window. Across six target-drafter pairs and diverse benchmarks of up to 256K tokens, FOLD predominantly delivers the highest speedup, with the best case more than doubling the speedup over autoregressive decoding, from 2.08$\times$ to 4.22$\times$.

Given $n$ distributions (hypotheses) $\mathcal H=\{H_1,\ldots,H_n\}$ and samples from an unknown target distribution $P$, proper hypothesis selection seeks a distribution whose total variation distance to $P$ is close to the best achievable within the known distributions. We give an algorithm that, using $O(\varepsilon^{-2}\log(n/\delta))$ target samples, running in $O(n\varepsilon^{-2}\log(n/\delta))$ time, with probability at least $1-\delta$, returns $H_{\hat i}$ satisfying $d_\mathrm{TV}(P,H_{\hat i})\leq 3\min_{i\in[n]}d_\mathrm{TV}(P,H_i)+\varepsilon.$ The algorithm achieves the optimal approximation factor and sample complexity. The running time improves the dependence on the failure probability from polynomial to logarithmic in the state-of-the-art bound $\tilde{O}(n\varepsilon^{-2}\delta^{-1})$ of Aamand, Aliakbarpour, Chen, and Silwal (COLT 2026), thereby answering their Question~2.

Neural partial differential equation (PDE) surrogates trained with mean squared error (MSE) can capture dominant dynamics but often lose high-frequency information and fine-scale structures. Generative models (e.g., Flow Matching) can capture the distribution of fine-scale details, yet stochastic errors may accumulate during autoregressive rollouts and compromise long-term stability. To address these limitations, we introduce Refine and Align(ReAl), a model-agnostic plug-in that augments pretrained PDE surrogates to improve the reconstruction of high-frequency structures associated with complex physical phenomena. In the refinement stage, a conditional flow-matching model learns the residual distribution around the deterministic base prediction, recovering missing fine-scale structures while retaining the dominant dynamics. In the alignment stage, to mitigate the generative discrepancies amplified in the autoregressive rollout, particularly in chaotic systems, we generate multiple trajectories from the same input and reinforce the refiner with trajectory-level rewards, thereby achieving long-horizon dynamical alignment. Experiments across diverse surrogate architectures and PDE tasks demonstrate that ReAl consistently improves high-frequency fidelity, forecasting accuracy, and long-horizon stability.

Neural operators learn mappings between function spaces, enabling fast surrogate solutions to partial differential equations. Despite remarkable architectural diversity, these methods often share a common input representation: raw coordinate-value pairs $(x, u(x))$. We ask whether inputs aligned with PDE differential structure can improve learning. Through Picard iteration on mild solutions, we show that derivatives of the input appear explicitly in the solution operator, suggesting that providing derivative features should reduce the network's implicit differentiation burden. We prove this intuition: providing derivative features improves approximation bounds from $O(W^{-(s-m)/d})$ to $O(W^{-s/d})$, where $W$ is parameter count, $s$ is input regularity, $m$ is the PDE order, and $d$ is spatial dimension. Our central finding, however, is a surprise: the optimal derivative order $\beta^*$ is strictly less than the PDE order $m$. This gap arises from a bias-variance tradeoff in spectral space that we characterize in closed form. Learning $\beta$ from data achieves automatic spectral regularization. We introduce $\partial$-NO (del-NO), for derivative-augmented neural operators, an architecture-agnostic augmentation that provides learnable fractional derivative features to any neural operator backbone. Across benchmark problems and architectures, $\partial$-NO consistently improves prediction accuracy, with learned orders that reflect a representation of known physics modulated by noise and finite-sample constraints.

Mixture-of-experts (MoE) language models activate only a few experts per token, yet all expert weights must be stored. Mixed-precision quantization reduces this storage cost by assigning higher bit-widths to sensitive experts and lower bit-widths to resilient ones, but expert rankings alone do not determine how strongly to weight their errors. To address this gap, we propose NatScale, a contrast-calibrated allocation framework for mixed-precision MoE quantization. It uses a model-specific power transformation to calibrate gradient-based expert weights to an information-theoretic contrast target while preserving rankings. We jointly evaluate each expert's gate, up and down configurations to estimate its output error. We then combine these errors and calibrated weights with an existing prior based on weight spectra, variance and precision decay to select configurations under a storage budget. Across three models, NatScale achieves the lowest native-to-quantized KL divergence and the highest top-token agreement in all nine settings against five allocation baselines. It also yields the lowest perplexity in seven settings. These findings highlight the importance of objective-aware precision allocation.

Preference optimization ranks final answers and trajectory RL maximizes aggregate returns, yet neither credits the local change that turns a flawed reasoning state into a better one. We introduce Lifted State Policy Optimization (LSPO), which establishes this finite, cost-adjusted transition as the primary unit of learning. Each textual answer is augmented with a learned continuous coordinate, forming a lifted state that an energy function evaluates and orders. A shaped reward drives energy descent net of edit and step costs, and an internalization loss absorbs selected low-energy answers into the direct generator. On Qwen3.5-27B, the resulting single-pass policy reaches 71.8% aggregate accuracy across mathematics, science, code, and logic benchmarks, matching test-time reflection at 71.9% with 28% lower latency and 25.8% fewer tokens. The pattern holds across dense and mixture-of-experts backbones, and matched controls confirm that transition credit and the lifted coordinate each contribute, as does answer internalization. Our code is available at https://github.com/Venomrko/lspo.

Asynchronous EEG event detection supports practical brain-computer interfaces by identifying event classes and temporal boundaries directly from continuous recordings without predefined event boundaries at inference time. The primary challenge lies in extracting event-related patterns embedded in ongoing background activity. To address this, we propose NeuroDETR, a discrete spatiotemporal multiscale framework that combines structured tokenization with event-aware feature refinement. Multiscale temporal codebooks capture brief responses and sustained dynamics, while Spatial-Pyramid VQ hierarchically encodes spatial structure across EEG channels. These complementary representations form a compact event memory for jointly classifying events and estimating their onsets and offsets. Before tokenization, we apply FOCAL, an event-aware sparse attention module that uses predicted event presence to guide temporal feature refinement and spatial aggregation, emphasizing likely event periods while preserving context across the recording. Experiments on eight EEG datasets that span diverse paradigms demonstrate state-of-the-art performance. These findings provide a basis for the development of BCI systems that recognize meaningful neural activity during continuous interaction and monitoring.

We study the finite-sample convergence of Q-learning algorithms for the average-reward formulation of Reinforcement Learning (RL) with options. While options allow temporarily extended and hierarchical actions, the average-reward formulation incorporates continual tasks beyond discounted and episodic RL. We establish the first $\tilde{O}(1/\text{iterations})$ convergence guarantees, in the mean-square sense, for average-reward option Q-learning algorithms in both the inter- and intra-option settings. First, we prove that both inter- and intra-option Bellman operators satisfy multi-step span contractions under unichain assumptions. Then, we propose synchronous estimators of these multi-step option Bellman operators leading to two variants of option Q-learning. Finally, we extend the stochastic approximation framework to prove convergence rates of these two algorithms under the minimal assumptions used in the literature.

Missing data is a pervasive challenge in machine learning, often degrading predictive performance and complicating model deployment. Most existing approaches treat imputation as a preprocessing step independent of the downstream task, a separation that becomes problematic under train-test mismatches in missingness mechanisms or rates. We introduce a unified framework that treats missing entries as variables in a task-conditioned optimization problem. We instantiate this framework in two settings: an amortized approach for scenarios with missing data at both training and test time, and a latent optimization approach for settings where only training data is incomplete. The evaluation is conducted on 98 tabular datasets, and robustness under train-test mismatches is assessed on 36 datasets. Results reveal that reconstruction error constitutes a poor proxy for predictive utility (Spearman rho approximately 0.16 to 0.32), and that task-aware imputation becomes critical in scenarios where classical methods fail to recover complete-data performance, achieving win rates of up to 80% in challenging train-test mismatch scenarios.

The success of transformers is attributed to several factors, including their capacity to express formal languages over variable-length inputs, and ability of the attention mechanism to focus on relevant input features. However, there is limited understanding of the training dynamics of shallow transformers, specifically how to decouple the learning of the attention and the output (feedforward) layer. A natural extension of the theory of one-step gradient feature learning in feedforward networks suggests that one could first learn the attention weights with a single gradient step, and then train the output layer. We show that this fails for a shallow transformer trained to recognize a star-free language from unbounded-length input. We prove that the transformer can be trained to recognize the language with a three-phase gradient descent: the output layer is updated first, followed by an attention update, and the output layer is fine-tuned in the third phase. In contrast, the language cannot be learned by training only the attention or output layer, or by a single attention-layer update followed by finetuning the output layer. We empirically show that “attention learning lagging output layer learning" is beneficial in other language recognition, regression, and in-context learning tasks as well.

Diffusion and flow matching are now dominant frameworks for generative modeling in continuous domains, but they typically require multiple network evaluations at inference. This has motivated extensive research on one-step generative modeling primarily built on diffusion and flow, though existing approaches often rely on complex training machinery. In this work, we introduce Priming Models, a simple two-stage framework for training one-step generators. Motivated by the difficulty of distributional training from scratch, Priming Models are first trained on a reconstruction objective, e.g., pixel-space denoising at a fixed noise level, before undergoing feature-space distributional post-training. Our central scientific finding is that this simple reconstruction stage is already enough to entirely alleviate the difficulty of distributional training. Empirically, across class-conditional image generation, text-to-image generation, and world modeling, Priming Models significantly advance the Pareto frontier of training compute vs. generation quality. On ImageNet at $256 \times 256$ resolution, we achieve a state-of-the-art FID of $1.19$ among one-step generators using approximately one-tenth the training compute of prior methods with comparable FID. We open-source our codebase at https://github.com/JaeyeonKim01/priming.

Integrated Sensing and Communication (ISAC) systems rely on accurate Direction-of-Arrival (DoA) estimation for effective beamforming and spectral-efficiency enhancement. While numerous classical and deep-learning-based DoA estimation methods have been reported in the literature, their suitability for real-time ISAC operation remains insufficiently understood because practical deployment requires consideration of both estimation accuracy and computational latency. This paper presents a unified evaluation framework for systematically comparing classical and learning-based DoA estimators within an ISAC beamforming pipeline. Representative classical and learning-based DoA estimators, together with an ensemble architecture, are integrated with Singular Value Decomposition (SVD)-based beamforming and evaluated under identical operating conditions. The impact of DoA estimation accuracy, inference latency, beamforming-weight generation time, and resulting effective spectral efficiency is investigated. Results show that different estimators occupy distinct operating points in the accuracy-latency-performance design space. Although learning-based approaches substantially reduce estimation time compared with MUSIC, the overall processing latency increasingly becomes dominated by the computational cost of SVD-based beamforming. Among the evaluated methods, the Regression Convolutional Neural Network (RCNN) exhibits a favorable balance between estimation accuracy, computational efficiency, and beamforming performance, making it a promising candidate for real-time ISAC deployment. The findings further suggest that future low-latency ISAC systems may benefit from beamforming strategies that reduce or avoid computationally intensive SVD-based beamforming-weight generation.

Reinforcement-learning policies for robot locomotion can fail at deployment when operating conditions shift (e.g., rough or slippery terrain, payload changes, sensing degradation), and retraining or manual recalibration is often infeasible under on-device latency and memory constraints. We study test-time adaptation (TTA) for robotic control: adapting a pretrained policy online and in a self-supervised manner during execution, without access to rewards. Our starting point is a lightweight baseline that updates only the actor using a frozen pretrained critic as a deployment-time performance surrogate. Building on this, we introduce TEMPO, a test-time entropy-regularized, memory-guided policy optimization method that stabilizes critic-driven updates under severe shift. TEMPO combines (i) an entropy-promoting regularizer on the critic's predictive distribution to mitigate overconfident extrapolation, and (ii) a score-based memory, inspired by prioritized replay, that prioritizes low-value ("hard") observations and applies importance sampling to focus limited computation on the most informative deployment conditions. Across Go1, Go2, and G1 in MuJoCo Playground under four representative shifts and multiple architectures, TEMPO yields consistent gains, reaching up to 80% improvement in a single-device setting. We further validate on a physical Unitree Go2 with an added calf payload, where fully on-device adaptation improves performance over the non-adapted baseline across real-world episodes.

Homogeneous turbulent flows exhibit recurring multiscale structures across spatially separated regions, suggesting that a single flow realization may contain sufficient information to learn representations of unresolved scales. We investigate this hypothesis through an extreme super-resolution framework in which a wide-activation deep super-resolution (WDSR) network is trained exclusively on overlapping patches extracted from a single high-resolution turbulent realization. Previously unseen flow fields are reconstructed through patchwise prediction followed by Hann-window-weighted overlap-add assembly. The framework is evaluated for two-dimensional homogeneous isotropic turbulence at super-resolution factors of x32 and x64, representing severe spatial under-resolution. Despite the limited training data, the proposed approach reconstructs coherent vortical structures and recovers fine-scale features more accurately than conventional interpolation. Spectral and statistical analyses further demonstrate improved recovery of high-wavenumber energy content and multiscale flow characteristics. To assess the effectiveness of exploiting internal spatial information, we compare the proposed framework against WDSR models trained on 1, 25, 50, and 100 complete high-resolution snapshots without patch extraction. This comparison distinguishes the benefits of localized learning from those associated with increasing the number of training realizations. The results demonstrate that exploiting spatial redundancy within a single turbulent realization enables accurate reconstruction of previously unseen flow fields, even under extreme spatial under-resolution. These findings establish single-realization patch-based learning as a promising data-efficient approach for turbulent super-resolution when high-resolution training data are scarce.

Orthogonal transforms have emerged as an effective tool for low-bit quantization of large language models (LLMs), as they reshape activation distributions without changing the underlying model function. Existing approaches typically rely either on fixed data-agnostic transforms, such as Hadamard rotations, or on calibration-time optimization of learned rotations. We study rotation selection from first principles and show that maximizing covariance leads to spectral alignment and provides a principled criterion for constructing quantization-friendly orthogonal transforms. Based on this insight, we propose SpectrumQuant, a closed-form rotation method that estimates activation covariance from calibration data and uses it to construct a covariance-aware orthogonal transform for post-training quantization. Our formulation characterizes quantization-friendly rotations as compositions of alignment and mixing components, while recovering Hadamard matrices as a special case. Interestingly, a class of butterfly matrices belongs to this category. In the realm of LLM quantization, SpectrumQuant bridges the gap between data-agnostic structured rotations and learned rotations, providing an effective and efficient data-aware alternative for post-training quantization. Experiments on Llama and Mistral models show that SpectrumQuant is competitive with state-of-the-art rotation strategies while requiring less than one-third of the GPU memory and significantly less time than learned rotations approaches like SpinQuant and DartQuant.

An agent can improve its behavior within an unresolved problem by changing how it acts and which experience it retains. We propose MMLA-RSI, a recursive self-improvement scheme with two implementations in Memory-Mediated Learning Architecture: Reasoning-Time Training (RTT) changes the policy state $\Phi$, while Reasoning-Time Memory Adaptation (RTMA) changes authoritative memory $M$. Each route also makes its adaptation method an object of improvement. A current numerical updater trains the policy proposing its successor; a current memory manager chooses the records available to the process proposing its successor. An independently admitted successor takes over the same role in the next generation. We give bounded executable rule languages, shared task/proposal interfaces, and one algorithm for either route or their composition. The RTT instance changes scalar schedules in a clipped-momentum update. The RTMA instance chooses NULL or a complete-row write with possible eviction. A fixed interpreter, trusted committer, and independent evaluator bound what can change. State versions, read closures, and conditional properties describe causal execution, accepted transitions, and finite work. Existing numerical-component studies motivate the construction. In four-candidate program selection, retaining LARC feedback updates reduces expected error by 24.65 and 36.65 percentage points for two trained initializations. In chronological continuous-integration replay, feedback binding is positive while retention increases loss. Completed SQL studies improve substantially over an unadapted substrate but do not establish the required additional online benefit. These results characterize their declared components. The two recursive routes and their joint realization are specified here; their beneficial recursive chains and discovery efficiency remain to be evaluated.

Large language models increasingly generate multiple retrieval actions jointly, while downstream systems often provide only one reward for the resulting set. Broadcasting this reward provides a valid score-function gradient estimator for the expected set-level objective, but does not determine a coalition-dependent within-set attribution. We introduce CASI (Credit Assignment via Set Intervention for Agentic Retrieval), which constructs the missing counterfactual information through snapshot-grounded set intervention: generate and retrieve once, hold replayable snapshot components fixed, and evaluate alternative subsets under common conditions. Shapley aggregation converts these marginals into within-set credit, which bounded zero-sum advantage shaping incorporates into policy optimization. For m >= 4, singleton, leave-one-out, and full-set endpoints do not generally determine the Shapley allocation; under additive set values, extra coalition evaluations are redundant. In a five-action sponsored-search setting, exhaustive auction replay over 1,200 requests reveals substantial coalition dependence. Under the training-time evaluator, CASI achieves the highest median cosine similarity to a replay-defined Shapley reference among evaluated credit rules; under a sensitivity backend, CASI does not outperform Singleton. Across five independent training runs, CASI-trained policies achieve higher held-out auction-replay set value than Singleton- or Broadcast-trained policies. In a randomized seven-day production A/B test on 10% of traffic, the CASI-trained policy yields an observed 3.51% lift in the primary advertiser-value metric over production control.

Conditional generative models are increasingly used for scientific prediction beyond the direct training support. Yet scientific questions often concern whether one intervention changes the effect of another. Such interactions can be of primary interest while explaining little of the total variation, allowing models to appear accurate overall without recovering the relevant scientific effect. It remains unclear how these models learn interactions and when these successfully extrapolate to unseen conditions. We therefore study interaction recovery in flow-matching models using a physiological time-series simulator, drug dose-response data, combinatorial cell perturbations, and molecular conformer generations, where we separate recovery from hallucinated interaction structure. In the controlled setting, individual effects are learned much earlier than interactions and models hallucinate interactions where none exist. Across settings, we find qualitatively different generalization problems, with successful prediction depending on whether condition structure continues from observed to held-out targets. When it does, interactions are recoverable. If not, models can generate plausible responses while missing the interaction. We furthermore find that hallucinations increase as targets become less identifiable, and that successful interaction recovery in output space can fail under nonlinear readouts. Finally, we show that aggregate fidelity metrics can conceal whether models learn and extrapolate interactions.