arXiv:2610.12358v1 Announce Type: cross Abstract: We study Gaussian regression under squared population $L_2$ loss in a known $m$-dimensional subspace of degree-at-most-$k$ functions on the $d$-dimensional Boolean cube. Random inputs can undersample regions essential for prediction, delaying the parametric rate even when the model is known. For fixed $q_0<1/2$, $1\le k\le q_0d$, and sufficiently large fixed $A$, the worst-subspace sample threshold for minimax error $A\sigma^2(m+t)/n$ with confidence $1-e^{-t}$, $t\ge\log4$, is \[ N=(m+t)\exp\{E_{d,k}+O(k^{1/3})\}, \quad E_{d,k}=d\Psi(k/d), \] where $\Psi(q)=\log2-\mathsf H(\tfrac12-\sqrt{q(1-q)})$ and $\mathsf H$ is binary entropy with natural logarithms. The upper bound holds for every feasible $m$; the matching lower bound holds when $m\le\binom d{\lfloor k^{1/3}\rfloor}$ or $t\ge m$. We sharpen the Polyanskiy--Samorodnitsky uncertainty principle in two respects. First, for fixed leakage $\rho\in(0,1)$, the smallest set carrying a fraction $1-\rho$ of a nonzero degree-at-most-$k$ polynomial's energy has probability $\exp\{-E_{d,k}+O_{\rho,q_0}(k^{1/3})\}$. An Airy-kernel construction proves that the remainder cannot be $o(k^{1/3})$ in general. Second, we construct a subspace of dimension $\binom d{\lfloor k^{1/3}\rfloor}$ such that every function in the subspace has at least a fraction $1-\rho$ of its energy on the same set, whose probability is at most $\exp\{-E_{d,k}+C_{\rho,q_0}k^{1/3}\}$. For sufficiently large $k$, this set is a Hamming ball. A striking consequence is an exponential cost of noise: the parametric rate can require $(m+t)4^k\exp\{-O(k^{1/3})\}$ samples, whereas $O((m+t)2^k)$ suffice for noiseless identification. As $k\to\infty$ with $k/d\to0$, the noisy threshold is $(m+t)\exp\{2k+o(k)\}$.
arXiv:2610.12338v1 Announce Type: cross Abstract: While caching key-value (KV) states accelerates Large Language Model (LLM) decoding, this cache can dominate memory usage at long context lengths. One solution is to compress this memory by exploiting inter-layer cache similarities. However, most existing techniques necessitate architectural changes to LLMs and incur substantial overhead. In this work, we propose a symmetry-aware value cache merging strategy that reduces cache memory while avoiding both harmful performance degradation and architectural overhead during decoding. Furthermore, we show that this approach can be exploited alongside existing cache compression techniques, composing with high-ratio quantization or key cache pruning to reach compression ratios that neither method reaches alone, with minimal additional cost. Ultimately, our findings reveal a major source of underutilized capacity in the value cache, offering a simple yet highly effective direction for scaling context windows under memory constraints.
arXiv:2610.12325v1 Announce Type: cross Abstract: Do LLM scientific agents rely only on their initial task context, or do they adapt their decisions in response to experimental feedback? We study this question in neural operator adaptation, where a large language model (LLM) selects fine-tuning configurations under a limited trial budget. Across transfers within and between partial differential equation (PDE) families, the LLM achieves lower held-out test nRMSE than random search and Bayesian optimisation in nearly every matched comparison. Endpoint performance alone cannot distinguish what happens, so we verify each attribution with controlled interventions. Before observing any validation score, the LLM's first configuration already ranks near the top of the corresponding random-search pool, indicating a useful initial bias. A complementary cold-start intervention shows that the selected base learning rate shifts with the PDE description. Once feedback becomes available, reassigning validation scores among evaluated configurations changes the next proposal in every case tested, whereas a value-preserving rewrite produces no comparable aggregate effect. These interventions establish that the LLM's decision-level actions respond to the given task and observed outcomes, showing that it combines a task-dependent prior with sensitivity to experimental feedback.
arXiv:2610.12321v1 Announce Type: cross Abstract: Spatial public goods models show that prescribed movement toward richer locations can generate spatial patterns. We ask how such patterns emerge when agents learn where to move and how learning rates shape their consequences for collective welfare. Fixed populations of cooperators and defectors independently learn movement policies using tabular Q-learning and local observations. Cooperator learning generates clusters around resource peaks, while co-adaptation changes their strength and motion. At a fixed training budget, the largest welfare losses occur when cooperators learn at high rates and defectors at low rates. In part of this regime, learned policies also generate traveling bands supported by a shared directional preference. The conditions supporting travel change with further training, so these patterns reflect training history rather than an established asymptotic outcome. Across the tested learning-rate conditions with cooperator learning, mean collective welfare falls below random movement because increased crowding outweighs gains in resource benefit. Charging agents for the crowding they impose on others during learning recovers much of the welfare loss in the tested conditions. These results connect learning rates to the emergence and welfare costs of spatial organization driven by individual rewards.
arXiv:2610.12168v1 Announce Type: cross Abstract: We introduce a self-improvement loop for reasoning models based on the following observation: Even when the difficulty of a problem exceeds the model's current solving abilities, an additionally supplied solution might enable the model to extract useful solution ideas in hindsight. We operationalize this by jointly training the same model to exhibit the following three capabilities: predicting solution ideas from problems alone, reverse-engineering ideas from problems and known solutions, and solving problems using provided ideas. The loop alternates between reverse engineering such ideas from problems with supplied solutions and using these ideas as additional supervision for joint training of all three capabilities. We give a formal specification of our method and a concrete instantiation for interactive theorem proving in the Lean theorem prover; empirical evaluation remains future work.
arXiv:2610.12052v1 Announce Type: cross Abstract: Despite their empirical success, why diffusion models overcome the bottlenecks of classical score-based samplers remains unclear. In this work, we leverage Gaussian distributions to isolate this phenomenon. We establish 2-Wasserstein convergence bounds for optimized hyperparameters, showing that diffusion processes achieve a sampling error of $O(\sqrt{d\lambda_{\max}}\log N/N)$, where $d$ is the dimension, $N$ the number of sampling steps, and $\lambda_{\max}$ the largest eigenvalue of the target covariance matrix. Unadjusted and underdamped Langevin dynamics suffer from an additional $\sqrt\kappa$ factor, where $\kappa$ is the condition number. These rates follow from spectral bounds which are sharp: we confirm them via matching first-order asymptotics as $N\rightarrow\infty$. Our analysis provides a rigorous characterization, in the Gaussian setting, of how time-dependent score trajectories remove condition-number dependence during sampling. By contrast, in the learning phase, we show that estimating the unnoised score by gradient descent leads to essentially the same estimator as estimating a noisy score, which suggests that the benefits of noising do not come from the learning phase.
arXiv:2610.11947v1 Announce Type: cross Abstract: Graphical approaches to causal abstraction transform a low-level causal directed acyclic graph (DAG) over many measured variables into a smaller, high-level DAG whose nodes cluster the original variables and whose edges summarize the causal relations between clusters. Such cluster DAGs are easier to interpret, but learning them requires finding the clusters and recovering the edges between them. Madaleno et al. (2026) learn the interventional coarsening (the cluster DAG that merges variables the interventions cannot distinguish) in two constraint-based phases: first the clusters, then the edges. We introduce COARSE, the first score-based method for this task: it keeps the two-phase structure but, under linear Gaussian assumptions, swaps the constraint-based edge phase for a score-based one. We show that the interventions themselves identify a causal order over the clusters, and learning the edges reduces to a single local search per cluster under a cluster-level BIC score. We prove that the procedure runs in polynomial time and, provided the variables affected by each intervention are correctly identified, that it is consistent. On synthetic and real-world interventional data, COARSE matches state-of-the-art edge recovery given enough samples, with an edge phase up to two orders of magnitude faster, including on dense graphs with hundreds of nodes.
arXiv:2610.11924v1 Announce Type: cross Abstract: Media-bridged time series forecasting is expanding to encompass traditional "multivariate" and emerging "multimodal" (e.g., through textual assistance). Existing Time Series Forecasting (TSF) models still rely on paradigm-specific relation, fusion, and temporal modules, hindering a common forecasting backbone across numerical and pre-aligned narrative-flow settings. To explore this, we propose the Multimedia Identity-Aware Prism Network (MIDAPN), a unified spatiotemporal forecasting backbone based on media-general graph adaptation and automatic temporal learning: (1) Following media pre-alignment, our Multimedia Identity-Aware Graph (MIDAG) revisits identity through static essence, dynamic behavior, and latent commonality, inducing affinities that extend variable-specific dependencies across media. Contextual Identity Modulation (CIM) further refines discriminative aggregation. (2) We develop Spectral Prism Convolution (SPConv) to automatically perform hierarchical temporal analysis, balancing coarse trends and fine-grained details. Meanwhile, its Adaptive Search Guidance configures a scale-efficient architecture for temporal-dimension reconstruction. These decoupled yet synergistic components jointly address media identity disentanglement and temporal-scale mismatch. Comprehensive evaluations involving 16 SOTA TSF models across 13 "multivariate" and 12 "multimodal" datasets, alongside targeted long-context comparisons against 14 time series foundation models and fused pretrained language models, demonstrate MIDAPN's consistent superiority and broad shared backbone compatibility. The code is available at \href{https://github.com/leijieruilq/MIDAPN/tree/main}{https://github.com/MIDAPN}.
arXiv:2610.11798v1 Announce Type: cross Abstract: Softmax attention, at the heart of Transformers, has demonstrated remarkable capabilities. Yet its underlying mechanisms remain only partially understood. Recent theoretical work studies Gaussian prompts, where the infinite-prompt limit reduces softmax attention to a linear map, but also removes the query-dependent selection that distinguishes it from linear attention. This work studies the infinite-prompt limit of softmax attention on Gaussian mixtures, which retain the tractability of Gaussian data while introducing latent structure, multimodality, and nonlinear dependencies. We show that softmax attention can represent and learn, via gradient-based methods, optimal solutions to a range of statistical tasks, including supervised classification and denoising. Our results highlight two complementary capabilities of softmax attention: it can recover linear tasks as effectively as its simpler linear counterpart, while also exploiting query-dependent context selection to solve nonlinear tasks beyond the reach of linear attention.
arXiv:2610.11794v1 Announce Type: cross Abstract: Learning to act in unfamiliar environments requires agents to infer how the world works and revise that understanding as new evidence arrives. Yet limited observations can support multiple world models that explain past interactions but predict different outcomes in unseen states. We introduce Memento 3, building on the Memento series to enable frozen LLM agents to continually learn explicit world models through external memory. The agent maintains a natural-language rulebook as persistent semantic memory, recording revisable hypotheses about environment dynamics while leaving unknown aspects underspecified. It compiles this rulebook into executable code for prediction and planning. Through a continual loop of observation, reflection, rule revision, compilation, and verification, the agent uses prediction errors to refine both the rulebook and its code. Updated code is accepted only when the LLM judges it faithful to the rulebook and cell-exact replay reproduces the observed transitions. We investigate this process as a model-based route to recursive self-improvement (RSI): the agent autonomously explores the environment, revises its world model, and uses verified updates to guide subsequent interaction and learning, while the underlying LLM remains fixed. A population extension maintains multiple world models in parallel, sharing interaction evidence and using their predictions to guide exploration. On ARC-AGI-3, the single-model agent clears every level of all 25 public games, achieves a mean Relative Human Action Efficiency (RHAE) of 100.0, and uses 44% of the human action count. In an Atari Pong case study, a learned feedback controller wins 21:0 in each of three evaluated episodes with different openings, without further LLM calls.
arXiv:2610.11759v1 Announce Type: cross Abstract: Near-term quantum approaches to combinatorial optimization are limited by qubit counts, circuit fidelity, sampling cost, and the difficulty of encoding constraints, while machine learning is increasingly used to configure and control quantum optimization workflows. We call such workflows adaptive: decisions conventionally fixed in advance, from formulation and penalties to shot budgets, backends, and whether to invoke a quantum processor at all, are made by learned policies that respond to the instance, the progress of the solve, or the hardware. This review examines three paradigms, AI for quantum optimization, quantum for AI-driven optimization, and AI-quantum co-optimization, and organizes the literature by the decision being learned rather than by application. A structured review of 119 papers, 67 coded in detail, shows that the evidence is considerably stronger for AI-assisted quantum optimization than for the reverse direction: learning already reduces quantum evaluations, improves initialization, supports decomposition and penalty control, and mitigates noise, whereas evidence that quantum computation improves learned optimizers remains largely confined to small-scale simulation. Experimental controls are thin: 25 of 57 studies include no classical baseline, the quantum contribution is fully isolated in 10 of 24 studies where an ablation applies, and the median experiment uses 17 qubits. We introduce an M0-M5 evidence hierarchy, from simulation to matched-resource practical advantage, and find no broadly convincing result at the highest level. We argue that scaling is increasingly a systems problem: the question is not only whether a problem fits on a quantum processor, but how classical and quantum resources should be allocated across the optimization process. The review is aimed at researchers in quantum computing, machine learning, and operations research.
arXiv:2610.11646v1 Announce Type: cross Abstract: German is a morphologically rich language whose syllable structure is exceptionally well-predicted by the Knuth--Liang hyphenation algorithm. We ask whether phonologically informed tokenization can serve as a competitive target for end-to-end speech recognition. We compare three tokenizer families on the Omnilingual ASR wav2vec 2.0 backbone fine-tuned with CTC: the pretrained multilingual character inventory, a data-driven Byte-Pair Encoding (BPE) over orthography, and phonologically informed units from Pyphen syllabification and grapheme-to-phoneme conversion. Across 40 fine-tunes, we evaluate on three German test sets spanning orthogonal shifts: in-domain read speech, dialectal spontaneous speech, and standard-German spontaneous speech. In-domain, all phonologically informed tokenizers match BPE and the multilingual character baseline on both WER and CER. Under domain shift the picture splits along vocabulary size rather than the linguistic axis of variation: at small vocabularies, syllable-aware tokenization improves on dialectal speech, where phonetic surface forms vary but syllable structure is preserved, and stays ahead on spontaneous speech, where new word-forms violate vocabulary closure. A phoneme-level confusion analysis further shows that all tokenizers commit the same canonical function-word errors, indicating that the acoustic encoder, not the tokenizer, dominates the error topology. Our findings suggest that tokenizer choice may depend on the vocabulary budget as much as on the distribution shift expected at deployment rather than reducing to a single universal optimum.
arXiv:2610.11619v1 Announce Type: cross Abstract: We develop a model-free policy gradient method for discrete-time mean-field control (MFC). In MFC, the policy affects the objective both through the controlled dynamics and through the population distribution. Standard REINFORCE estimators capture the first effect but not the second. We introduce Transport REINFORCE, a transport map-based approach that perturbs a suitable transformation of the population distribution to estimate this missing mean-field contribution. The method applies to both finite and continuous state spaces. In finite state spaces, we perturb the population distribution directly on the probability simplex through a convex combination of the current population weights and random weights. In continuous state spaces, we project the population distribution onto the manifold of Gaussian mixtures, and then randomize it via a transport map that ensures the perturbed law remains within this manifold. We prove consistency of the perturbed objective and gradient as the perturbation vanishes, and derive bias and mean-square error bounds for the resulting sample-based gradient estimator. Numerical experiments on several MFC benchmarks show that Transport REINFORCE improves over standard REINFORCE.