Papers

The dynamics of generative models exhibit two apparently distinct temporal windows: a speciation window, in which a sample commits to a semantic class, and a nonlocality window, in which local context windows become insufficient for generation. Motivated by evidence of their near-concurrence in a variety of frontier models, we investigate their relationship through the spatial distribution of semantic information. Under a "common cause" hypothesis, we prove that the nonlocality window must lie in the speciation window. This hypothesis postulates that semantic labels explain a fraction of the correlations between distant tokens, a condition that is natural for many real datasets. We further give conditions under which both windows shrink to a single limiting time as system size grows, defining a "phase transition", and verify this behavior analytically in Gaussian mixtures. Together, these results identify conditions under which semantic information explains the concurrence of speciation and nonlocality, connecting two complementary perspectives on the emergence of semantic structure in generative modeling.

Linear attention replaces growing KV caches with fixed-size recurrent states, yet these persistent states can become a substantial memory bottleneck under concurrent serving. Directly quantizing recurrent states to low precision often leads to severe accuracy degradation, as quantization errors propagate through successive state updates. We discover that the impact of these errors depends on two complementary dimensions: temporally, errors in long-lived memory can persist across many decoding steps; spatially, errors in different key rows affect model outputs differently, while state magnitudes vary substantially along both rows and columns. Motivated by these observations, we propose STEPQuant, a spatial-temporal post-training quantization framework for Delta-rule recurrent states. STEPQuant allocates precision according to error magnitude and memory lifetime, and jointly fits key-row and value-column scales based on state distributions and key-row impact on output error. Experiments on Qwen3.8-27B and Kimi-Linear-48B-A3B-Instruct across both long- and short-generation benchmarks show that STEPQuant closely matches FP32-state accuracy under a nominal 6-bit budget and outperforms uniform INT8 in its 4-bit configuration. Integrated into SGLang with optimized GPU kernels, 6-bit STEPQuant achieves over 5x recurrent-state compression and reduces total serving memory by up to 68.7%. Our code is available at https://github.com/Dreamer-Toby/STEPQuant.

Recent LLMs increasingly adopt hybrid designs that replace standard attention with linear attention, such as Gated DeltaNet (GDN) and Kimi Delta Attention (KDA). Although they compress the context into a fixed-size recurrent state and substantially reduce the cost of long-context processing, repeatedly reading and updating that state remains a major inference bottleneck. Quantization offers a natural way to reduce this cost, but can significantly degrade model quality, due to the accumulation of rounding errors and the presence of outlier rows and columns in the state. To address these challenges, we propose LeapQuant, a training-free method that achieves near-lossless performance under 8-bit recurrent-state quantization. First, to mitigate error accumulation, we propose per-window quantization, which leaps over a window of tokens and quantizes the state only once at its end. Within a window, outputs are computed from the fixed low-bit state together with high-precision buffered updates. Second, to reduce the error introduced by each quantization, LeapQuant retains the state's largest outliers as a few high-precision Compensator Tokens, which share the update path of real tokens. We then smooth the remaining residual before quantization to further reduce the error. Comprehensive experiments across the Qwen, Kimi, and GLM model families show that LeapQuant substantially reduces memory and compute costs during inference. With accuracy comparable to the FP32 baseline, it achieves average speedups of 2.05–3.70$\times$ at the kernel level and 1.47$\times$ for end-to-end inference on NVIDIA B200, RTX PRO 6000, and RTX 5090 GPUs.

The landscape of satellite imagery time series datasets and boundary-pushing architectures for cropland segmentation has never been richer. However, in this gold rush, important truths are being missed on both fronts, as a drive for the most novel concepts or the largest datasets pushes finer details to the side. In this paper, we present our hybrid transformer-convolutional model, Cropland Parallel Attention and Refinement Network for Segmentation (PAtteRNS), the first model to use self-attention mechanisms separately for each of the temporal, spectral, and spatial aspects of Sentinel-2 multispectral SITS data. To achieve fully-factorised attention in our proposed model, we introduce a novel parallel transformer architecture which significantly reduces the computational complexity of triple-factorised self-attention. We validate our architecture with an in-depth ablation study, and analyse the performance of our model against state-of-the-art crop segmentation models on multiple tile-size variants of the popular PASTIS and MTLCC datasets. Our findings show our model to outperform all others in the task of crop class segmentation, verified across multiple important segmentation metrics, with especially strong performance against compared models seen in the often under-reported parcel delineation quality, for which we use the Boundary IoU metric. We also find that flawed class groupings within datasets can have a significant negative impact on model performance, and report that alternate tile-size variants of crop segmentation datasets produce results incomparable to one-another, invalidating fair comparison between model performance when trained on different tile-sizes. Based on these findings, we suggest further work is required to standardise best practices when constructing SITS crop segmentation datasets, and to enable future dynamic-tile-sizing for ideal model performance.

Evaluations of graph reconstruction by language models typically report a single aggregate distance between the original and the reconstructed graph. We prove that for the Wasserstein distance between Laplacian spectra such a summary is bracketed by two edge counts, the net change in edge number from below and the symmetric difference from above, each scaled by $2/n$ where $n$ is the number of vertices. The bracket is sharp: its two ends coincide exactly when the reconstruction only adds edges or only deletes them, and on that class the distance is a rescaled edge count that says nothing about which edges changed. When the ends differ, the residual between the distance and the lower end is positive only if the reconstruction both invented and lost edges, which turns it into a certificate of mixed editing computable from the reported summaries alone. We characterize these regimes in 135 reconstructions produced by three open-weight models over 45 synthetic graphs. Seventy-seven outputs are one-sided and 29 mixed outputs have $X > 0$, including cases where edge count is exactly preserved while nineteen edges were simultaneously invented and lost. The three models differ in editing policy, ranging from copying the input to attempting completion at the cost of large hallucination volume, a distinction that aggregate distortion does not reveal.

Answering questions about long videos often requires connecting events involving the same objects across hours or days. Chronological descriptions and text-derived entities can leave physical identity unresolved: different objects may share a description, while observations of the same object remain disconnected across events. Retrieving relevant events therefore does not necessarily recover the "biography" of the particular entity a question concerns. To address this, we introduce Grounded Entity Biographies (GEB), a long-video memory framework that groups visually grounded observations of the same physical instance across clips into retrievable biographies while preserving the context of each moment. During question answering, the biography is retrieved alongside episodic evidence, allowing the model to follow an entity through events using identity links established during memory construction. Evaluations across four benchmarks, including day-long and week-long recordings, demonstrate improvements over prior memory frameworks in both multiple-choice and open-ended question answering. On EgoLifeQA, GEB achieves 72.0% accuracy, 4.4 percentage points above the best published result. Ablations show that grounded identity association and biography reading both contribute to the gains, which additional descriptions alone do not fully recover.

Agent performance depends on both reasoning ability and the environment in which it acts. We study test-time AI-for-AI, asking how a Builder can learn to construct better execution environments for a Target while both models' weights remain fixed. To make the Builder's experience reusable, we introduce Meta-Skill: principles specifying when support is needed and what resources to provide. The Builder learns these principles from Target's execution feedback on the development set, then uses the frozen skill bank to construct harnesses for unseen tasks. Across Harness-Bench and NewtonBench, full-bank meta-skills improve macro-average performance by 8.95 percentage points over no-skill construction, and 12.02 points over direct delivery of the same bank to the Target. These results highlight the value of translating experience into executable support. Gains when the same model serves both roles further suggest a path to system level self-improvement through learning to build better environments.

A small trainable advisor can steer a frozen language-model executor using natural-language advice. In addition to learning from task rewards, the advisor can use feedback from completed interactions to improve its advice. However, a plausible correction need not change execution, yet learning from such corrections can still affect the advisor's future decisions in other contexts. In a shared-parameter model, we prove that such corrections can limit learning if their targets favor useful advice less strongly than those of other corrections. Keeping them less often than the rest improves the model's eventual performance compared to learning from every correction. Motivated by this, our method, Advisor Self-Distillation (AdviSD), pairs outcome-based reinforcement learning with self-distillation from a feedback-conditioned copy of the advisor selectively. Reflection proposes corrections, and the advisor scores the same recorded executor response with and without its issued advice, using the magnitude of the difference to select decisions for supervision. This approach does not require executor likelihoods or additional executor rollouts. Experiments with Qwen3-8B advisors for Gemini and Claude show that AdviSD outperforms advisor-GRPO by 4.2-6.4 percentage points on BFCL-v3 and by 3.9-5.1 score points on EnvScaler. The trained advisors generalize to out-of-domain tasks and transfer across different executor versions and model families. AdviSD also beats matched-count random selection, supporting the value of its selection rule.

Generative modeling is widely used for producing diverse objects from complex, multimodal distributions. However, its expressivity does not, in general, come with formal guarantees that the generated objects satisfy hard constraints or requirements. In multi-agent generation, this problem becomes more challenging because a hard requirement can depend on multiple agents, while each agent may need to determine its own guidance input without relying on the simultaneously computed guidance inputs of other agents. To this end, we introduce DeGG-Flow, a general framework for multi-agent flow matching with decoupled generative guidance. By representing the generative process as a control-affine dynamical system, we develop guidance conditions for two classes of coupled requirements: shared requirements whose satisfaction depends on multiple agents together, and private requirements associated with each individual agent dependent on its neighbors. For both classes, we establish feasibility conditions and finite-horizon convergence guarantees. We further derive a Wasserstein bound that characterizes the distributional deviation induced by the guidance. We demonstrate DeGG-Flow on multi-robot collaboration for crossing a spatial gap by reconfiguring the environment, and on multi-object scene generation with affordance requirements. Across both applications, DeGG-Flow directly generates objects that satisfy all corresponding hard requirements, including at team sizes unseen during training.

We study average-reward weakly-coupled Markov decision processes (WCMDPs), where a WCMDP consists of $N$ smaller MDPs, called arms, that share multiple per-step budget constraints. We consider the setting where the arms have identical model parameters, multiple actions, and state- and action-dependent costs. For restless bandits (RBs), a well-studied special case of WCMDPs, prior work has developed policies that achieve an $O(1/\sqrt{N})$ optimality gap under general conditions, and has further identified conditions under which policies can achieve a better-than-$1/\sqrt{N}$ optimality gap. However, for general WCMDPs, no prior result achieves an optimality gap better than $1/\sqrt{N}$. In this paper, we identify conditions analogous to those for RBs under which a better-than-$1/\sqrt{N}$ optimality gap is achievable, and design a policy that attains an $O(1/N)$ optimality gap. Notably, unlike prior approaches based on generalizing priority orderings, our policy is not priority-based but rather is designed to induce locally linear mean-field dynamics.

KV cache memory and bandwidth costs grow with context length and batch size, which limits efficient long-context inference. To address this bottleneck, we introduce WUSH-KV for low-bit KV-cache quantization. It adapts WUSH, which constructs a data-aware transform from the second-order statistics of both factors in a matrix product to reduce quantization error. WUSH-KV uses calibration data to construct separate key and value transforms, with the value transform folded into the model weights and the key transform applied after RoPE. The transforms can be paired with clipped quantizers. For one such quantizer, QuEST INT, we show that, under mild assumptions, the WUSH transform is near-optimal. With this quantizer, WUSH-KV reduces layerwise reconstruction error and achieves the lowest end-to-end perplexity among other tested transforms. For end-to-end evaluation, we integrate WUSH-KV into SGLang using OSCAR-style percentile-clipped affine quantization. At 2-bit, WUSH-KV performs comparably to or outperforms the OSCAR transform across all evaluated models and downstream tasks.

Many applications of black-box predictive models require controlling task-relevant error rates, such as missed lesion pixels in segmentation or missed labels in multilabel classification. Conformal risk control (CRC; Angelopoulos et al., arXiv:2208.02814) gives distribution-free guarantees for such losses, but it calibrates a single threshold shared by all inputs. Because conditional risk varies with the input, this marginal guarantee often overprotects easy cases and underprotects hard ones. We propose ReCIRC (Rectified Conformal Risk Control), which inverts each input's estimated local risk curve to reparameterize the calibrated threshold as a risk budget $a$ representing a common target conditional risk, and then applies CRC unchanged to the resulting family. ReCIRC retains CRC's finite-sample marginal guarantee regardless of the accuracy of the estimated curves, while accurate curves yield approximate conditional risk control and, under additional conditions, asymptotically exact conditional risk control; they also support a risk-calibration diagnostic. Across three synthetic and five real-data settings spanning segmentation, multilabel and multiclass classification, and regression, ReCIRC attained the lowest average worst-group risk and mean positive group excess in every setting, while maintaining marginal risk close to the target, whereas changes in prediction size were application-dependent.

The attention operation is naively position invariant. However, positional information is fundamental to natural language, and therefore a variety of explicit position encodings have been developed in transformer-based models, such as rotary position encoding (RoPE). Although explicit position encodings have long been assumed to be required, recent methods that interleave local mixing layers, such as sliding window attention (SWA) and gated linear attention, while not encoding position (NoPE) in global attention layers has recently been shown to be successful at scale. How and why this approach works is not well-understood. In this paper, we develop an explanation of how hybrid models of this sort can implicitly encode position at global NoPE layers. Supported by both theoretical and empirical evidence, our central argument is that SWA and gated linear attention induce a recency bias in the residual stream that propagates to, and is selected by, the global attention logits. Moreover, in contrast to the implicit position encodings found in models with only global NoPE attention, in which positional information arises solely from the causal mask, the recency bias in hybrid models can be maintained across long sequences. In addition to deepening our understanding of how hybrid models encode position, these findings may provide insights for how to encode position in a way that can extrapolate to longer sequence lengths indefinitely.

Large language models (LLMs) enable agents to solve long-horizon tasks by generating a plan and then executing it in an environment. However, successful planning requires two distinct capabilities: selecting an appropriate plan for the task and executing it faithfully. Existing planner–executor systems can fail at either stage, while final task success alone cannot distinguish selection from execution failures. We therefore study the Plan Declaration–Execution Gap and introduce Planning-as-Routing, where an LLM declares one of four planning modes: Predefined, Sequential, Hierarchical, or Search, and a deterministic router dispatches the task to the corresponding pattern-specific executor. Across four benchmarks and three LLMs, we find three consistent patterns. First, generic Plan+ReAct often fails to preserve declared planning structure, especially for longer plans: across three benchmarks, only (22)–(45%) of trajectories preserve it, whereas pattern-specific executors enforce the intended structure. Second, planning-mode effectiveness varies across environments and models: Search performs best on ALFWorld, Hierarchical on SWE-bench, and the strongest pattern can vary across models within the same benchmark. Third, the largest gains come from execution: pattern-specific executors improve task success from (0.48) to (0.92) on ALFWorld and from (0.36) to (0.44) on SWE-bench Verified over Plan+ReAct. Current LLMs, however, do not reliably select the strongest mode for each task, although few-shot examples improve selection in some benchmark–model combinations. Overall, reliable agent planning requires both effective mode selection and faithful execution: routing substantially closes the execution gap, while task-specific mode selection remains open.

Power-sharpened sampling is an inference-time alternative to reinforcement-learning (RL) post-training for enhancing reasoning in large language models (LLMs). High-probability sequences are amplified under the base model without parameter updates or external rewards, avoiding the costly optimization and jagged generalization of RL. However, this approach faces a fundamental exploration–exploitation trade-off, as % strong sharpening restricts exploration, trapping samplers in plausible but incorrect reasoning trajectories, whereas weak sharpening leaves the answer distribution diffuse. To resolve this trade-off, we introduce Parallel Power Tempering (PPT), instantiating power-sharpened LLM sampling via parallel tempering. Running multiple interacting replicas in parallel at different sharpening levels allows lower-power replicas to explore diverse reasoning trajectories and higher-power chains to further exploit higher-likelihood responses favored by the sharpened target. Specifically, we tailor \method{} to inference-time sampling by mitigating a truncation bias, identified in prior power samplers, and investigate effective swap strategies under finite memory and compute budgets. Extensive experimentation shows that \method{} substantially improves single-chain power-sharpened sampling and outperforms RL-post-trained models, producing higher-quality reasoning traces and even achieving performance comparable to frontier models.

Policies with similar mean returns can differ sharply in rare failures, yet estimating lower-tail conditional value-at-risk (CVaR) accurately can require many costly rollouts. When different conditional components of a stochastic workflow can be queried separately, we ask how to allocate a fixed evaluation budget to estimate a fixed policy's CVaR most accurately. We derive a tail influence for each queryable conditional law that aggregates how its uncertainty affects CVaR across every Bellman reuse. Its variance yields the fixed-design efficiency bound and the oracle Neyman allocation. Tail-Influence Sampling (TIS) estimates these influence scales from a pilot model and reallocates fresh queries toward kernels that matter most for the tail; a visitation-anchored variant protects against pilot underallocation. Under fixed dimension and a positive quantile margin, TIS attains oracle asymptotic variance and first-order MSE including pilot cost, while the anchored variant is within a factor two of the oracle. We also characterize an exact-grid regime in which tail- and mean-optimal allocations coincide. On CliffWalking, TIS reduces MSE by 41% versus learned occupancy and 76% versus complete rollouts at the same charged transition budget. In frozen language-model review workflows, anchored TIS beats an equally regularized mean-influence blend in 23 of 24 MMLU-Pro settings and reaches 2.4-3.4$\times$ lower MSE than rollouts on six-call FinQA reviews.

Backpropagation (BP) dominates deep learning but imposes a massive memory tax. For example, training OPT-30B with Adam requires $\approx$ 600GB of GPU memory (assuming batch size 8 and sequence length 2048). Alternatively, zero-order optimization (ZOO) trains in inference-mode (requiring only $\approx$ 60GB for the same model): no stored activations, no gradients, and no optimizer states. However, ZOO convergence has lagged behind BP. In this work, we evaluate two methods to close this gap. First, we show that reallocating training compute budget from many steps to large effective batch sizes with many perturbations (or probes) but fewer steps, allows 1SPSA (Spall, 1992) to outperform zero order methods like MeZO (Malladi et al., 2023) with less training compute. Next, we introduce 1.5-SPSA, adding a single "clean" forward-pass per step to 1SPSA to calculate a cheap diagonal preconditioner in probe-space, which improves convergence rate and convergence by down-weighting high curvature directions. Benchmarking on 6 post-training datasets on both Qwen3 and OPT model families, we show that 1.5-SPSA achieves State-of-the-Art results over previous ZOO solvers with much less optimization steps. For example, we train OPT-13B (for direct comparison to MeZO) and find 1.5-SPSA achieves +3.1% accuracy on SST-2 over both MeZO and BP in only 70 steps vs. MeZO's 100,000 steps. Finally, we combine an 8-bit-packing random generator, triton fused unpack/apply kernels, and distributed parallelism to achieve fast and stable training of models as large as OPT-30B in-place on commodity GPUs (e.g. A100).

Dimensional homogeneity is a fundamental constraint on physically meaningful models, requiring invariance under changes of units. We present a data-driven method for constructing surrogate models that satisfy this constraint at the level of the hypothesis class. Starting from a dimension matrix of measured variables, the method derives Buckingham $\Pi$-groups, constructs admissible dimensional prefactors, and approximates the remaining dimensionless dependence using truncated harmonic expansions on normalized invariant domains. Once the prefactor and dictionary are fixed, the coefficients are obtained from a regularized linear regression problem. We test the approach on the simple pendulum, Planck's black-body law, the double-pendulum Lyapunov field, and an experimental COBE/FIRAS black-body spectrum dataset. The results show that dimensional constraints improve conditioning, robustness to noise, and sample efficiency relative to unconstrained baselines, while the choice of dictionary becomes important in non-periodic or multi-invariant settings. The learned expressions are explicit and inexpensive to evaluate, which makes them useful as surrogate models for structured physical problems.

Mixture-of-Experts (MoE) models are a compelling architecture for scaling model capacity, making them especially attractive for deployment on resource-constrained, single-GPU systems. However, this benefit is difficult to realize because expert parameters dominate memory, and token-level routing is dynamic, unpredictable, and skewed. Prior work using offloading and caching remains fundamentally reactive, as systems wait for router outputs before moving experts, leading to inefficient cache utilization and an inability to overlap transfers with compute under tight VRAM budgets. To address these challenges, we propose Mira, an algorithm-system co-design that enables high-capacity MoE inference on a single GPU. Mira shifts from a reactive to a proactive stance by coupling predictive expert management with a tailored quantization format. It introduces lightweight per-layer predictors that anticipate expert usage two layers ahead, enabling proactive prefetching. These predictions feed a two-tier HOT+STAGE GPU cache managed by token-level routing telemetry to retain frequently used experts while staging predicted ones. To minimize transfer overhead, Mira implements a custom compression for expert parameters, which reduces metadata and improves packing efficiency, while minimally degrading accuracy. Mira is implemented as a fully integrated runtime that coordinates predictors, caching policies, and quantized transfers to maximize overlap between communication and compute. Our experiments show that Mira reduces expert-induced stalls. Compared against state-of-the-art baselines, Mira achieves a 5.71x speedup in average throughput on a memory-constrained GPU. It accelerates Time-to-First-Token by 11.71x and achieves a 3.84$x average speedup in beam search inference, demonstrating its effectiveness across diverse inference scenarios.

Ship structural vibrations contribute to noise, fatigue, and equipment damage, while dynamic-compliance topology optimization can produce pathological designs near resonance. This study extends neural-reparameterized topology optimization using a convolutional Kolmogorov-Arnold network (KATO) to forced-vibration design with active input power (AIP) as the objective. Applications include a 100 Hz engine-supporting deck panel and an 18 Hz thruster foundation frame. Helmholtz PDE filtering and Heaviside projection control feature sizes and manufacturing tolerance. Across both deck families, all eight optimized layouts reduce AIP relative to size-optimized references and, after finite-depth extrusion, also achieve lower static compliance. For unrestricted, manufacturing-aware, and stress-aware frame variants, KATO matches GCMMA in AIP within 0.5 dB while yielding 22-36x lower static compliance after matched-volume binary re-analysis. In a near-resonant 300 Hz case, both methods reduce initial AIP by more than 32 dB; KATO maintains a connected design, achieves 59x lower binary static compliance, and reduces maximum AIP over 1-500 Hz by 2.7 dB. KATO runs 6.4-10.4x faster than GCMMA for the implemented stress-aware formulations. The results demonstrate neural AIP-driven topology optimization as an efficient approach for designing connected, feature-size-controlled ship structures with improved forced-vibration performance.

On a single task, deep networks can learn many solutions, depending on their optimizer, training data, architecture, and hyperparameters. Many of these solutions are mode-connected: rather than isolated points in weight space, they are connected by low-loss regions. Yet how their internal computation varies within these regions is unknown. A parallel line of work has identified the degeneracy of neural representations: many networks reach similar training loss with distinct internal structures. However, it is unclear how these solutions are related in weight space. We unify these subfields and show for the first time that many different internal mechanisms exist within a local mode-connected region in weight space. To do so, we introduce Hessian Null Space Continuation (HNC), a scalable method that uses local curvature to traverse regions of weight space that preserve network function, and can be steered toward solutions with specified properties. In RNNs trained on a memory task, HNC reaches drastically different representations and dynamics with maintained behavior. In ImageNet-trained Vision Transformers, HNC finds representations that differ more from the original network than any independently trained model with a different architecture or objective. In reinforcement-learning agents, HNC uncovers a distinct navigation strategy at comparable return and exposes reward hacking in an AI Safety Gridworld. Finally, HNC measures the local geometry of the solution set, showing how model size and task complexity shape its dimension and functional sensitivity. Our results show that a surprisingly large amount of representational diversity exists near a single trained solution, unseen by standard gradient-based optimization. HNC identifies and quantifies this diversity, opening new possibilities for mechanistic understanding of solution spaces and for model merging, editing, and fine-tuning.

We study exact learning with membership queries for concept classes $\mathcal C\subseteq\{0,1\}^N$, focusing on the relationships among their deterministic, randomized, and quantum query complexities, denoted $\mathsf{D}(\mathcal C)$, $\mathsf{R}(\mathcal C)$, and $\mathsf{Q}(\mathcal C)$, respectively. The two canonical quantum speedups in this model are witnessed by Grover search and Bernstein-Vazirani, leading to the longstanding conjecture $$ \mathsf{R}(\mathcal C)=O(\mathsf{Q}(\mathcal C)^2+\mathsf{Q}(\mathcal C)\log N). $$ We first refute this conjecture by constructing concept classes $\mathcal C$ and $\mathcal C'$ satisfying \[ \mathsf{R}(\mathcal C)=\Omega\!\left(\frac{\mathsf{Q}(\mathcal C)^3\log N}{\log \mathsf{Q}(\mathcal C)}\right) \qquad\text{and}\qquad \mathsf{D}(\mathcal C')=\Omega(\mathsf{Q}(\mathcal C')^3\log N). \] The first bound matches the upper bound of Arunachalam et al.~[Quantum'21] up to constant factors, while the second matches the upper bound of Servedio and Gortler~[SICOMP'04]. In particular, this shows that the saving in the randomized upper bound of Arunachalam et al. fundamentally relies on randomness. Apart from characterizing the optimal relationship between classical and quantum query complexity, our results are the first to show that quantum speedups for learning can go beyond the Grover and Bernstein-Vazirani paradigms.

Scientific foundation models are commonly evaluated after heterogeneous physical problems have already been translated into a compatible gridded, tokenized or symbolic representation. This leaves the scientific interface outside both the pretrained model and the audit of what is actually reused. We study the complementary setting in which boundary histories, sparse monitor records and loading histories retain their native inference classes and their outputs remain on Cartesian, latitude-longitude and unstructured domains. GEODE couples task-specific scientific interfaces to a shared routed library of wavelet operators. A single jointly pretrained model represents cavity flow, radiation dose and elastoplastic stress, then acquires a heat exchanger and a reactor subchannel by training a private interface containing 2.1% of its parameters. Earlier predictions remain unchanged by parameter isolation, whereas unrestricted fine-tuning degrades them by factors of 14-29. Crucially, preservation alone does not establish reuse: norm-matched randomized-library controls show that the contribution of pretrained computation is conditional on the task and data regime. A separate decomposition shows that full-field relative L2 error can substantially understate error relative to spatial variation when field level dominates the norm. Task-specific operators remain more accurate on three of the five problems. These results distinguish multi-task coverage, preservation and pretrained reuse as separate properties that must be tested independently when scientific foundation models span heterogeneous interfaces.

Discrete diffusion language models can generate multiple tokens in parallel, but reducing the number of denoising steps can lead to inconsistent predictions. Standard cross-entropy training fits conditional token marginals, whereas parallel generation requires consistent joint predictions. We introduce Alpha Diffusion Language Models (AlphaDLM), trained with a sequence-level alpha loss that recovers cross-entropy in the limit of vanishing alpha and has a joint-mode optimum at alpha one. Our analysis characterizes how the objective and factorization jointly determine the fitted distribution. We identify conditions under which intermediate alpha preserves multiple valid completions while excluding invalid token combinations. Trained on TinyGSM, our method achieves 34.6% accuracy on GSM8K with only four model evaluations. We further scale the method to SDAR-1.7B and evaluate it on code and mathematics benchmarks. These results show that changing the training objective can improve the accuracy-computation trade-off of factorized diffusion language models.

Training agents to follow arbitrary instructions is an important goal of multi-task reinforcement learning (RL). Linear temporal logic (LTL) provides a precise and structured formalism for specifying instructions to agents, and has been successfully adopted for training generalist multi-task policies. However, differences in implementations, task distributions, and evaluation protocols make existing methods difficult to compare, while high computational costs limit the scale and statistical reliability of experiments. We introduce Jaxolotl, a unified high-performance benchmark suite for multi-task LTL-RL to address these concerns. Jaxolotl provides a modular, end-to-end JAX implementation of six representative algorithms and four environments, together with newly curated task suites and a standardised, statistically robust evaluation protocol. By precompiling symbolic task representations into static arrays, Jaxolotl enables fully JIT-compiled training and evaluation, achieving end-to-end speedups of up to $220\times$ and supporting controlled comparisons at substantially greater experimental scale. We use this framework to systematically evaluate existing approaches, revealing complementary strengths and limitations: general methods capable of non-myopic reasoning struggle as the number of propositions grows, while methods with stronger scaling rely on environment-specific assumptions and suffer from myopia.

Time Series Foundation Models (TSFMs) currently provide state-of-the-art results in forecasting tasks. They are available out-of-the-box and rely on in-context learning to make their predictions, which makes the quality of their performance highly sensitive to the user-selected lookback, covariates, horizon and training data distributions. In practise, the quality of the forecasts are variable but complementary, which highlights the need for a principled ensembling approach, rather than selecting the best context. This paper introduces Latent Inference-Time Guidance for TSFMs, which adaptively combines a pool of TSFM forecasts through a time-dependent latent space with independent components. The framework comes equipped with identifiability and reconstruction guarantees, whilst maintaining the off-the-shelf aspect of foundation models. We provide experiments on datasets at various frequencies and from multiple domains: these show that the approach is competitive with traditional ensembling approaches.

Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite-dimensional spaces. Functional Flow Matching (FFM) extends Flow Matching to this setting, learning a velocity field whose flow transports a Gaussian prior to the data distribution, but it inherits the independent endpoint pairing of standard Flow Matching: in each batch, prior and data samples are matched arbitrarily, so the conditional bridge must traverse both the shared global structure of the dataset and instance-specific residuals. In function space this is harder to fix than in finite dimensions, since optimal transport (OT) on function spaces is delicate to formulate and a flat Euclidean surrogate ignores the geometry that distinguishes function-valued data. We propose kernel Functional Flow Matching (kFFM), which replaces the independent pairing by entropic OT under a kernel-induced cost, the coupling underlying the Hilbert Sinkhorn Divergence (HSD), leaving the FFM neural-operator architecture unchanged. We prove that the kernel cost and the HSD objective are uniformly bounded and well-posed on Banach ambient spaces, derive an error decomposition against quadratic-cost OT on compact metric spaces that isolates an irreducible kernel-cost mismatch term, and prove a discretization-invariance bound whose rate is governed by Sobolev regularity. Empirically, kFFM improves distributional matching over FFM, diffusion, adversarial, and finite-dimensional OT baselines on time-series and PDE benchmarks, with significant paired-seed gains over FFM and improvements that persist under non-kernel and physics-based diagnostics, including a turbulent Navier-Stokes benchmark. Bounded kernel costs already outperform raw $L^2$ Sinkhorn, and function-space-aware kernels (signature, Sobolev RBF) give further gains on rough or path-valued data.

We give an explicit solution to the five expert prediction with expert advice partial differential equation (PDE) in the finite-time horizon setting. The solution formula establishes that the adversary's rank strategy $(1,0,1,0,0)$ is globally optimal, and the COMB strategy $(1,0,1,0,1)$ is optimal exactly on the set where $x_1=x_2$ and $x_3=x_4$. The formula is derived from the solution of the geometric-stopping problem given in our companion paper through the transform principle of Bayraktar, Ekren and Zhang, which links the two problems by a Laplace transform. Inverting the transform term by term expresses the solution through a series of Gaussian and complementary error function kernels. The optimality of $(1,0,1,0,0)$ is reduced to the signs of $41$ one-variable Gaussian series, which are certified with computer assistance by Poisson summation, first-mode domination and interval arithmetic on $1616$ rational cells. The proofs of our main theorems, certificates included, are also formalized in the Lean proof assistant.

Autonomous vehicles interacting with passengers through natural language must reason beyond immediate commands. Passenger intent may span multiple stages of behavior, depend on future events, refer to surrounding agents or landmarks, and remain relevant as driving conditions evolve. Existing language-enabled driving datasets largely focus on short, localized interactions, leaving these longer-horizon forms of passenger intent comparatively underexplored. We introduce doPlan, to our knowledge the first publicly available, human-annotated real-world dataset designed to study passenger language as persistent task context. Built on nuPlan, doPlan contains 5,154 human-written passenger instructions spanning 169.1 hours of cumulative instruction-aligned context over 50.9 hours of unique driving, with annotation windows ranging from 30.0 to 508.8 s. The annotations capture immediate, deferred, event-conditioned, persistent, and multi-stage passenger intent. The dataset, annotation interface, and supporting resources are publicly available at https://github.com/Mi3-Lab/doPlan. We evaluate four language-conditioned driving models and find that sensitivity to passenger language does not reliably translate into behavior consistent with the requested direction. More broadly, among 2,161 examples with a matched future maneuver, the first associated maneuver occurs a median of 24.6 s after the evaluation point, and only 9.8% occur within the models' common 5 s prediction horizon. These findings highlight the need to connect persistent passenger intent with successive planning decisions. doPlan provides a setting for studying how unresolved goals can be retained, grounded in evolving scenes, and tracked across multiple stages, including how a planner determines when a future goal becomes relevant to the current plan.

On-policy distillation (OPD) trains a student on its own generated responses using dense, token-level supervision from a stronger teacher. Vanilla OPD treats all teacher signals equally, assuming that the teacher's supervision is equally important for every token. However, teacher signals at different tokens may have very different effects on the student's performance: some correct important reasoning errors, while others have little effect on the final answer. Motivated by this observation, we introduce Dr. OPD (OPD Done Right), which defines the optimal weighted OPD to maximize the student's performance. We formulate Dr. OPD as a bilevel optimization problem in which the student learns from weighted teacher supervision, while the weights are selected to maximize the expected reward of the resulting student. To solve Dr. OPD, we develop an efficient iterative solver that updates the token weights and student policy alternatively. At each round, it updates weights in closed form and then takes one gradient step on the resulting weighted OPD objective. Under regularity conditions, we show that this weighted update achieves a higher expected reward than a vanilla OPD update. Empirically, across strong-to-weak and same-size distillation on math and code, Dr. OPD consistently outperforms all evaluated baselines. In particular, in the strong-to-weak distillation setting, Dr. OPD improves average math performance by $9.7$ points over vanilla OPD, and enables the smaller student to surpass its larger teacher.