Papers

With the growing number of LLMs available, selecting which one to use for a prompt has become a key question. A large part of the routing literature relies on semantically embedding prompts into a vector space and then applying a lightweight classifier to the embedded representations. These methods perform robustly in-distribution but they struggle to generalize to unseen tasks. By studying the geometry of semantic embeddings, we trace a clear failure mode: features that determine the neighbors of unseen prompts are an unreliable proxy for LLM selection. We therefore replace the semantic embedding with the following map: we run a partial forward pass of Qwen2.5-7B-Instruct on the prompt and use the hidden state of its last token at a deep layer as the representation. When applying kNN and other simple classifiers to this new representation, we obtain a clear result in generalization: on average across cost penalties, their performance improves. Moreover, kNN and another simple classifier that we propose outperform every evaluated semantic-embedding baseline. Our two simple methods also beat a recent SoTA hidden-states based router on RouterBench.

Wildfire decisions are made in hours, yet most learned spread models predict daily on targets including burned area. We propose FireGraphNet which formulates 12-hour growth as node classification on directed H3 graphs, with candidates ahead of the front and wind alignment, terrain, fuel continuity and barriers on edges. On satellite perimeters it achieves average precision 1.7-1.9x the strongest distance baseline on test California fires and 1.62x out of state. We show this skill comes from message passing rather than cell features or the aggregator, is highest on young fires in state, is carried deep along the wind by its edges, and is hidden by pooling. A convolutional network matches this ranking once trained on new growth, at worse calibration, so candidate construction, target definition, and aggregation shape conclusions about model skill. Editing fuel and barrier attributes reduces predicted spread more under guided than random placement, extending FireGraphNet to operational intervention analysis.

Scientific imaging data involving medical (e.g., 3D radiographic, microscopic images) and astronomical sensors pose different challenges from natural images. One key challenge is that these datasets are often orders of magnitude larger than natural images. Efficient training and inference on such data is challenging due to the increased hardware requirements, often needing bespoke solutions. Moreover, the relevant objects such as tumors and astronomical phenomena are sparsely distributed with respect to the background information. Standard efficiency techniques like quantization and pruning apply uniform scaling of all regions, potentially compromising the precision/fidelity of predictions. Thus, efficient methods that reduce computational requirements without losing resolution for relevant parts of the data and with uncertainty estimates on predictions are essential. We present Conformal Adaptation with risk guarantees for uncertainty-aware sparse computations. Our formalism is general, spanning dense pixel-level classification and regression tasks where hierarchical models predict at low resolution, certify the signal using conformal risk control, and refine the certified predictions. We benchmark our method on multiple tasks such as 3D medical image segmentation, 2D galaxy flux prediction, and 1D calcium spike rate prediction, achieving $2.5$–$72\times$ wall-clock speedup across the various tasks, including on commodity CPUs.

Full waveform inversion (FWI) is a powerful tool for high-resolution subsurface model reconstruction, but it remains highly nonlinear and ill-posed, especially when the initial model is inaccurate or the acquired data are noisy and incomplete. Annealed Stein variational gradient descent (ASVGD) provides a particle-based Bayesian framework for FWI by approximating the posterior distribution with an ensemble of velocity models, thereby enabling uncertainty quantification beyond a single deterministic solution. However, conventional ASVGD-FWI commonly relies on simple handcrafted priors, such as Gaussian or smoothing assumptions, which are often insufficient to represent complex geological structures. To address this limitation, we introduce a learned diffusion model (DM) as an implicit regularization mechanism within the ASVGD-FWI framework. Instead of explicitly evaluating the diffusion prior density, the trained diffusion model acts as a learned geological projection operator that guides updated particles toward the distribution of plausible velocity models. In this way, the proposed method combines data consistency from FWI, posterior diversity from ASVGD, and structural realism from the diffusion prior. Numerical experiments demonstrate that the diffusion-regularized ASVGD-FWI produces more geologically consistent mean models, suppresses nonphysical artifacts, and yields uncertainty estimates that are more concentrated around structurally complex and poorly constrained regions. These results suggest that learned diffusion priors can effectively enhance Bayesian FWI by improving both inversion stability and the interpretability of posterior uncertainty.

We study packet routing in queuing systems where queues act as selfish, myopic agents that use no-regret learning algorithms to select servers with unknown service rates. To model the small buffers used in data centers, we assume that each server has a single-packet buffer. Even such a tiny buffer already captures the features of buffering: routers can exploit multiple servers while accepted packets remain in service, but packets can occupy servers for multiple rounds, complicating future service and learning. We first analyze a single queue routing packets to $m$ buffered servers with service rates $\mu_1, \dots, \mu_m$. This setting is equivalent to an instance of the recharging bandits problem with geometric recharge. We prove that any no-regret learner achieves a long-run average throughput of at least the Hamacher sum of the server rates, and that this bound is tight. Consequently, a single no-regret queue is stable if and only if its arrival rate is below the Hamacher sum of the server rates. Moreover, comparing against an optimal policy, we show that any no-regret learner is at least $0.77$-competitive, which is also tight. We then study multi-queue systems where $n$ queues with arrival rates $\lambda_1, \dots, \lambda_n$, each at most $\lambda_{\max}$, compete for service from $m$ buffered servers. We show that the smallest overprovisioning factor that guarantees the system to be stable under high-probability no-regret learning is $\frac{1}{1-\lambda_{\max}}$. Equivalently, in terms of the total arrival and service rates, the condition $\sum_{i=1}^n \lambda_i < (1-\lambda_{\max})\sum_{j=1}^m \mu_j$ is sufficient, and sometimes necessary, for stability under no-regret learning. In particular, for $\lambda_{\max} = 1/2$, this improves the upper bound of Abel et al. (EC 2026) from $3$ to $2$, matching their lower bound and resolving their open question.

Before deploying clinical prediction models, their reliability must be assessed to ensure safe use. Errors may arise from distribution shifts between training and deployment or from heterogeneous performance where the model systematically underperforms for certain patient subgroups. Yet most post-hoc diagnostic methods evaluate reliability only at the population level, checking whether the deployment data resemble the training data and whether the model performs well on average, without accounting for heterogeneity that may cause some patients to be disproportionately affected. We propose a unified diagnostic pipeline that combines both perspectives. MED3pa first discovers interpretable low-confidence patient profiles, and Detectron is then applied within each profile to test whether its degradation is associated with a detectable harmful covariate shift. Across three clinical prediction tasks and three injected subgroup shifts in MIMIC-IV, we find that shift detectability itself is informative. An injected age shift, undetectable at the population level, was nonetheless localized to specific degraded profiles, whereas sex- and race-related shifts were detected broadly and therefore offered little guidance for identifying the most affected patients.

Can AI agents carry out research on open scientific problems? We introduce Into the Unknown, a benchmark that provides an agent with a science paper along with a research direction to pursue and tasks it to write a follow-up paper. We work with scientists at US Department of Energy (DOE) national laboratories, who each contribute an unpublished follow-up direction from their own work together with the necessary conditions a submission must meet. While assessing the quality of a follow-up paper is challenging in general, using these conditions to form a rubric makes evaluation more tractable for research problems that have no reference answer. We have nine frontier agents write 15 follow-ups each, spanning quantum computing, plasma physics, computational chemistry, materials science, and scientific machine learning domains. None of the 135 submissions satisfies all the conditions, and 114 fail our integrity check, most often because the paper claims work that was never done or reports numbers that contradict the recorded evidence. Overall, agents readily produce papers that look like follow-ups, but none meets the standard of the domain scientist, leaving substantial headroom. Our code and data are publicly available.

On-policy distillation (OPD) is increasingly studied as a cheaper alternative to reinforcement learning, yet it remains a form of knowledge distillation (KD) that relies on teacher supervision. We revisit OPD from the KD perspective by asking where the teacher's advantage lies along student-generated trajectories. Controlled token flips at teacher-student disagreements directly measure the accuracy gained from teacher corrections. Single-token flips yield a modest average gain on selected failed trajectories, whereas repeated flips raise accuracy from 28.4% to 74.5%, close to the teacher's 76.9%. Gains continue to accumulate with more flips, but mass- and KL-based selection outperform random flips by 15-18 percentage points at counts of similar magnitude. Selective intervention remains useful after OPD, but greater argmax agreement does not consistently improve accuracy across model pairs. We advocate training schedules that learn more valuable teacher corrections while maintaining distributional stability. Controlled flips and fork-resolution analysis evaluate OPD beyond accuracy by measuring which teacher preferences the student acquires and what further correction can recover.

Graph Neural Networks on large graphs commonly rely on in-memory graph storage with ad hoc data processing pipelines for both training and inference. Graph databases provide scalable storage and efficient traversal for graphs that can evolve over time, but their applicability in GNN training and inference are rarely studied. We show that graph DBs can be used in GNN training and inference directly, executing sampling, feature retrieval, and even the full forward pass. We show different GNN training pipelines can perform on-the-fly sampling and retrieval in graph DBs using Cypher. We further provide optimisations that speed up the training process by \~2.5x while maintaining the same accuracy. We illustrate that fully in-DB inference is possible, independent of how the GNNs are trained. Our inference setup can be >10x faster than cold loading the graph into RAM with no extra memory overhead on real-world graphs. Our work lays the foundation for in-graph-DB GNN training and inference.

Tokenization is an essential preprocessing step in almost all large language models (LLMs). One of the most popular frameworks is BPE tokenization, which consists of special token segmentation, pretokenization, and byte-pair encoding (BPE). However, existing algorithms are sequential, with each stage only processing complete output from the previous stage. In order to reduce latency and memory footprints, recent works (Jiang and Gong, ICML 2026) (Li, Yang and Mamouras, ASPLOS 2026) (Mamouras, Li and Yang, PLDI 2026) have initiated the study of online algorithms for subroutines such as pretokenization and BPE with a goal of streaming input to output as the input arrives online. However, the search for efficient online tokenization remains open. In this work, we formalize and resolve online tokenization. We introduce the notion of delay for online tokenization which characterizes the extent to which the algorithm output lags behind the (possibly computationally intractable) optimum. We give a near-linear time algorithm with optimal delay (up to constant factors). We complement this algorithm with a conditional lower bound: unless $\mathbf{P} = \mathbf{NP}$, there is no polynomial time algorithm that beats the delay of our algorithm by more than a constant factor. We implement a practical variant for tokenizers from OpenAI's tiktoken and HuggingFace's tokenizers. We obtain a $7.9\times$-$34.8\times$ latency advantage (measured as time to first token) over tiktoken (as well as the recent gigatoken tokenizer) and our implementation maintains approximately constant memory usage independent of input size. Our implementation also achieves a $2.4\times$-$7.0\times$ improvement in throughput over tiktoken and $15.8\times$-$38.1\times$ over tokenizers.

How well can a language model turn a large, incomplete and partly contradictory body of documents into a plan when no single correct answer exists? We introduce Mission Analysis (MA)-Bench, built on mission analysis, the first step of military operational planning, in which a staff reads the full situation and states the problem before anyone proposes a solution. Its 10 expert-built scenarios pair synthetic packets of ten to twelve documents with 1,257 expert-written pass/fail requirements, each containing information on their source, question type, and importance level. A reasoning-model judge grades each brief against the requirements without seeing the documents; it grades like a fifth credentialed planner, leaving a four-planner panel's agreement unchanged (Fleiss $\kappa$ 0.42 to 0.41), and a judge from a second provider reproduces the model ranking (Spearman 0.94). Across twenty frontier and open-weights models the best gets 62% of the rubric items right. Models are strongest on facts stated in the documents (58%) and weakest on judgments that must be inferred (33%), and six failures in ten are omissions rather than errors. MA-Bench grades the determinations, not the prose. We release the packets, rubrics, prompts, scorer and every graded brief with item-level verdicts.

This paper extends the applicability of probabilistic graphical models to non Gaussian data. It establishes a characterization of the pairwise Markov property in undirected probabilistic graphical models in terms of copula densities. Building on this characterization, we derive a necessary condition for the pairwise Markov property in Student copula Markov networks. An Expectation-Conditional Maximization algorithm (ECM) is provided to facilitate the penalized maximum likelihood estimation and graph selection. The performance of the proposed algorithm is evaluated through simulation studies, which demonstrate its effectiveness in estimating model parameters and recovering the underlying graph structure.

Indirect prompt injection uses untrusted retrieved content, tool outputs, or agent messages to override an LLM's intended behavior. We show that defense robustness is channel-conditioned: the same attack succeeds 18% of the time as a follow-up message but 53% when placed in retrieved context. We propose TRACER (Trace-Regularized Adversarial Channel Exposure with Reward-shaping), a channel-aware adversarial training method that samples presentation wrappers and combines an answer-anchored, evidence-gated reward with ATRC, which aligns attacked reasoning with clean evidence when an injection is invalid. On GSM8K with Qwen2.5-3B-Instruct, TRACER reduces RAG-framed ASR from 65.5% to 6.1% while preserving 78-82% clean accuracy. Joint RAG+tool training achieves 13.9% average ASR across framings at 3B scale, while a single epoch at 7B reaches 9.4%. These results demonstrate that robust defenses must explicitly train and evaluate across deployment channels.

Training from offline data has allowed for substantial progress in domains such as robotics, leading to general-purpose policies that can be easily applied zero-shot or efficiently finetuned for downstream tasks. However, these policies can still have poor generalization, both due to the choice of modeling objective and from learning from a static dataset. In this work, we focus on the challenging task of zero-shot goal generalization, where a policy is evaluated on unseen tasks that require combining its existing knowledge (compositional generalization). An avenue for improving a policy's generalization is by generating new experience with world models; however, such generation has proven difficult for longer horizons. Thus, to alleviate this issue, we propose TD-Aug, which samples from a geometric horizon model and allows for directly imagining novel outcomes that can be achieved by composing existing knowledge. We demonstrate that training on these future outcomes as goals for goal-conditioned BC policies significantly improves generalization in stitching-based OGBench tasks.

Generating novel molecules with desired properties is a central challenge in drug discovery. Although foundational work focused on de novo generation, practical use cases require a more complex setting: conditioning on an initial seed molecule, optimizing multiple properties, and operating in data-sparse regimes. We introduce PairIT, a flexible training framework for autoregressive transformers over SMILES sequences that enables seeded generation by learning from pairs of structurally similar molecules. By leveraging matched pairs, the model learns to generate local, chemically meaningful edits that improve a property of the seed molecule. Prompt tokens extend this framework by specifying the target property, desired direction, and approximate magnitude of change. Multiple prompt tokens can be concatenated to enable multi-property optimization at inference time. For properties where pair supervision alone is insufficient, reinforcement learning post-training can further improve optimization, providing a tunable trade-off between proximity to the seed and the optimization objective. PairIT naturally supports pretraining on a large dataset and fine-tuning on a smaller dataset, which is critical for performance in data-sparse regimes. Surprisingly, we observe diminishing returns to the scale of the pretraining dataset. We demonstrate empirically on MoleculeNet and Therapeutics Data Commons datasets that, with appropriate paired-data curation, a standard transformer model of modest size (68M parameters) can achieve robust seeded molecular optimization in low-data regimes.

Structured pruning reduces LLM inference costs by removing model components to produce smaller dense models. However, existing methods can cause reasoning performance to collapse on long-form reasoning tasks such as AIME. We propose LayerTrim, a training-free structured pruning method that identifies redundant decoder layers and selectively trims their MLP features while preserving attention and decoder depth. LayerTrim is the first training-free structured pruning method designed to preserve long-form reasoning without gradients or recovery training. Across three reasoning language models and five benchmarks, LayerTrim outperforms existing structured pruning methods in most evaluated settings, improving average accuracy by up to 21.4 percentage points over RESP. On Qwen3-14B, LayerTrim achieves 1.24$\times$ faster prefill and 19.7% lower peak GPU memory than the dense model, while better preserving reasoning ability. It also achieves the shortest average generation length among evaluated pruned models, while retaining the highest average accuracy. These results demonstrate that LayerTrim improves reasoning efficiency through both structural compression and reduced token generation.

Activation steering controls large language models at inference time, but its effectiveness depends on the choice of reference data. We introduce genesis steering, which derives a genesis vector from contrastive examples in the model's own fine-tuning data. When these data are unavailable, we draw on the membership inference literature to identify likely training examples and construct a proxy dataset. We establish two theoretical results on optimal displacement to the decision boundary and reduced proxy-estimation bias. We evaluate genesis steering and membership-based proxy construction on Tülu-3-8B, whose fine-tuning data are publicly available, and Llama-3.1-8B-Instruct as a control. We find that safety data from Tülu-3-8B's training mixture yield stronger steering than external datasets on both models. On Tülu-3-8B, membership scores largely agree in identifying training examples, and vectors built from top-ranked examples achieve competitive performance against random subsets of the same size. In contrast, the results on Llama-3.1-8B-Instruct hint that a MIA method will only have a positive effect if the mean direction shift with MIA-filtered in-distribution data is much less severe than the direction shift with OoD data.

In-context learning (ICL) allows language models to adapt their behavior from instructions and demonstrations in a prompt, but accuracy alone does not reveal how contextual information controls their predictions. We study the acquisition and trainability of ICL with a controlled diagnostic that separates copying a nearby demonstration from integrating information across the prompt. Across 17 models, about a third prefer the copied answer, a few are undecided, and the rest prefer the rule-consistent answer, which goes with higher accuracy and with control by the requested value rather than the closest conflicting example. Checkpoint analyses show that models begin prioritizing task-relevant prompt tokens over conflicting examples long before their accuracy improves beyond chance level. In matched training experiments, synthetic documents that define endings and then query them shift models toward compositional responses on the controlled diagnostic, whereas fine-tuning on definition exercises built from rewritten real documents improves accuracy when prompts reassign label meanings. The results suggest that ICL is not acquired as a single, uniform capability. Instead, prompt control, answer preference, construction without candidates, and transfer can develop along distinct trajectories.

Learning an individualized treatment rule (ITR) with many treatments requires estimating treatment-specific effects from limited observations per arm. Treatments with similar conditional responses can share information, but linear contrast models may miss nonlinear heterogeneity. We propose nonlinear supervised clustering fusion (NSCF), a neural Q-learning framework with a shared nonlinear covariate representation and low-dimensional treatment embeddings. Pairwise fusion groups treatments with similar learned contrasts, yielding an ITR and an interpretable partition. An alternating algorithm combines neural training, embedding fusion, validation-based partition selection, and unpenalized grouped refitting. NSCF lowers regret relative to a strong neural reference in nonlinear exact-sharing simulations; perturbations characterize the limits of hard sharing. In a melanoma xenograft application, NSCF improves average policy value over the neural reference. These results support nonlinear representation learning with supervised treatment fusion when treatment effects exhibit shared structure.

Group-based reinforcement learning enables large language model agents to learn from sparse outcome rewards in long-horizon tasks. Recent methods derive step-level credit by comparing observation-matched experiences across trajectories. However, identical observations can occur in different contexts, and matched peers are not equally informative for a given decision. Moreover, favorable terminal outcomes can obscure redundant actions or detours within successful trajectories. To address these two challenges, we propose Contextual Credit Policy Optimization (CCPO). For the first, CCPO weights observation-matched peers from other trajectories by contextual similarity, computed from frozen LLM representations and accumulated trajectory statistics, allowing peers from similar contexts to contribute more to a step's baseline. For the second, CCPO pairs historical credit, which compares the realized return against the weighted peer baseline, with future credit, which measures the change in contextual outcome value over a short realized continuation. A step is thus credited for the progress it makes, not only for its trajectory's eventual outcome. Both credits are computed in hindsight from rollouts already collected for training, enabling CCPO to address these challenges without an auxiliary value critic. Across two Qwen2.5-Instruct backbones (1.5B and 7B), CCPO achieves up to 97.4% success on ALFWorld and 79.4% on WebShop and outperforms GRPO by up to 21.6 and 18.5 points. Ablations show that contextual weighting outperforms uniform weighting, and that historical and future credit serve as complementary learning signals.

Chatbot Arena ranks language models with the Bradley-Terry model, which gives each model one score and so assumes Luce's choice axiom. Choice theory predicts where this fails: near-copies are told apart more decisively than their scores imply. On 1.8 million Arena votes, votes between versions of one model are 1.37 times as decisive as Bradley-Terry predicts, between sizes of one generation 1.26 times and between models of one lab 1.12 times; a release a year later gives consistent multipliers, and the effect survives alternative tie treatments, prompt subsets and topics, and timing checks. How alike two models' answers are worded and formatted tracks the effect. A correction with four to six parameters predicts held-out votes better than Bradley-Terry and than models with hundreds of parameters, mostly by modelling ties; frozen and carried to new releases in a test fixed in advance, its gains are concentrated in ties, and better head-to-head odds are not established. The leaderboard order barely moves. With language-model judges and three-answer menus, a near-copy takes votes mostly from its twin when choices are pooled over prompts (log-odds shift +0.10, 95% interval 0.05 to 0.16); within a prompt the shift is smaller and clear for two of four judges.

Automatic prompt optimization (APO) uses feedback from model responses to improve prompts automatically. However, its effectiveness is usually measured through overall scores, which do not reveal which questions become correct, which previously correct answers become wrong, or whether improvements extend to unseen questions. We introduce Reflective Feedback-Driven Prompt Optimization (RFDPO), a tool that tracks recoveries (incorrect to correct), regressions (correct to incorrect), and churn (all changed outcomes). RFDPO uses this feedback to guide subsequent revisions and records prompt changes throughout optimization. We evaluate RFDPO across five benchmarks covering law, knowledge, instruction following, mathematics, and privacy, using GPT-5 as the optimizer and GPT-4o-mini and GPT-4.1 Mini as solvers. Our results show that overall accuracy can hide substantial changes: in five of nine configurations, churn was at least five times the absolute net change, and a single-item net change concealed up to 17 changed outcomes. Average validation gains were 7.9 percentage points, compared with 5.2 points on held-out tests. In a controlled ablation on LegalBench-Hearsay, item-level feedback reduced churn by 40% ($p=0.024$) while maintaining similar net gains. These findings motivate reporting recovery, regression, churn, and performance on unseen data alongside overall accuracy.

Reinforcement learning (RL) has substantially improved the reasoning of autoregressive and discrete-diffusion language models. Language models that generate continuous token embeddings are emerging as a strong alternative, but RL post-training for them remains understudied. We propose \method{}, a post-training framework for continuous flow language models. Such a model denoises token embeddings over multiple steps and decodes them into discrete tokens only at the last step. To obtain pathwise gradients, which backpropagate through continuous actions and have much lower variance than REINFORCE, we introduce a critic that estimates the value of intermediate token embeddings, bypassing the non-differentiable decoding step. The critic must also keep track of the value function as the policy changes; to this end, we design a critic that predicts a value from every token representation and improves policy optimization. Across four reasoning tasks, \method{} reliably improves a continuous flow language model through RL post-training and outperforms baseline methods of the same type.

Reliable uncertainty quantification remains an important challenge in AI. Hierarchical Bayesian methods provide a principled framework for this by representing unknown quantities through posterior distributions. Joint inference of neural-network parameters and prior hyperparameters is challenging for conventional Markov chain Monte Carlo (MCMC) methods due to strong dependencies. In this work, we introduce the multilevel particle marginal Metropolis-Hastings (MLPMMH) method, which combines pseudo-marginal inference for the hyperparameters with coupled sequential Monte Carlo (SMC) across hierarchy of network-width truncations for conditional parameter inference. The hierarchy is induced by a trace-class neural network (TNN) prior with width-dependent decay, motivated empirically by the compressible structure observed in trained neural-network parameters. Under standard multilevel coupling assumptions, we establish that MLPMMH achieves mean-square error (MSE) $\mathcal{O}(\varepsilon^2)$ at expected computational cost $\mathcal{O}(\varepsilon^{-2})$, and verify the predicted rate on a Bayesian regression problem. To address larger-scale applications, we further introduce S-MLPMMH, a practical approximation that replaces the exact sampling components with a PCA-based hierarchy and scalable Bayesian Monte Carlo. Experiments on MNIST demonstrate competitive predictive performance and uncertainty quantification while exploiting the parallel structure of the approximation. Software has been made publicly available at https://github.com/submission-code-anon/mlpmmh-anon.

Generative retrieval (GR) has emerged as a strong candidate generator for sequential recommendation as language models and semantic-item identifiers have improved. However, GR is not a uniformly stronger replacement of dense retrieval (DR) in online retail candidate generation. We examine their differences on two Amazon Toys datasets under different metrics. GR leads on best relevant item value among users both methods cover, while DR leads on exact-target recall and relevant value across the ranked list. With deep analysis, we find that popularity contributes the most to GR's measured value lead. Adding the same static item value to DR in one reranking step reverses this lead and keeps recall above GR. Finally, on an industrial-scale internal e-commerce dataset with LLM-judged relevance, we show that a 14B SID-LLM still underperforms a $47\times$ smaller dense encoder.

Training large language models (LLMs) across geographically distributed and poorly interconnected compute pools or data centers has become a topic of significant interest. This has led to increased study of local optimization methods such as DiLoco for LLMs, especially those that use local (or inner) adaptive or preconditioned optimizers, which are critical for high-performance LLM training. However, a central challenge remains: it is well known that increasing the number of model replicas (replica scaling) while fixing the total training budget leads to monotonically decreasing performance. Existing work has empirically demonstrated that the choice of inner optimizer (Muon v.s. AdamW) can significantly improve this trend, but offers only limited explanation of the performance difference. In this work, we consider a range of inner-optimizers and identify two important factors that impact replica scaling: (1) the covariance structure of the pseudo-gradients and (2) the impact of batch size on the pseudogradient's noise scale. Based on these insights, we theoretically and empirically demonstrate that whitening-based pre-conditioning is a powerful inner-optimizer desideratum. Our empirical evaluation extends the results to reveal that whitening-based inner-optimizers achieve strong replica scaling (for 8-96 replicas), with performance relative to DP improving as parameters and data are scaled.

Compartment models of infectious diseases are often linear in coefficients that are physical parameters or products or ratios of them. We exploit this with closed-form least squares and equip the estimates with distribution-free uncertainty. Physics-informed regression (PIR) fits the parameters to finite-difference derivatives of the data; we introduce physics-informed weak regression (PIWR), which integrates the model in time instead, needs no derivatives of the data, estimates the initial state jointly and is high-order accurate. To quantify uncertainty we wrap both estimators in split conformal prediction, with a calibration population generated by the physics-based model itself, giving simultaneous intervals for all parameters with a finite-sample coverage guarantee. A residual-adaptive factor, computed without ground truth, scales the intervals to each data set (PIWR-RACC). On the eleven benchmark models of disease-informed neural networks (DINNs), PIWR or PIR-FD6 is one to four orders of magnitude more accurate than the reported DINN results wherever the sampling resolves the dynamics, in about a millisecond per fit instead of minutes to hours of training, and the 90% intervals achieve 87-92% coverage in all 88 settings. On the S3I3R model of the original PIR study, PIWR lowers the reported PIR errors by about three orders of magnitude. On real data from the 1978 boarding-school influenza outbreak, a variable-projection variant gives calibrated 95% intervals that overlap those of a Bayesian analysis. On a time-varying transmission benchmark, a B-spline expansion of beta(t) keeps PIR and PIWR linear; they are more accurate than physics-informed neural networks in three of four cases and comparable in the noisiest, with simultaneous bands for beta(t). The complete conformal calibration takes less than two minutes for every benchmark.

Inference of phylogenetic trees from sequences plays a central role in understanding evolutionary relationships, with applications ranging from tracking pathogen spread to reconstructing the history of life. Conventionally, practitioners obtain posteriors over trees using likelihood-based methods like MCMC. However, likelihoods are only available for simple evolutionary models with restrictive assumptions. For realistic evolutionary models, inference using conventional methods is prohibitively expensive, inaccurate, or even impossible. In practice, practitioners settle for using as flexible a conventional method as possible, even though they expect it is misspecified. In principle, we could use simulation-based inference: simulate tree and sequence data from an evolutionary model and train a neural network to predict the posterior over trees given sequences. However it is a mathematical challenge to represent and train complex posterior distributions over trees. Here we present a flexible family of conditional generative models over trees. Our models iteratively build trees using three natural paradigms – top-down, middle-out, or bottom-up – and are trained using a discrete diffusion framework. For real and synthetic datasets of up to $65$ taxa and $>10^5$ tokens, our models recover MCMC posteriors much more accurately than the previous state-of-the-art simulation-based method Phyloformer 2. Finally, we compare to IQ-Tree, a popular flexible-but-misspecified conventional method. Our models match its tree estimates on simple data, but on more realistic data, our method is reliably more accurate.

Coordinators that act on what they infer about teammates are usually certified by the accuracy of those inferences. We argue that accuracy is the wrong certificate, for two reasons. First, the accuracy needed to act depends on what a wrong action costs, so the bar belongs to the deployment, not the module. Second, a module's errors are rarely independent, and dependence has a sign: positively associated errors help where their damage overlaps and hurt where it compounds, so an accuracy threshold fails in a predictable direction, and once wrong beliefs interact and can do harm, no rule based on accuracy is right for every module. We test these predictions in task assignment, Level-Based Foraging and Hanabi, with injected errors, trained and Bayesian modules and five language models, and in human judgments. Accuracy fails in both directions, approving harmful language-model deployments in Hanabi, where shared errors compound, and rejecting beneficial ones in task assignment, where costly errors are rare. In our tasks it also buys far less redundancy than independence predicts: from GPT-5.4-mini to Claude Opus 5.5, error on teammates the models have evidence about falls from 32% to 11%, but the chance that all three observers misread one falls only from 16% to 9% (independence: 3.4% to 0.15%). We propose certifying the deployment, with a Blind-Spot Gate that prices error costs, pairwise interactions and measured dependence without deploying the module. On held-out data from the cells it was developed on, it makes no significant false approval in 20 splits (accuracy: 3.2 per split), and in preregistered tests on modules it was not developed on, it recovers what accuracy rejects (seven classifiers: regret 0.004 against 0.479) and catches what accuracy approves (a Bayesian module: significant false approvals in 17 of 20 splits for accuracy, 1 for the gate).

Information-theoretic exploration is of primary interest in methodological studies of reinforcement learning (RL) and computational cognitive neuroscience, while the established RL theory builds regret guarantees on confidence sets. This situation leaves open the conditions under which the information-driven exploration found in nature is more advantageous than the exploration of the established RL theory. We put the state-of-the-art methods of these two paradigms, Active Inference (AIF) and Bayes-UCBVI, on an equal footing: both act through the same state abstraction of a tabular MDP with $S$ states, and their greedy forms differ only in the exploration term. We find that AIF's information gain decays too fast to serve as a confidence width, locking greedy agents that explore by it out of the optimal action. Calibrating the information gain by a square root yields calibrated AIF, which attains regret of order $\sqrt T$ for an exact abstraction, but no better guarantee than Bayes-UCBVI for a fixed reward. When an adversary chooses rewards from the agent's data, Bayes-UCBVI's value-specific widths lock out, whereas calibrated AIF pays a factor $\sqrt S$, which no goal-memoryless agent avoids on some MDP whose start states the adversary also chooses. Calibrated information gain thus acts as a reward-agnostic $\ell_1$ confidence set, preferable to value-specific widths when rewards are chosen from the agent's data, not when they are fixed.