Papers

Black-box Optimization (BO) is a powerful framework for optimizing expensive objective functions or unknown functions with a limited number of evaluations. A central step of standard BO such as Bayesian optimization is the optimization of a surrogate-based acquisition criterion, which is commonly performed using nonlinear optimization or heuristic search. Therefore, conventional black-box optimization generally does not guarantee global optimality in candidate selection. In this study, we propose Integer Linear Programming-based Black-box Optimization (ILP-BO), a quasi-Bayesian optimization framework that transforms kernel-based surrogate optimization over discrete domains into an Integer Linear Programming (ILP) problem. The key idea is to represent nonlinear kernel functions exactly on finite discrete distance levels by introducing binary one-hot auxiliary variables. This transformation converts the nonlinear surrogate into a linear objective with linear constraints and binary variables. To incorporate exploration while preserving the linear structure, we further introduce a Hamming-distance margin that excludes neighborhoods around previously observed points. We derive the proposed formulation for several standard kernels and obtain an analytical upper bound on the Hamming-distance threshold based on the measure in the binary search space. The resulting candidate-selection problem can be solved by integer programming solvers with certificates of optimality. Thus, our methodology has the potential to serve as a highly transparent black-box optimization framework. Experiments on synthetic and discrete optimization benchmarks show that ILP-BO achieves competitive optimization performance compared with practical Bayesian optimization methods.

As the bridge between protein modality and discrete modeling, protein structure tokenization still largely relies on heavily engineered training objectives tailored to specific downstream tasks and large training datasets, which hinders its transfer to broader application scenarios. To address this issue, we propose ProFiT, a lightweight flow matching tokenizer. With simple training strategies that encourage healthy codebook utilization, ProFiT can be trained efficiently and naturally learns semantically meaningful representations without any manual semantic alignment, while achieving reconstruction quality and generalization that match or surpass those of substantially larger tokenizers. We conduct extensive evaluations across a wide range of settings and demonstrate that ProFiT is a plug-and-play tokenizer adaptable to diverse downstream tasks. This study further reveals the significant potential of the flow matching tokenizer paradigm. Our code is publicly available at https://github.com/QDKStorm/ProFiT.

Offline-to-Online Reinforcement Learning (O2O RL) has emerged as a practical paradigm that pre-trains the policy using static offline datasets and subsequently adapts the policy through online interactions. Existing O2O methods primarily address the transition through value calibration, while generally treating the offline-trained policy as a given initialization. We instead study O2O adaptation from the perspective of network plasticity, asking whether the offline-trained policy remains sufficiently adaptable for online learning. Controlled experiments show that prolonged optimization on static offline data progressively reduces network plasticity even after offline performance has largely saturated, and that lower plasticity is associated with weaker subsequent online improvement. Motivated by these observations, we propose REstoring plasticity via Fresh Initialization and policy Transfer (REFIT), a lightweight model-level method for the O2O transition. Before online fine-tuning, REFIT distills the offline policy into a freshly initialized student while temporarily freezing a random subset of student units, transferring the learned offline behavior to a more plastic policy initialization. Extensive experiments on D4RL and OGBench demonstrate that REFIT consistently achieves higher aggregate performance than existing O2O plug-in methods across both Cal-QL and IQL backbones, while plasticity diagnostics and ablations provide further evidence of restored network plasticity.

Group-relative reinforcement learning (RL) relies on reward variation among sampled responses to estimate informative relative advantages. As language models become increasingly capable, existing training data can become reward-saturated: all sampled responses to the same problem might receive equally high rewards, where the group-relative learning signals vanish and leave previously useful data obsolete. In this work, we investigate whether useful learning signals can be recovered from such saturated data. We study interventions at four levels of group-policy RL pipelines—data, rollout, reward, and advantage—and conduct extensive RL training on saturated reasoning data only. While standard GRPO on saturated data would almost always yield near-0 advantages and near-noise signals, diverse interventions successfully recycle and repurpose such data: among the proposed strategies, interventions at rollout generation are consistently most effective: nudging the policy to generate “high-quality”, incorrect solutions introduces rollouts with poor rewards into saturated groups as negative samples, which turns out to improve GRPO by 6.4% to 9.0% across Qwen3-1.7B and 4B. Other interventions such as increasing rollout temperature or adding auxiliary rewards can also restore non-zero advantages, but yield less consistent gains. Further analyses show that effective negative rollouts require informative negative trajectories, that the method remains effective alongside unsaturated data, and that it supports iterative recycling of newly saturated examples. While increasingly stronger LLMs would render more data as saturated, our results demonstrate that don't waste your saturated data: with the right strategies they can be recycled into useful RL training signals in an increasingly data-scarce world.

Electrical distribution grid operations require inference across heterogeneous networks from sparse, noisy, and incomplete time series measurements. In this work, we identify challenges and explore solutions towards a unified model that can perform diverse tasks grounded in the physics of the electric grid and generalize to unseen distribution networks. We define a unified grid ontology that represents variable sized distribution networks as heterogeneous graphs while preserving native topology, asset types, and electrical relationships across networks. We develop a physics based data simulation pipeline that combines reference and procedurally generated distribution networks with network reconfigurations, fault scenarios, and configurable sensing conditions. We present Mycelium, a heterogeneous graph transformer with structure aware communication edges and electrical reference features that encode network position and nominal phase orientation, together with task specific temporal readouts which generate per task outputs. We train Mycelium on reference as well as synthetic grids, and study its generalization on benchmark networks completely excluded from training and validation. Mycelium is observed to outperform task specific neural baselines on most reported benchmark metrics. Architectural ablations and the aforementioned studies reveal Mycelium's capability to learn representations of the underlying physics which serves to enhance cross-task performance, thereby addressing a significant challenge in unified grid models.

Multimodal large language models (MLLMs) can now interpret a standard ten-second, twelve-lead electrocardiogram (ECG) with clinically grounded, reward-verified reasoning. Real cardiac monitoring is different. Ambulatory (Holter) and telemetry recordings span hours to days and are read as they stream in, and their clinically decisive findings are paroxysmal, brief episodes buried in an otherwise unremarkable trace. Such a recording cannot be held in one context at diagnostic resolution, and its future has not yet happened, so a reader must work online, deciding what to measure now, committing evidence to memory as it passes, and reporting events as they occur. We recast long-duration ECG interpretation as a long-horizon, online (streaming, causal) sequential decision process and introduce ECG-Scroll. As a benchmark, long ambulatory recordings are streamed to an agent chunk by chunk, and it must localize, quantify, and promptly flag paroxysmal events without access to future signal; because the underlying signal is retained, every answer is checkable against objective ground truth, giving rule-based rather than judge-based rewards, and the streaming formulation adds a metric batch evaluation cannot express, the detection latency between an event's onset and the moment the agent records it. As an agent environment, it is a fixed, gym-style interaction layer that exercises three competencies single-glance ECG models never touch: Memory, Tool use through signal-grounded measurement rather than reading pixels, and Planning of what to measure now and when to commit. We release 390 whole-recording instances spanning 2,536 hours of two-lead ambulatory ECG and evaluate a signal-threshold rule agent alongside off-the-shelf LLM agents online, characterizing how they use memory, tools, and planning and where the benchmark's head-room lies.

For decades, statistical inference has largely been developed one problem at a time. Given a scientific target, such as a treatment effect or a regression function, statisticians design a problem-specific estimator together with a procedure for quantifying its uncertainty. This paper proposes a different paradigm. We focus on a classical problem in statistical inference, confidence interval construction, and develop TabCon, an amortized inference system built on a tabular foundation model that produces confidence intervals for new datasets through a simple forward pass. The key methodological ingredients of TabCon are a sparse mixture-of-experts architecture and reinforcement-learning-based post-training that calibrate the resulting confidence intervals to a desired coverage level. Across a wide range of benchmark datasets, TabCon attains near-nominal coverage while producing short confidence intervals. At inference time, it also offers considerably greater computational efficiency, running 50 times faster than the classical bootstrap procedure, even when the latter uses only 50 bootstrap samples.

Gaussian process stochastic differential equations (GP-SDEs) provide a flexible Bayesian model for unknown continuous-time state dynamics with uncertainty quantification, but learning and inference from noisy and irregular observations remain computationally challenging. To address this issue, we propose GP-SDE Matching, a simulation-free variational framework for Bayesian GP drift learning and continuous-time state smoothing. We analytically marginalize the sparse GP posterior to derive a tractable drift-matching objective that accounts for both the posterior mean and uncertainty of the unknown drift. To handle irregular observations, we further introduce an irregular-time-aware variational state posterior that incorporates the actual observation times during both encoding and continuous-time marginal querying. Experiments on the stochastic Lorenz–63 system demonstrate substantially improved drift recovery and state reconstruction under irregular observations, while five system identification benchmarks show robust forecasting under increasing observation sparsity and competitive performance against existing latent-SDE and state-space methods.

Joint-Embedding Predictive Architectures (JEPAs) provide a framework for learning compact representations without directly reconstructing high-dimensional observations. However, in parameterized physical systems, learned representations can entangle geometry with operating conditions and task-specific physical responses, limiting their reuse across prediction tasks. We introduce D-JEPA (Design-recoverable JEPA), a geometry-centric JEPA that computes a compact representation from geometry alone and reuses it across operating conditions and physical response spaces through lightweight physics-specific decoders. An explicit design-recoverability objective encourages the geometry latent to preserve information about the underlying design variables, enabling the representation to support design analysis and optimization. We further identify a case-level collapse failure mode in which target representations become nearly invariant across distinct geometries despite low reconstruction error, and mitigate it using case-level variation constraints and auxiliary target reconstruction. Across four 3D aerodynamic, hydrodynamic, and structural benchmarks, D-JEPA maintains or improves full-field prediction accuracy while achieving near-perfect linear recoverability of design parameters. The frozen geometry representation can be reused at held-out operating conditions and transferred to a structural response task with fewer trainable parameters. Finally, the representation supports differentiable design optimization, with designs validated using high-fidelity CFD, preserving the predicted ranking of candidate designs. These results demonstrate that separating a reusable geometry representation from physics-specific prediction provides a practical representation for scientific surrogate modeling and design.

Pretrained macro-placement policies can reduce repeated optimization across circuits, but deployment often exposes them to unfamiliar designs when the original training data are unavailable. Repeatedly fine-tuning a single serving model can overwrite earlier improvements, while simply saving checkpoints does not determine where they can be reliably reused. We introduce Continual Adaptation through the Reuse of Validated Expertise (CARVE), a framework that represents accumulated expertise as a frozen base policy, immutable specialists, and task-specific credentials obtained through local validation. For a new task, CARVE first checks existing specialists and trains a new specialist from the frozen base only when none qualifies. Under fixed task distributions and validation rules that control cumulative error, we establish expected-performance guarantees for repeated reuse. For bounded losses, we also derive matching worst-case bounds on the local samples needed for reliable reuse. In macro placement, a reuse-first follow-up reduces recorded training time by 58.5% (9.66 to 4.01 hours), while mean HPWL gain changes only from 8.41% to 7.86%. In a simulated receiving deployment, imported specialists are reused on six of seven new IBM circuits with no receiver-side training, achieving a 5.76% mean HPWL gain. Navigation studies provide complementary evidence on repair retention and repeated adaptation.

Little is known about how to manually design agents capable of dexterous manipulation. Some design principles have been inferred from close examination of how animals manipulate objects, but these structures and behaviors have so far resisted biomimicry and may not be optimal for artificial machines. Here we evolve freeform robots to pick up, hold, rotate, and use diverse objects. Unlike other approaches to optimizing robot hands, we do not presuppose the presence, articulation, or geometry of any part of the body. Although familiar prehensile forms such as tails, beaks, paws and claws may emerge spontaneously under certain conditions–and while such conditions could be of interest to evolutionary biologists–de novo manipulator design can also reveal whole new solutions, overlooked or unknown structures which may be better suited for the task at hand. We use contrastive learning to create a highly searchable genetic embedding of design space, an autoregressive developmental model to decode designs, evolutionary strategies to find good designs, and reinforcement learning to train each evolved design. Winning designs were automatically converted into a manufacturable blueprint, printed, assembled and tested in the real world in a zero-shot manner. The results represent the state-of-the-art in evolutionary robotics in terms of performance, diversity and complexity.

Linear attention replaces the growing key–value (KV) cache of standard attention with a fixed-size recurrent state, substantially reducing memory growth with context length. This efficiency, however, changes how past information is stored: many tokens must share and repeatedly update the same memory. We study how this recurrent state functions as a memory system. Using an analytical decomposition together with controlled causal interventions in pretrained GLA and GDN models, we trace how recalled information is written, retained, and later accessed. We find that fact-specific information enters recurrent memory through concentrated, content-dependent writes and is later accessed through concentrated query-time read pathways. Multiple facts can remain selectively accessible within the same state, yet their internal representations exhibit cross-fact causal coupling rather than independent KV-like storage. As memory load increases, both recall and targeted editability degrade, whereas elapsed context alone has a substantially smaller effect within the tested regime. Causal interventions on subsequent writes further show that interference is shaped by their overlap with existing memory. Finally, in hybrid architectures that combine recurrent layers with full attention, the runtime memory directly supporting recall shifts predominantly to the full-attention KV state. Together, these results reveal how fixed-size recurrent memory supports selective recall despite shared storage, while exposing the interference and capacity limits that distinguish it from token-addressable KV memory.

The geometry of latent representations governs which components should interact and how information should propagate, making geometry-aware operator design a fundamental ingredient of structured deep representation learning. However, existing neural architectures typically rely on generic operator templates or geometry-specific constructions, creating a need for a unified framework that can derive admissible operators directly from fixed structural information while remaining adaptive to changing contexts. We introduce Geometry-Induced Operator Families (GIOF), a general framework that converts fixed geometry into a structured family of propagation operators and dynamically selects an appropriate member of this family according to the current context. GIOF first transforms geometry-derived interaction channels into reusable generator bases, then combines them through a context-dependent selector and adaptive propagation scale, and finally realizes the selected operator through stable continuous-time propagation and a bottleneck residual layer. We establish theoretical guarantees covering parameter compression, identifiability, stability, locality, compositional structure, and oversmoothing behavior, while controlled experiments validate these mechanisms and experiments on PEMS-BAY and METR-LA achieve the lowest mean MAE across all reported regional-outage settings, improving over the strongest retained baseline by 2.4%–8.8% at 30% missing sensors.

Current approaches to aligning language models often make it hard to know what behavior is being rewarded or to change that reward in a targeted way. In particular, standard preference-based methods collapse multiple considerations into aggregate human judgments, obscuring what drives the resulting reward, while principle-based methods specify high-level values without fully operationalizing them. To address this gap, we develop a rubric-based framework to transform a general-purpose constitution into an interpretable and tunable reward model, using constitution-guided AI feedback to estimate initial weights for the constituent rubric items. We then reweight those dimensions to construct modified rewards for training. Across experiments on political alignment and safety-helpfulness tradeoffs, reweighting individual dimensions predictably changes targeted behaviors largely independently while navigating tradeoffs between conflicting alignment objectives. We show that the same framework can mitigate label bias encoded in preference judgments – including sycophancy and demographic bias – by reducing their influence on the training reward. Our results demonstrate that constitution-derived, interpretable rewards can translate high-level alignment principles into more transparent and controllable model behavior.

Automatic differentiation (AD) lets neural networks compute derivatives of governing equations to machine precision, and this precision has made it the computational backbone of physics-informed machine learning. Yet exactness in the mathematical sense is not the same as fidelity to the physics. Here I argue that a derivative can be numerically perfect and still be the wrong derivative for the problem at hand, because AD, by construction, has no notion of the physical structure a solution must obey. Convection and its associated directionality, diffusion, and dispersion are only the most visible instances of a much longer list that spans all branches of computational science and engineering, including conservation, thermodynamic consistency, symmetry, symplectic structure, positivity, monotonicity, and boundedness. Recognizing this broader gap reframes how the field should build the next generation of PDE-driven neural surrogates.

Three-dimensional dense convolutional networks are the strongest performers on volumetric medical image segmentation, but their parameter counts scale poorly: moving a dense k x k convolution to k x k x k multiplies its weights by k. We observe that depthwise separable factorization does not share this penalty. Because the cubic kernel term applies only to the depthwise stage while the pointwise projection, which dominates the parameter count, is unchanged, the same architecture grows by 5 % from 2D to 3D where a dense convolutional U-Net grows by 200 %. We exploit this asymmetry to build a 3D U-Net with 536,990 parameters, 24x fewer than an identical dense 3D U-Net. On MSD Task03 Liver (the Medical Segmentation Decathlon liver task, derived from LiTS), evaluated per case under five-fold cross-validation over all 131 public volumes, the model reaches a tumor Dice of 0.577 (95% CI [0.518, 0.633]) and a liver Dice of 0.947 (95% CI [0.941, 0.952]). Its liver Dice exceeds previously reported performance. Its tumor Dice exceeds their low-resolution configuration (0.4701) by 0.107 and their 2D configuration (0.5394), at approximately one twenty-fourth of the parameters and roughly half the in-plane resolution. Trained under identical conditions on a common held-out split, it exceeds a dense 3D U-Net on liver by +0.031 Dice (paired p = 0.006) and on tumor by +0.041 (95 % CI [+0.005, +0.081], paired p = 0.056), suggesting the factorization also acts as a regularizer in the small-data regime characteristic of medical imaging. We further show, on both LiTS and a 2D endoscopy benchmark, that a large fraction of the network's learnable spatial filters can be replaced by fixed shifts at no cost in accuracy, but that replacing all of them is measurably worse, the placement of spatial capacity matters more than its total amount.

High-performance GPU kernels are essential to modern machine learning systems, yet automatically generating kernels that are both correct and efficient remains challenging. Existing LLM-based approaches face two major limitations: the scarcity of high-quality training data aligned with the model's current capabilities, and the inherent trade-off between kernel correctness and performance. To address these challenges, we propose KernelZero, a co-evolution framework that continuously improves GPU kernel generation through two specialized models: a Proposer that generates Torch modules from API sets and a Coder that translates them into CUDA or Triton kernels. KernelZero uses a frontier-driven module generation mechanism to continuously produce capability-aligned training modules based on the Coder's current weaknesses. It further introduces Correctness-Aware Group Relative Policy Optimization (CA-GRPO), which optimizes performance only after correctness becomes sufficiently reliable. By alternating the optimization of the Proposer and Coder, KernelZero forms an automatic curriculum that enables targeted and training-efficient capability improvement. Empirically, KernelZero-7B surpasses Claude-4.5-Sonnet on CUDA and DeepSeek-V4-Pro on Triton. On KernelBench Level 1 and 2, it achieves CUDA pass@1 scores of 75.8% and 69.6%, respectively, with pass@10 reaching 100% and 97%. On Triton, it achieves pass@1 scores of 77.2% and 72.5%, respectively.

In this work, we consider algorithmic harms that may arise as generative models are incorporated into machine learning platforms. We argue that existing harm taxonomies and threat models require extension to (1) address novel causal drivers of well-studied representational and quality-of-service harms; and (2) anticipate and mitigate endogenous harms, such as sanitization, which may arise when system inputs are misaligned with the system designer's objectives, or the generative model's inductive priors. To this end, we introduce an expanded taxonomy of algorithmic harms associated with the use of generative models in non-conversational recommendation systems. In addition, we offer a causal analysis of how problematic subsets of the (input, output) joint distribution can arise, in an effort to inform harms detection and mitigation efforts.

Contemporary neural inference architectures rely on dense floating-point weight matrices stored in high-bandwidth memory (VRAM), incurring severe memory-wall bottlenecks and preventing native execution inside deterministic virtual machines like the Ethereum Virtual Machine (EVM). Verifying termination and arithmetic invariants for recursive dynamical systems over continuous domains is generally undecidable in the Blum-Shub-Smale model. Here, we present the formal verification and bare-metal empirical validation of WERR (Waves & Errors) and Phase III Orbital Error Dynamics (OED), a non-tensor decision paradigm that procedurally synthesizes non-linear decision boundaries on demand from a 24-byte coordinate seed $\Theta = (c_x, c_y, \text{zoom})$ along the boundary of the Mandelbrot set ($\partial\mathcal{M}$). By projecting the recurrence $z_{n+1} = z_n^2 + c$ onto the modular residue ring $\mathbb{Z}/9\mathbb{Z}$ and the fixed-point domain $\mathbb{Q}_{16.16}$, we establish ten machine-verified theorems in Lean 4 (v4.34.1) with Mathlib4 and zero unproven conjectures (sorry): proving $\mathcal{I}_3 = \{0,3,6\} \subset \mathbb{Z}/9\mathbb{Z}$ ideal closure, universal fuel-bounded halting ($\le 9$ and $\le 12$ steps), absence of $\mathbb{Q}_{16.16}$ square overflow below $2^{63}-1$, non-constant boundary escape sensitivity, and a parametric EVM gas bound ($\le 22,557 \le 24,000$ gas). Evaluated on a 40-core Dual Intel Xeon server, the vectorized 36-iteration CPU kernel processes 100,000 decisions in 6.49 s (15,397 decisions/s, 0 Bytes VRAM, 15.15x speedup), while a sigmoidal outlier gate suppresses 100.00% of adversarial spikes while preserving 89.60% of clean baseline signals.

Large language model (LLM) assistants can now search the web and consult external sources while completing user requests. These sources can provide useful evidence, but they can also introduce additional content into the model's context. Can such passive exposure steer a decision even when the added content provides no reason to change it? We examine the stability of model decisions on the same tasks with and without such external content. Across all open-weight and closed-weight models we test, exposure systematically shifts decisions, with effects reaching nearly 50 percentage points in closed-weight models. The same pattern appears with real-world online opinions. The influence also extends beyond subjective preferences. Such exposure can steer models toward choices that violate explicit user requirements and increase their acceptance of false claims. In short, what enters an LLM's context can influence its decision even when it should not determine it.

Speech therapists often face difficulties diagnosing impairments due to the lack of efficient tools for transcribing speech into the International Phonetic Alphabet (IPA). This work addresses this challenge with Broca, a Conformer-based deep learning system pretrained on 8 days of adult speech and fine-tuned on a 165-minute dataset of Italian child speech collected through a range of standardized diagnostic tests for children aged 3.5-6.5. Broca was optimized to handle phonetic variability in children's speech, including tone, accent, and speech errors, and achieved a state-of-the-art weighted Phoneme Error Rate of 13.36% on Italian speech. Remarkably, this performance was obtained using less than three hours of child-specific data, underscoring the model's efficiency and robustness in low-resource clinical settings. This work demonstrates that accurate, vocabulary-independent speech-to-IPA transcription can be achieved with minimal data, paving the way for more accessible, data-efficient tools to support speech assessment and diagnosis.

Financial question answering often requires precise numerical extraction, unit handling, and arithmetic over tables and text, but applying expensive verification uniformly wastes test-time compute. We propose BudgetVerify, a budget-tiered generator-verifier framework that routes each generated answer to one of three verification tiers: no verification, lightweight check-and-revise, or higher-cost solve-first-then-compare verification. The router is trained from offline correctness and token-cost outcomes and, at test time, selects a verification tier using information available before verification, including the question, context statistics, the generated answer, and associated generator metadata. The selected tier either returns the generated answer directly or invokes the corresponding verifier. Across six commercial and open-weight base models, BudgetVerify consistently produces more efficient accuracy-cost Pareto frontiers than fixed verification policies by selectively allocating stronger verification only when it is useful. Although absolute performance varies across models, these efficiency gains and the resulting qualitative frontier shape are consistent across generator models.

Hybrid-attention models replace most softmax attention layers with linear attention, reducing KV-cache growth and enabling larger decode batches where recurrent-state access becomes a major bottleneck. ReplaySSM amortizes state updates by buffering keys and values, but each new query still requires a full-state read even though the state remains unchanged between state updates. We observe that low-rank state-weighted query approximation accurately preserves state-read outputs. Although future queries are unknown, the basis vectors used to approximate them can be fixed offline. Based on this observation, we introduce SketchSSM, which preserves full-state updates while approximating reads. At each state update, SketchSSM reads the full state once to precompute outputs for these basis vectors, storing them in a compact sketch. Each subsequent decode step combines the sketch vectors with query-dependent coefficients to reconstruct the output without a full-state read. Across four Mamba-2-, GDN-, and KDA-based models, SketchSSM at a mean sketch rank of 8 reduces state-access traffic by approximately 10$\times$ while matching the average accuracy of the FP32 full-state baseline across four decode benchmarks, and preserves recall on four RULER retrieval tasks. At this rank on one NVIDIA B300, linear-attention kernel speedups over the Standard vLLM baseline reach 7.30$\times$, 5.02$\times$, and 5.24$\times$ for Mamba-2, GDN, and KDA, respectively, with up to 2.77$\times$ higher decode throughput on Nemotron 3 Super.

Understanding how individual brain development unfolds over childhood requires modeling developmental trajectories from sparse longitudinal observations. Long-term neurodevelopmental forecasting is challenging because each child is typically observed at only a few irregularly spaced visits, while developmental dynamics vary across individuals and age. Generic continuous-time models accommodate irregular timing but often absorb these factors into a single flexible transition function, providing little structure for how population progression, individual variability, and developmental age shape the dynamics. We propose DevelopmentODE, a structured continuous-time framework that organizes population- and subject-specific variation within a shared developmental geometry while allowing the governing dynamics to evolve with age. The model builds this geometry around a developmental canal representing the population trajectory, whose local direction provides a reference for organizing subject-specific variation. Subject deviation velocities are constrained relative to this direction, while a shared nonlinear deviation field captures individual developmental motion without disrupting population-level progression. DevelopmentODE further models developmental non-stationarity through ordered age-dependent deformations of the shared vector field, progressively adapting a common dynamical structure as age changes, while elapsed time determines the integration horizon. This formulation uses population-level developmental structure to guide learning from sparse individual trajectories while allowing dynamics to evolve smoothly with age. We evaluate DevelopmentODE on longitudinal fMRI by predicting future functional connectivity of the same child from earlier observations. DevelopmentODE consistently outperforms competing baselines across short- and long-horizon predictions.

Matrix optimizers such as Muon transform each momentum matrix through an approximate orthogonalization, typically implemented by a small number of Newton-Schulz matrix multiplications. The quality and cost of this approximation depend strongly on the singular-value spectrum of its input, yet existing implementations use the same fixed polynomial routine for every layer and throughout training. We show that this uniform treatment is unnecessary: the computations in the Newton-Schulz method already reveal enough information to make the method adaptive. The Gram matrices formed inside Newton-Schulz iterations yield spectral moments through inexpensive scalar reductions, requiring no additional matrix multiplications. From these moments, we recover an estimate of the empirical singular-value distribution and use it to select a polynomial routine specialized to the current matrix. This turns Newton–Schulz orthogonalization into a spectrum-adaptive procedure that responds to differences across both layers and training time. On saved momentum matrices, spectral estimation substantially reduces orthogonalization error at a fixed iteration budget or reaches the same accuracy with fewer iterations, and in GPT pretraining up to 1B parameters it lowers the validation loss of two matrix optimizers. Our results suggest that matrix-function operations inside optimizers need not be designed for a conservative worst-case spectrum: they can cheaply measure the spectrum they are already processing and specialize computations accordingly.

Learning-rate warmup is a standard technique in language-model training, yet its duration remains largely heuristic. Common approaches use either a fixed number of updates or a fixed fraction of the training horizon, two choices that imply very different scaling as training gets longer. When should warmup stay fixed, and when should it grow with the horizon? We address this question with a quadratic model whose modes respond differently to the peak learning rate. Warmup slows progress in directions that already contract well at the peak rate, but can remove persistent error in directions near the stability edge, with higher peak rates shifting the balance toward longer warmup durations. This yields a compact horizon scaling law that captures regimes ranging from essentially no warmup, through fixed-duration warmup, to durations that grow with the training horizon, and explains how the preferred regime changes with peak learning rate. Because the law captures the tradeoff between giving up early progress and improving the trajectory that follows, it can be fit using shorter runs and used to predict warmup at substantially longer horizons. Together, our results explain several familiar properties of warmup through a single tradeoff and suggest treating warmup duration as a horizon-dependent hyperparameter rather than a fixed training heuristic.

We propose DAST (Diversifying Arithmetic Sampling with TokenTour), a method that increases the diversity of LLM outputs without any change to the marginal distribution and with negligible generation-time overhead (a few microseconds). We observe that token IDs are often arranged in a meaningless order and reassign them so that tokens with similar meanings appear consecutively. This can be done in advance in a few hundred seconds per model, and the resulting order can be reused for all subsequent generations. By combining this order with arithmetic sampling (or quasi-Monte Carlo methods), we make similar tokens less likely to be generated across runs while preserving the distribution. Our method not only produces qualitatively good ideas but also significantly improves performance on the downstream task of ProtoQA.

Retrieval-augmented generation (RAG) lets language models answer questions more accurately by consulting relevant documents. Many valuable collections, such as medical records, cannot be pooled because of privacy rules. Federated RAG leaves each collection with its owner, or node, which scores candidate answers from its own documents; a central hub combines the scores. Some nodes, called Byzantine, may be compromised, faulty, or misled by instructions hidden in documents, and report arbitrary scores. Conformal prediction returns a set containing the correct answer with a chosen probability, using a cutoff set in a calibration step on questions with known answers. An unknown group of nodes, no larger than a declared bound, may misreport both in this step and at query time. Existing methods assume every node is honest or protect only the calibration step. We observe that the honest nodes are the same in both steps. The hub therefore has all nodes score the same calibration questions, and keeps a candidate only if some plausible group of honest nodes, using its own scores in both steps, would keep it. We prove that the resulting sets contain the correct answer with the chosen probability in finite samples, whatever the Byzantine nodes report. No method using the same information can return smaller sets without risking the loss of an answer the honest nodes support. If nodes fail at random, the guarantee weakens only by the probability that more nodes fail than declared. In simulations, on real question-answering tasks including medical exams, and with language models as nodes, some hijacked, our sets reached the target whenever no more nodes misbehaved than declared, while plain averaging could miss it. They were also clearly smaller than those of simpler methods with the same protection, most of all when the declared bound was generous, so a cautious bound costs little.

Reinforcement learning with verifiable rewards improves mathematical reasoning when a final answer can be checked, but a correct answer does not certify the derivation behind it, and proof problems offer no answer to check. Replacing the check with a reasoning model as an in-loop verifier faces a fundamental obstacle: the policy must already produce occasional correct attempts for any reward to exist, which it may never do at olympiad level. We instead move verification and repair out of the training loop and into offline data generation with SPLICE, a workflow in which a second model, given only a reference solution, edits a reasoning model's traces as they are generated: it verifies progress, truncates a failed trace at its last verified step, and splices in an adaptively strengthened hint until progress resumes. The resulting dataset includes repaired examples whose sampled unaided trajectory failed, with failed continuations removed and progress repeatedly checked against the reference solution. A model finetuned on SPLICE traces outperforms the same model distilled from the reasoning model's unedited traces on AIME and, under a grading protocol validated against human grades, on olympiad proofs. The trained model's own traces show a corresponding behavioral signature: at difficult points it announces a branch in the style of the spliced hints and takes riskier steps, with predictive entropy rising there and just after, a pattern absent from the model trained on unedited traces.

Post-training large language models (LLMs) on two-player zero-sum games provides a verifiable reward, and the gains have been shown to transfer to general reasoning. Existing pipelines, however, rely on a handful of hand-written games and on advantage estimators tied to them, so both the supply of games and the advantage estimate on a large corpus limit scaling. We present GameSmith, which scales both. An LLM synthesises games inside templates whose reward, observation, and hidden-information code is fixed. Each game is verified by seed-paired replay and by an independent re-implementation of its specification, then expanded into encoding, rule, and size variants, giving 26 new games in 29 families and 336 verified variants from the three SPIRAL templates. The model is distilled from the self-play of a larger teacher (Qwen3-32B) on these games and then trained by self-play reinforcement learning with CRAB, an advantage estimator that credits each decision against a shrinkage estimate of the expected return of its position and is defined on every variant. On Qwen3-4B-Base, distillation raises the 13-benchmark mean pass@1 from 45.5 to 62.5, above the three SPIRAL games at the same budget, and self-play with CRAB reaches 64.9. The ordering holds across models, and transfer grows with the number of game families.