OpenThoughts-Agent: Data Recipes for Agentic Models

Agentic language models dramatically expand the applications of AI yet little is publicly known about how to curate training data for broadly capable agents. Existing open efforts such as SWE-Smith, SERA, and Nemotron-Terminal typically target a single benchmark, leaving open the question of how to train models that generalize across diverse agentic tasks. The OpenThoughts-Agent (OT-Agent) project addresses this gap with a fully open data curation pipeline for training agentic models. We conduct more than 100 controlled ablation experiments to systematically investigate each stage of the pipeline, yielding insights on the importance of task sources and diversity. We then assemble a training set of 100K examples from our pipeline and fine-tune Qwen3-32B on this dataset, which yields an average accuracy of 44.8% across seven agentic benchmarks and a 3.9 percentage point improvement over the strongest existing open data agentic model (Nemotron-Terminal-32B, 40.9%). Moreover, our training data exhibits strong scaling properties, outperforming alternative open datasets at every training set size in compute-controlled comparisons. We publicly release our training sets, data pipeline, experimental data, and models at openthoughts.ai to support future open research on agentic model training.

Human-AI Teaming Through the Lens of Calibration

We study models for human-AI teaming through the lens of statistical calibration. We assume the team consists of an AI model and human -- both of which are calibrated with respect to some partitioning of the feature space -- and expose how the calibration assumptions propagate into the teaming framework. In particular, we consider frameworks that either (i) combine human and model predictions or (ii) delegate prediction responsibility to either a human or model. We show via theoretical and empirical results that existing methods for combination do not preserve the human's degree of calibration. Methods for delegation (by the very act of delegation) preserve calibration of the downstream predictors but shift the burden onto the rejector meta-model that decides who predicts. The rejector must be calibrated finely enough to locate where each member is superior, a demand that grows with the human's expertise and becomes unattainable when the human relies on information the system cannot observe.

Data-Constrained Language Model Pretraining: Improved Regularization and Scaling Laws

Classical scaling laws for language model pretraining balance model size against training dataset size under a fixed compute budget, assuming abundant data and a single pass over the corpus. As training compute grows faster than the supply of natural language data, pretraining is likely to enter a data-constrained, compute-rich regime where models train for multiple epochs over a finite dataset. We study data-constrained pretraining along two axes, regularization and scaling. For regularization, we study masked-input regularization (MIR), an auxiliary next-token prediction loss on randomly masked inputs. MIR tests whether the random masking central to diffusion language models can benefit autoregressive pretraining without architectural changes or inference overhead. Across 72M to 1.4B parameter models, we find that MIR added on top of strong weight decay improves validation loss over autoregressive strong-weight-decay-only models, with downstream gains at 1.4B. For scaling, we propose SoftQ, a scaling law that couples model size and data size to capture their interaction under repeated data. Classical alternatives such as the Chinchilla law use an additive form that decouples these terms, making them misspecified in the data-constrained regime. We find that SoftQ fits data-constrained experiments substantially better than these alternatives, and estimates MIR's gains as equivalent to roughly 1.3 times as much unique training data. We release our code at https://github.com/yixinw-lab/dc_pretrain.

Agents' Last Exam

Recent AI systems have achieved strong results on a wide range of benchmarks, yet these gains have not translated into economically meaningful deployment across many professional domains. We argue that this gap is largely an evaluation problem: widely used benchmarks lack sustained performance measurement on real and economically valuable workflows. This paper introduces Agents' Last Exam (ALE), a benchmark designed to evaluate AI agents on long-horizon, economically valuable, real-world tasks with verifiable outcomes. Developed in collaboration with 250+ industry experts, ALE covers non-physical industries defined with reference to O*NET / SOC 2018 (the U.S. federal occupational taxonomy). It is organized around a task taxonomy with 55 subfields grouped into 13 industry clusters covering 1K+ tasks. Current results show that the hardest tier remains far from saturated: across mainstream harness and backbone configurations, the average full pass rate is 2.6%. ALE is designed as a living benchmark: its task pool grows continuously as new workflows and industries are onboarded. More broadly, ALE is intended not merely as another leaderboard, but as an instrument for closing the gap between benchmark success and GDP-relevant impact.

Learning to Extrapolate to New Tasks: A Relational Approach to Task Extrapolation

Modern learning systems excel at interpolation but struggle to generalize to unseen tasks outside the training distribution's support. This failure occurs even in simple settings, such as handling task parameters beyond the training range, and persists despite advances in foundation models. To this end, we develop the Relational Task Extrapolator (RTE), an algorithm designed to enable systematic extrapolation to novel tasks. The key observation is that extrapolation is inherently relational: extrapolating to unseen tasks requires learning how tasks transform into one another. If a model learns the transformation between tasks A and B during training, it can apply that same transformation to relate known tasks to unseen ones at test time. RTE operationalizes this idea by decomposing each target task into a known anchor task and a transformation linking the anchor and target. It then learns a relational operator, mapping an anchor-transformation pair to predictions for the target task. We instantiate RTE across multiple task extrapolation regimes in function prediction, e.g. where target tasks use out-of-range parameters (parameter extrapolation), have greater compositional depth (length extrapolation), and/or recombine function primitives in unseen ways (compositional extrapolation). We further extend RTE to sequence prediction, integrating it into fine-tuning algorithms for foundation models. Across empirical studies, we find that RTE substantially outperforms existing approaches on extrapolation to novel, unseen tasks.

Programmatic Context Augmentation for LLM-based Symbolic Regression

Symbolic regression (SR), the task of discovering mathematical expressions that best describe a given dataset, remains a fundamental challenge in scientific discovery. Traditional approaches, primarily based on genetic algorithms and related evolutionary methods, have proven useful but suffer from scalability and expressivity limitations. Recently, large language model (LLM)-based evolutionary search methods have been introduced into SR and show promise. However, existing LLM-based approaches typically rely on scalar evaluation metrics, such as mean squared error, as the sole source of feedback during the search process, thereby overlooking the rich information embedded in the dataset. To address this limitation, we propose a novel LLM-based evolutionary search framework that incorporates programmatic context augmentation. By enabling code-based interactions with the dataset, our method can actively perform data analysis and extract informative signals, beyond aggregated evaluation scores. We evaluate our framework on advanced benchmarks, such as LLM-SRBench, and demonstrate superior efficiency and accuracy compared to strong baselines.

Taming the Instability: A Robust Second-Order Optimizer for Federated Learning over Non-IID Data

In this paper, we present Federated Robust Curvature Optimization (FedRCO), a novel second-order optimization framework designed to improve convergence speed and reduce communication cost in Federated Learning systems under statistical heterogeneity. Existing second-order optimization methods are often computationally expensive and numerically unstable in distributed settings. In contrast, FedRCO addresses these challenges by integrating an efficient approximate curvature optimizer with a provable stability mechanism. Specifically, FedRCO incorporates three key components: (1) a Gradient Anomaly Monitor that detects and mitigates exploding gradients in real-time, (2) a Fail-Safe Resilience protocol that resets optimization states upon numerical instability, and (3) a Curvature-Preserving Adaptive Aggregation strategy that safely integrates global knowledge without erasing the local curvature geometry. Theoretical analysis shows that FedRCO can effectively mitigate instability and prevent unbounded updates while preserving optimization efficiency. Extensive experiments show that FedRCO achieves superior robustness against diverse non-IID scenarios while achieving higher accuracy and faster convergence than both state-of-the-art first-order and second-order methods.

Discrete Causal Representation Learning

Causal representation learning seeks to uncover causal relationships among high-level latent variables from low-level, entangled, and noisy observations. Existing approaches often either rely on deep neural networks, which lack interpretability and formal guarantees, or impose restrictive assumptions like linearity, continuous-only observations, and strong structural priors. These limitations particularly challenge applications with a large number of discrete latent variables and mixed-type observations. To address these challenges, we propose discrete causal representation learning (DCRL), a generative framework that models a directed acyclic graph among discrete latent variables, along with a sparse bipartite graph linking latent and observed layers. This design accommodates continuous, count, and binary responses through flexible measurement models while maintaining interpretability. Under mild conditions, we prove that both the bipartite measurement graph and the latent causal graph are identifiable from the observed data distribution alone. We further propose a three-stage estimate-resample-discovery pipeline: penalized estimation of the generative model parameters, resampling of latent configurations from the fitted model, and score-based causal discovery on the resampled latents. We establish the consistency of this procedure, ensuring reliable recovery of the latent causal structure. Empirical studies on educational assessment and synthetic image data demonstrate that DCRL recovers sparse and interpretable latent causal structures.

Problems with Chinchilla Approach 2: Systematic Biases in IsoFLOP Parabola Fits

Chinchilla Approach 2 is among the most widely used methods for fitting neural scaling laws. Its parabolic approximation introduces systematic biases in compute-optimal allocation estimates, even on noise-free synthetic data. Applied to published Llama 3 IsoFLOP data at open frontier compute scales, these biases imply a parameter underallocation corresponding to 6.5% of the $3.8\times10^{25}$ FLOP training budget and \$1.4M (90% CI: \$412K-\$2.9M) in unnecessary compute at 50% H100 MFU. Simulated multimodal model misallocations show even greater opportunity costs due to higher loss surface asymmetry. Three sources of this error are examined: IsoFLOP sampling grid width (Taylor approximation accuracy), uncentered IsoFLOP sampling, and loss surface asymmetry ($α\neq β$). Chinchilla Approach 3 largely eliminates these biases but is often regarded as less data-efficient, numerically unstable, prone to local minima, and harder to implement. Each concern is shown to be unfounded or addressable, especially when the partially linear structure of the objective is exploited via Variable Projection, enabling unbiased inference on all five loss surface parameters through a two-dimensional optimization that is well-conditioned, analytically differentiable, and amenable to dense, or even exhaustive, grid search. It may serve as a more convenient replacement for Approach 2 or a more scalable alternative for adaptations of Approach 3 to richer scaling law formulations. See https://github.com/Open-Athena/vpnls for details and https://openathena.ai/scaling-law-analysis for other results from this study.

Beyond Distance: Quantifying Point Cloud Dynamics with Persistent Homology and Dynamic Optimal Transport

We introduce a framework for analyzing topological tipping in time-evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological, and higher-order relations into one metric, its global scalar distance can obscure transient, localized structural reorganizations during dynamic phase transitions. To overcome this limitation, we present a hierarchical dynamic evaluation framework driven by a novel topological and hypergraph reconstruction strategy. Instead of directly interpolating abstract network parameters, our method interpolates the underlying spatial geometry and rigorously recomputes the valid topological structures, ensuring physical fidelity. Along this geodesic, we introduce a set of multi-scale indicators: macroscopic metrics (Topological Distortion and Persistence Entropy) to capture global shifts, and a novel mesoscopic dual-perspective Hypergraph Entropy (node-perspective and edge-perspective) to detect highly sensitive, asynchronous local rewirings. We further propagate the cycle-level entropy change onto individual vertices to form a point-level topological field. Extensive evaluations on physical dynamical systems (Rayleigh-Van der Pol limit cycles, Double-Well cluster fusion), high-dimensional biological aggregation (D'Orsogna model), and longitudinal stroke fMRI data demonstrate the utility of combining transport-based alignment with multi-scale entropy diagnostics for dynamic topological analysis.