Causal Foundation Models

Causal inference is the practice of estimating the effect of a treatment or intervention from data. It traditionally requires a bespoke pipeline for every new problem: first proposing a causal mechanism, selecting a compatible estimator, and finally training it. Meanwhile, across diverse settings and modalities, much of machine learning has shifted to the paradigm of foundation models: networks pretrained once at scale and applied to new tasks without fine-tuning. Causal foundation models (CFMs) bring this paradigm to causal inference. CFMs are pretrained neural networks that estimate causal quantities, such as the average treatment effect, on entirely new datasets using in-context learning without requiring model updates. This work provides a practical introduction to this emerging area. We summarize the necessary background in causal inference and machine learning before discussing CFMs. Throughout, we include example code and Jupyter notebooks.

Effective Learning Rate Governs Loss Dynamics in Language Model Pretraining

We uncover ELR collapse in language model pretraining: learning rate (LR) and parameter norm govern loss dynamics primarily through their ratio, the effective learning rate (ELR). When ELR is matched across runs, their loss trajectories collapse throughout training despite substantially different LRs and parameter norms. Across optimizers, architectures, datasets, and model scales, mean collapse errors are typically a few x 10^-3, below the seed-to-seed variation measured in a representative configuration. Systematic ablations identify normalization design and the timescale of LR-norm variation as key determinants of collapse precision. Controlled interventions further show that weight decay and Hyperball shape loss dynamics primarily through the ELR schedules they induce. Replacing LR with ELR enables a fitted functional scaling law (FSL) to transfer across norm-control methods. The resulting ELR-based FSL also explains delayed acceleration, a recurring effect of norm control. Together, these results establish ELR as a common coordinate linking LR scheduling, norm control, and loss dynamics.

Scale-Aware Pretraining of Time Series Foundation Models via Multi-Patch Token Alignment and Hybrid Masking

Pretraining time series foundation models across heterogeneous datasets necessitates effective handling of varying sampling frequencies. Current methods either employ dataset-specific patch sizes and separate FFNs, leading to fragmented representations, or enforce a fixed patch size that neglects inherent temporal variations. To address this, we propose SATS, featuring a scale-aware token alignment mechanism that treats patch size as an explicit notion of scale. By incorporating a contrastive-inspired alignment regularizer, SATS aligns representation spaces across scales while preserving distinct modeling capacities. Furthermore, a hybrid masking strategy combining random and contiguous masking is introduced to capture multi-scale temporal structures. Experimental results on LSTF benchmarks demonstrate that SATS achieves a 9.2% improvement in MSE and an 8.3% gain in GIFT-Eval MASE compared to competitive baselines. Notably, SATS consistently delivers SOTA performance while achieving a 65.6% increase in model efficiency over advanced baselines, highlighting its effectiveness and scalability in time series pretraining.

PluRel-to-RDB-PFN: Schema-Guided Synthetic Relational Pretraining

Relational Foundation Models (RFMs) require large-scale synthetic relational databases for pretraining, but existing approaches tightly couple data generation with the model training pipeline. We study whether PluRel, a general-purpose synthetic relational database generator, can serve as an external data source for RDB-PFN, a relational in-context learner originally pretrained with a 600K-task single-table warm-up followed by an approximately 1.8M-task adaptation stage. We build a conversion pipeline that maps PluRel-generated databases, including externally constructed binary prediction tasks, into the RDB-PFN training format and evaluate three curriculum strategies: SCHEMA-GUIDED FIRST (real-world schema then fully synthetic), FULLY SYNTHETIC (diverse synthetic schemas throughout), and SCHEMA-GUIDED LAST (fully synthetic then real-world schema). Using only approximately 5,500 relational databases (approximately 33K tasks), roughly 55x fewer tasks than the original protocol, and no single-table warm-up, our best curriculum (SCHEMA-GUIDED FIRST) achieves 0.6346 average ROC-AUC across 19 real benchmark tasks at 1024-shot context, recovering 87.6% of the published RDB-PFN performance (0.7245). At 64-shot context, the gap narrows to 93.8% (0.6116 vs. 0.6517). Our results demonstrate that external synthetic generators can provide useful pretraining signals for RFMs when combined with appropriate curriculum design and that exposure to a real-world schema early in training is substantially more effective than late-stage schema adaptation.

Bridging Compute- and Data-Optimal Pretraining

Classical compute-optimal scaling laws assume an unbounded supply of fresh pretraining data, yet pretraining is increasingly entering a regime in which compute grows faster than the availability of high-quality data. We propose Compute-Data (CD) scaling laws, a unified framework that bridges compute-optimal scaling, where data scales freely with compute, and data-optimal scaling, where the corpus is fixed while compute can grow without bound. CD scaling extends classical scaling laws by introducing a token-effectiveness function, $η$, which quantifies the value of a derived token-produced, for example, through multi-epoch repetition or paraphrasing-relative to a fresh token, ranging from a perfect substitute to having no value. We fit $η$ for two data-expansion strategies, multi-epoch repetition and paraphrasing, across model sizes from 14M to 600M parameters using the Dolma-3 corpus. We find that token effectiveness is far from constant: it depends jointly on model size, the tokens-per-parameter ratio, and the amount of derived data, and it saturates as the corpus is expanded. The functional form of $η$ implies diminishing returns when substituting compute for data as either model size or data availability increases. It also partitions training into three operational regimes---compute-bound, data-bound, and model-bound---and shows that classical compute-optimal allocation is suboptimal across most practically relevant settings.

Towards Evaluating Data Priors for Tabular Foundation Models

Data-generating priors are a central component of tabular foundation models because they define the task distribution used during pretraining. However, priors are rarely evaluated as independent components, making it difficult to understand how much they affect downstream model behavior. This raises a methodological question: how can priors from different tabular foundation models be compared independently of the architectures and training protocols they were introduced with? To study this question, we implement a unified interface for publicly available priors from recent tabular foundation models and priors constructed from real datasets. We generate training tasks from each prior, train the same model architecture under a fixed training protocol, and evaluate the resulting models on shared downstream classification tasks. We compare priors through both generated-task statistics and downstream predictive performance. Our results show that different priors favor different downstream behaviors, with some achieving stronger absolute performance and others exhibiting more consistent relative rankings across datasets. We further find that data-level similarity only partially explains downstream behavior. Our code is available at https://github.com/automl/TFM-Playground/tree/prior-dev.

The Simulacrum: Decision-Theoretic Pretraining for Near-Optimal Time-Series Forecasting and Inference

We introduce a neural network-based framework for learning time series estimators through a process we term decision-theoretic pretraining. Analysts specify a generative world, a distribution over data-generating processes, and a target decision objective. A neural network trained on stratified simulations from this world approximates the corresponding optimal decision rule, yielding a neural estimator that provides forecasts, parameter estimates, predictive intervals, or model-selection for zero-shot inference on previously unseen time series. The joint specification of the generative world and objective enables the estimators to directly approximate process-level, finite-sample properties: near-optimal risk, bias control, minimax performance, and uniform calibration. Our experiments demonstrate that these neural estimators can outperform traditional baselines such as maximum likelihood estimation and model selection via AICc, for the same model structural model classes. Furthermore, even when trained purely on simulations of structural models, they achieve competitive or state-of-the-art forecasting accuracy on major real-world benchmarks, compared with statistical, neural or large pre-trained models. We illustrate the framework by addressing two longstanding challenges: finite-sample bias and miscalibration in AR(p) models, and the forecast combination puzzle. These applications highlight the approach's main advantage: its ability to approximate solutions to analytically intractable or computationally prohibitive time series problems, including complex structural equations or optimality criteria. Ultimately, by enabling explicit control over decision-theoretic trade-offs, the framework equips analysts with highly efficient estimation tools tailored to their specific analytical needs.

Mix, Don't Pick: Why Synthetic Corpus Composition Matters for Time Series Foundation Model Pretraining

Choosing the wrong synthetic generator for time-series foundation model pretraining is costly: under identical training budgets, the best and worst generators produce up to a $2\times$ gap in forecasting error, yet the field has no principled way to make this choice. The problem is compounded by the fact that generator rankings are not stable across architectures: across 11 generator families evaluated on Chronos-T5-Mini and Moirai-Small trained from scratch, we find that which generators are useful depends on the model architecture. Rather than solving the generator selection problem, we sidestep it: a simple equal-weight mixture of all generators matches or beats the best individual generator for both architectures, and composing this mixture with real data yields the strongest pretraining corpora overall. Synthetic pretraining is therefore a corpus composition problem, not a generator selection problem, and composition choices should be validated per model family rather than assumed to transfer.

Segment-driven Structural Induction and Semantic Alignment for Heterogeneous Tabular Representation

Real-world domains often contain heterogeneous tables whose headers vary while their underlying attribute semantics are shared, making it difficult to induce domain-specialized semantics from table-local evidence alone. Existing encoders model parts of this problem, but often underuse column-level value distributions and apply uniform objectives across attributes with different semantic roles. We propose NAVI, a segment-centric pretraining framework that treats each header-value pair as the unit for aggregating schema-level structural evidence and column-level distributional evidence. We realize this design through Masked Segment Modeling and Entropy-driven Segment Alignment, which jointly enforce structured header-value coupling and semantic alignment across stable and instance-specific attributes. Experiments on heterogeneous in-domain tables show improved reconstruction, semantic consistency, and downstream utility across evaluation settings overall.