Learning Curve Prediction

Training high-performing neural networks often involves evaluating populations of candidate models with varying hyperparameters, architectures, or random seeds. Training every candidate to completion is computationally expensive, yet stopping seemingly weaker runs early risks discarding models that would ultimately perform better, as learning curves can cross. To address this challenge, we investigate whether intermediate training checkpoints can predict future model accuracy and enable more informed pruning decisions. Our nowcasters predict test accuracy five epochs ahead or at the end of training. They are trained with accuracy and loss histories, weight statistics, and SANE representations as inputs. SANE is a transformer autoencoder that encodes a checkpoint as a sequence of latent tokens. We then use the nowcasters in Survival-of-the-Fittest (SOTF) training. SOTF repeatedly ranks runs during training by predicted accuracy and stops the lowest-ranked ones. Our results show that weight statistics work best for five-epoch forecasts, and SANE representations work best for final accuracy prediction. For evaluation, we compare SOTF with pruning the population by current accuracy. In homogeneous model zoos such as the CNN zoos, pruning by current accuracy already retains a final model only slightly worse than the best. Model zoos with a larger spread in performance, such as the ResNet-18 and ViT zoos, are more difficult to prune by current accuracy alone. In these zoos, SOTF with nowcasted final accuracy almost closes the gap to the best model.

Scaling laws predict the outcome of large, expensive training runs by extrapolating trends from smaller, cheaper runs. On downstream accuracy evaluations, these predictions fail when the weaker models produced by the cheaper runs score near zero accuracy, because these scores give no trend to extrapolate to larger scales. We introduce hinted scaling laws, which use privileged information to turn a benchmark into a continuum of easier versions so that even the small models score above zero. We find that accuracy rises smoothly and predictably with the hint level, enabling new types of scaling laws that operate below the noise threshold. On the Delphi pretraining ladder, a hinted scaling law fit on models trained with at most $10^{20}$ FLOPs forecasts the GSM8K accuracy of a $10^{23}$ FLOP model (25.9%) to within 3 percentage points; a standard scaling law under-forecasts it by 13 percentage points when fit on the same models and by 12 even with models up to $10^{22}$ FLOPs in the fit. Across both this pretraining ladder and a collection of post-trained model families, hinted scaling laws reduce the median forecasting error on GSM8K, AIME and HLE from 21 percentage points to 4.3. Hinting also reduces the number of test examples needed to tell whether one model is better than another by widening the accuracy gaps between models while approximately preserving their order: a single hinted rollout per problem ranks nearly indistinguishable models as accurately as five unhinted rollouts. Our results suggest that hinting is a general primitive for improving the accuracy and cost of downstream scaling laws and other prediction tasks in model development.

Every neural-network training run produces not only a model, but also evidence about how models learn. Can these accumulated experiments enable us to predict and compare new training runs before executing them? We study meta-models: models that predict the learning behavior of other models. From this perspective, final-performance prediction, learning-curve prediction, and hyperparameter selection are different queries to the same training response function. We take a first, humble empirical step toward this goal: treating real language-model training records as native numeric data, we find that an off-the-shelf tabular in-context learner, TabPFN, can match or outperform a fine-tuned LLM meta-model in multiple evaluated settings. Whereas recent work fine-tunes LLMs on tokenized configurations at a cost of tens to hundreds of GPU-hours, TabPFN requires seconds of fit-and-predict time without task-specific weight updates. We argue that meta-modeling is better treated as its own numeric modality rather than as a text task for LLMs. Going one step further, augmenting TabPFN with Kolmogorov-Arnold Networks (KANs) further improves accuracy on selected prediction tasks. Finally, we pre-registered a forecast of the Marin Hero Run, a 535B-parameter public training run, whose ground truth is revealed point by point as training progresses, putting meta-model predictions to the test against training outcomes not yet observed at the time of forecasting.

The research presented here focuses on modeling machine-learning performance. The thesis introduces Seer, a system that generates empirical observations of classification-learning performance and then uses those observations to create statistical models. The models can be used to predict the number of training examples needed to achieve a desired level and the maximum accuracy possible given an unlimited number of training examples. Seer advances the state of the art with 1) models that embody the best constraints for classification learning and most useful parameters, 2) algorithms that efficiently find maximum-likelihood models, and 3) a demonstration on real-world data from three domains of a practicable application of such modeling. The first part of the thesis gives an overview of the requirements for a good maximum-likelihood model of classification-learning performance. Next, reasonable design choices for such models are explored. Selection among such models is a task of nonlinear programming, but by exploiting appropriate problem constraints, the task is reduced to a nonlinear regression task that can be solved with an efficient iterative algorithm. The latter part of the thesis describes almost 100 experiments in the domains of soybean disease, heart disease, and audiological problems. The tests show that Seer is excellent at characterizing learning-performance and that it seems to be as good as possible at predicting learning performance. Finally, recommendations for choosing a regression model for a particular situation are made and directions for further research are identified.

EEG-based brain-computer interfaces support a broad range of applications, yet designing decoding architectures that perform well across diverse tasks remains challenging. We introduce AutoBCI, an agentic framework in which a Designer Agent and a Forecaster Agent support the discovery and selection of EEG decoding architectures across tasks. The Designer Agent performs Pool-Guided Architecture Discovery (PGAD), generating and refining architectures through training and validation across multiple EEG tasks, such as emotion recognition, motor imagery, and sleep staging. The Forecaster Agent performs Performance Estimation from Early Knowledge (PEEK), using architecture code, the training protocol, and early learning curves to predict full-budget validation performance and select promising candidates for continued training. Across 14 EEG datasets spanning motor imagery, emotion recognition, and sleep staging, we evaluate AutoBCI with six LLMs, including Opus 5.5 and GPT 5.6 Sol, and compare the architectures selected by the search procedure against ten baselines: six conventional EEG models and four foundation models. The architecture discovered by AutoBCI with Claude Opus 5.5 achieves 64.16% average test balanced accuracy (bAcc), compared with 63.87% for REVE, the strongest baseline on this metric. Using ten observed epochs, PEEK reduces mean absolute error in predicting average validation bAcc from 2.20 to 1.36 percentage points, a 38.1% reduction relative to the best-observed-score baseline. Code is available at https://github.com/Jiang-Muyun/AutoBCI

Neural architecture search (NAS) evaluates candidate networks, but fully training enough architectures to rank an entire space is expensive. Zero-cost proxies score architectures at initialization, yet their ranking quality varies across search spaces. Learned predictors reduce evaluation cost but typically require fully trained labels or partial-training features for individual candidates. We introduce $\textbf{RiPPLE}$, $\underline{\textbf{R}}$anking v$\underline{\textbf{i}}$a $\underline{\textbf{P}}$refix-$\underline{\textbf{P}}$ropagated $\underline{\textbf{L}}$abel $\underline{\textbf{E}}$xtrapolation, which treats partial training as a source of labels for a small coverage set of anchors. RiPPLE trains these anchors to an early prefix, extrapolates their learning curves to surrogate labels, and propagates the labels over label-free architecture features. The early-training signal remains a label on the anchors rather than a per-candidate feature. Feature, readout, and encoding rules are selected without held-out accuracy and reused across search spaces. We evaluate the method on twelve benchmark cells from four search-space families and on the larger DARTS space. The results examine ranking quality, label efficiency, architecture selection, and the roles of readout, coverage, and propagation. RiPPLE provides a whole-space ranking from a fractional anchor-training budget, with comparisons interpreted under their respective evaluation and cost protocols.

Zero-cost proxies rank architectures cheaply, but their reliability varies across search spaces. We introduce CoRA-NAS (COarse Ranking + Anchor-residual), a two-stage framework combining a static ranking prior with low-cost learning-curve refinement. CoRA-Rank aggregates capacity and structure-at-initialization proxies through an equal-weight log-rank consensus and a target-free consensus gate. CoRA-Refine samples anchors across this prior, extrapolates their early validation curves, and propagates a learned residual correction with an ExtraTrees model. The refinement uses approximately 1% of the cost of fully training the candidate set. Fully trained architecture-accuracy labels are not used to fit the ranker. One configuration is used across spaces, with space-specific architecture encodings. Across NAS-Bench-201, NAS-Bench-101, TransNAS-Bench-101, and NATS-SSS, CoRA-Refine achieves mean Spearman correlations of 0.946, 0.715, 0.786, and 0.894, respectively. Its worst-space correlation of 0.715 is the highest among the compared methods. On NAS-Bench-201/CIFAR-100, its selected architecture reaches 73.32% accuracy, near the reported ground-truth best of 73.37%. On the pure size space, refinement recovers the static prior's shortfall relative to parameter count, while remaining tied with the strongest capacity proxies within noise. The resulting framework combines cross-space ranking robustness with low-cost architecture selection.

Large hyperparameter sweeps for deep neural networks spend substantial compute on configurations that are effectively doomed from the first few epochs. We study whether a single training run's own early telemetry - per-epoch loss, training accuracy, gradient signal-to-noise ratio, weight-norm growth, and an activation-saturation snapshot - together with its sampled hyperparameters, can predict that run's eventual outcome without reference to other runs. We evaluate three prediction tasks: final test accuracy, relative performance within a domain, and training-dynamics failure, including numerical divergence. Across 23,788 training runs spanning six architecture/dataset combinations, gradient-boosted trees using only the first five epochs of telemetry achieve R^2 = 0.92-0.99 for final-accuracy regression and ROC-AUC = 0.983-0.998 for relative classification on a permanently held-out set of hyperparameter configurations. Useful prediction is already available after a single epoch. A paired ablation shows that gradient- and weight-level telemetry provides a statistically consistent improvement over loss and accuracy curves alone, although the practical gain varies by domain. Transfer is strong between similar architectures, while cross-dataset transfer is limited mainly by differences in accuracy scale rather than loss of the underlying relationship. These results suggest that early-training telemetry can provide a practical decision-support signal for compute allocation while motivating human oversight for any automated intervention.

Active learning (AL) promises to reduce the cost of medical imaging projects by lowering the number of clinical labels required. However, practical deployment requires committing to a sampling strategy before the full annotation budget is spent, and choosing the wrong strategy can increase rather than decrease costs. We propose Active-Learning Deployment Advisor (ALDA), a deployment-oriented framework for AL method selection under clinical performance constraints. Given a short pilot phase, ALDA fits a parametric learning-curve model to each candidate strategy, estimates whether that strategy is expected to reach a required clinical performance target, and predicts the number of expert annotations needed to do so. In addition to absolute annotation cost, ALDA introduces a deployment window that quantifies the sensitivity of this cost estimate to uncertainty in the clinical threshold. The final recommendation follows a risk-aware rule: among strategies with near-optimal predicted cost, ALDA prefers the strategy with the narrowest deployment window, the most robust to threshold revisions. Experiments on four medical imaging classification domains show that ALDA predicts the deployment-optimal method from a pilot of 15-30% of the intended budget and reduces annotation costs by up to 82% compared with a poor strategy choice. Rather than introducing a new sampling heuristic, ALDA provides a practical decision layer that answers a deployment-critical question: how many labels are enough?

We study kernel regression with common rotation-invariant kernels on real datasets including CIFAR-5m, SVHN, and ImageNet. We give a theoretical framework that predicts learning curves (test risk vs. sample size) from only two measurements: the empirical data covariance matrix and an empirical polynomial decomposition of the target function $f_*$. The key new idea is an analytical approximation of a kernel's eigenvalues and eigenfunctions with respect to an anisotropic data distribution. The eigenfunctions resemble Hermite polynomials of the data, so we call this approximation the Hermite eigenstructure ansatz (HEA). We prove the HEA for Gaussian data, but we find that real image data is often "Gaussian enough" for the HEA to hold well in practice, enabling us to predict learning curves by applying prior results relating kernel eigenstructure to test risk. Extending beyond kernel regression, we empirically find that MLPs in the feature-learning regime learn Hermite polynomials in the order predicted by the HEA. Our HEA framework is a proof of concept that an end-to-end theory of learning which maps dataset structure all the way to model performance is possible for nontrivial learning algorithms on real datasets.