Best-Epoch Metrics

Machine-learning systems are built almost exclusively on a few large Python-orchestrated frameworks, and they inherit those stacks' engineering costs: environments of hundreds of version-coupled packages, separate export toolchains for deployment, and the split between the language research is written in and the language products ship in. We report on the construction and verification of numbat, a machine-learning stack written in one general-purpose language (Zig) with no third-party runtime dependencies. The stack spans tensor computation, automatic differentiation, neural-network modules, mixed precision, multi-GPU training, data loading and monitoring; an SDK exposes it behind a stable, additively versioned C ABI of over 1,400 entry points, with bindings for six languages; and its clinical domain planes encode regulatory requirements as executable acceptance gates rather than documentation. Verifying such a stack is the harder half of building it: a defective training run rarely fails, it converges quietly to a slightly worse model. We treat a widely used reference implementation as an executable specification and verify against it at five levels, from operator gradient checks to an automated trajectory gate against a same-machine reference run - the arrangement our companion study formalizes as a trajectory-level differential oracle. The protocol surfaced ten silent recipe divergences, which we catalog with mechanisms and symptoms. As the acceptance test, we train a 25.9M-parameter detector of the YOLOv8m class from random initialization on COCO 2017 for the full 500-epoch schedule: the exported weights score 0.4956 mAP50-95 under the official protocol, scored by the reference stack's own validator (published endpoint 0.502), with single-GPU step time at parity on identical hardware. Weights, per-epoch metrics and the full run manifest are released.

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.

Autoregressive rollout generation is a major computational cost in reinforcement learning for large language models. Reusing each rollout batch for additional learner updates amortizes this cost, but later updates become increasingly off-policy as the learner departs from the behavior policy. At a token position, exact off-policy correction must account for both the current action and the probability of reaching its prefix. The cumulative importance ratio provides this correction, but its product form can produce an unwieldy dynamic range. We study Prefix-Normalized Policy Optimization (PNPO), which replaces the cumulative ratio with the geometric mean of likelihood ratios along each causal prefix, preserving causal-prefix dependence at each position while compressing the log-weight scale. In controlled long-context mathematical reasoning experiments, we induce two off-policy regimes by using one or four policy-update epochs per rollout batch. PNPO does not consistently outperform GSPO with one epoch. With four epochs, it attains the highest observed Avg@32 on each benchmark; the unweighted mean of the three independently selected benchmark peaks is 50.24, 3.00 percentage points above GSPO. Under a matched 2,400-update budget, four-epoch PNPO reaches a final macro Avg@32 of 49.66 after 150 rollout batches, comparable to the 49.56 reached after 600 batches with one epoch. These results provide preliminary evidence that PNPO can be advantageous as training moves further off-policy.

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.

Deep learning systems often fail due to subtle implementation faults that alter training behavior. Recent work has studied how to detect and diagnose such failures from changes observed across training epochs. However, the software engineering community still lacks a public dataset of per-epoch training runs with documented fault history, feature extraction details, and clear reuse support for fault detection and diagnosis tasks. We present Deep4ge, a controlled benchmark of 14,227 training runs generated from 59 adapted TensorFlow/Keras deep neural network (DNN) programs collected from Stack Overflow. We generated faulty variants using 27 source-code transformations that introduce known faults across seven categories. The dataset contains 9,845 faulty runs and 4,382 correct baseline runs. For each run, we record 4 evaluation metrics and 26 features that measure training behavior at every epoch. These features capture weights, gradients, activations, accuracy and loss trends, learning rate, and hardware use. Deep4ge supports binary fault detection, multi-class fault diagnosis, and early fault prediction from partial training runs. We release the dataset and fault-injection framework at https://doi.org/10.5281/zenodo.20337241.

This paper studies the problem of regret minimization in Markovian bandits with \emph{non-observable states} and possibly \emph{constrained} decision epochs. The focus is restricted to a ``pure'' regret benchmark, that compares the performance of the learning algorithm to the best \emph{pure policy} which -- akin to optimal policies of stochastic bandits -- picks the optimal arm from start to finish without ever switching. We introduce a generalization of rested Markovian bandits, \emph{self-degrading Markovian bandits}, for which pure policies are always asymptotically optimal.We show that without prior knowledge on the underlying bandit, the regret of algorithms that switch arms rarely necessarily scales super-logarithmically for every bandit, i.e., as $ω(\log(T))$, where $T$ is the learning horizon. Despite the unreachability of the logarithmic regime, we design UCB-NOM, an optimistic algorithm inspired by UCB, of which the regret is nearly logarithmic. Lastly, we show that given prior knowledge on the Markovian bandit in the form of a bound on the bias functions of its arm, a proper instantiation of UCB-NOM achieves $O(\log(T))$ regret. We further show that this prior knowledge allows for a $O(\sqrt{T \log(T)})$ worst-case regret bound for UCB-NOM. Notably, our regret bounds do not depend on the number of states of the underlying Markov chains. Our findings suggest that the non-observability of states is a mild inconvenience in self-degrading Markovian bandits.

Self-improving agents are state-of-the-art (SOTA) on agentic coding benchmarks and have recently been extended to general domains. However, their search methods generally assume a stationary evaluation criterion: a fixed verifier, benchmark, or labeled dataset that remains valid as the agent improves. This ignores a central feature of evolution: species adapt as their environments change with them. We aim to bring the same principle to recursive self-improvement, making evaluation part of the improvement loop and opening search to evolving evaluators, adversarial objectives, and dynamic utilities that may surpass static benchmarks. We introduce the Red Queen Godel Machine (RQGM), an evolutionary framework for recursive self-improvement under non-stationary utilities. The RQGM makes this possible through controlled utility evolution: search is organized into epochs with a fixed within-epoch evaluation criterion, while the utility can be updated at epoch boundaries, so self-improvement guarantees hold per epoch as the objective evolves across them. We begin by showing that even on verifiable coding tasks, the RQGM improves test pass rate over the prior SOTA by adding a complementary agent-as-a-judge code-review signal. This signal is cheaper and the RQGM uses 1.35x-1.72x fewer tokens. We then turn to scientific paper writing and reviewing, and Olympiad-level proof writing and grading, where the RQGM improves performance over prior self-improving agents: co-evolved writers reach 1.78x-1.86x higher acceptance rates under a diverse agent-as-a-judge panel, while co-evolved graders reach 9% higher ground-truth accuracy. In paper reviewing, the strongest baseline reviewer over-accepts AI-generated papers at up to 1.91x the human rate. The RQGM corrects this by introducing an adversarial objective that discovers reviewers equally stringent on AI and human work.

A network of oscillators that synchronizes perfectly computes nothing further, so an attention architecture built from synchronization must locate its computation in structured departures from agreement. We introduce the Frustrated Synchronization Network (FSN), whose token states are phases on a torus and whose entire value pathway is one learned complex coupling kernel over harmonics and a one-step delay. Each component of the kernel is a frustration in the sense of the synchronization literature. The complex phases are static Kuramoto-Sakaguchi frustration angles, the signed harmonics are repulsive Daido components, and the delay term, which couples each token to the successors of the tokens it attends to, is algebraically identical to Kuramoto-Sakaguchi coupling whose frustration angle is the data's own transition, so next-token prediction is implemented as synchronization frustrated by the data. At matched one-million-parameter and training budgets on character-level text and code, the FSN's validation loss is below a tuned RoPE-SwiGLU transformer's at every epoch measured, and the comparison survives training the baseline to convergence: every thirty-epoch enwik8 seed finishes below the transformer's converged fifty-epoch loss of 1.611, and the FSN's completed fifty-epoch runs converge to 1.5953 +/- 0.0014. A variant with every feed-forward block replaced by mean-field coupling to learned collective modes, leaving no multilayer perceptron in the stack, tracks the transformer. On natural text the unfrustrated base layer falls behind the converged transformer at every copy depth, worst on long-range copy events; the kernel reverses the deficit at every depth of four and beyond. Headline comparisons are at the one-million-parameter scale; a scale ladder is complete through four million parameters with the advantage persisting, and remaining arms are marked as in progress.

As AI labs approach a data ceiling where compute capacity outpaces the rate of new high-quality text generation, language model pretraining is shifting toward a data-constrained, compute-abundant regime that demands productive multi-epoch training on fixed corpora. Standard autoregressive (AR) pretraining overfits severely in this setting, reaching its optimum early and then continuously deteriorating. We investigate training-time data augmentation as a regularizer to mitigate this overfitting and enable productive training for hundreds of epochs on the same data. We introduce three orthogonal categories of augmentation for AR pretraining: token-level noise (masking, random replacement), sequence permutations (right-to-left prediction, Fill-in-the-Middle), and target offset prediction ($x_{t+i}$ for $i > 1$). Through systematic ablations, we find that individual augmentations delay overfitting and lower validation loss relative to the baseline, with random token replacement achieving the best minimum loss among individual methods. Combining augmentation categories further lowers the minimum validation loss. Our experiments demonstrate that data augmentations mitigate AR pretraining's data inefficiency and offer a promising solution to the data-constrained regime~\footnote{All code and data are available at https://github.com/ michaelchen-lab/ data-augmentations-for-pretraining.

Multi-epoch training is becoming the standard now that compute is growing faster than the supply of high-quality text. But pretraining a single model saturates within a few passes, long before the compute budget is exhausted. We argue this calls for a conceptual shift from training a single model toward exploring a population of models and aggregating their predictions. We introduce hyper-epoch pretraining (q0), which turns a multi-epoch budget into a population of diverse models whose combined predictions reach a lower validation loss than a single refined model. q0 reduces to three core primitives. A cyclic schedule with anti-correlated learning rate and weight decay collects diverse models from a few parallel trajectories. Chain distillation trains each model against its predecessor so that model quality compounds across the population. A learned prior, fit on a held out set, selects and weights members for any inference budget. On a 1.8B-parameter model trained on 100M FineWeb tokens, q0 matches a strong 256-epoch ensemble baseline using only ~56 epochs (~4.6x fewer), or ~67 epochs (~3.8x fewer) when matched to the baseline's ensemble size, and continues to improve beyond it. These gains reach cumulative ~12.9x data efficiency under the Slowrun setting and transfer to downstream benchmarks. Crucially, the optimal allocation shifts with the budget, so we give prescriptive recipes for how to spend a given epoch budget to maximize generalization, from a single epoch up to the largest budgets.

Scaling laws for dense LLMs under infinite data are well explored, but how sparsity interacts with limited data is not. In this work, we study sparse training in data-constrained regimes where limited unique tokens require multi-epoch training. Our experiments span models up to 1.92B parameters in the fitting set, sparsity up to 93.75%, unique data budgets up to 2.6B tokens, and total training tokens up to 41.6B over 16 epochs; we further validate extrapolation on held-out dense-equivalent models up to 7.68B parameters. We find that: 1. Sparse scaling in data-limited settings: We introduce a scaling law that models loss as a function of active parameters, unique tokens, data repetition, and sparsity, accurately predicting performance across compute and data budgets. 2. Delayed data saturation: sparse training postpones diminishing returns from repeated data, making multi-epoch training more effective. 3. Resource trade-offs: With fixed data, loss-optimal sparsity is moderate ~ 50%, while compute-optimal sparsity is higher and grows with data scale. Overall, sparsity is not just a tool for efficiency, but a mechanism for improving scaling trade-offs under data scarcity. Our code is available at: https://github.com/boqian333/sparse-dc-scaling.

Legal NLP benchmarks evaluate models on randomly split data, implicitly assuming that legal language is stationary. We test this assumption by fine-tuning four transformer encoders -- XLM-RoBERTa (base and large) and their legal-domain variants -- on Ukrainian court decisions from three temporal epochs defined by geopolitical disruptions: pre-war (2008-2013), hybrid war (2014-2021), and full-scale invasion (2022-2026). Each model is trained on one epoch and evaluated on all three, producing a 3x3 cross-temporal generalization matrix. Four findings emerge. (1) Forward degradation is severe: models trained on pre-war data lose up to 27.2 percentage points of macro-F1 when applied to full-scale invasion era decisions. (2) The degradation is asymmetric: backward transfer (full-scale to pre-war) is substantially more robust than forward transfer, consistent with the hypothesis that legal language is additive. (3) Legal-domain pretraining (Legal-XLM-R) does not improve absolute performance but reduces forward degradation magnitude and asymmetry. (4) Chronological continual learning eliminates catastrophic forgetting for general XLM-R: pre-war knowledge is fully retained (+1.8 to +6.2 pp) while full-scale performance gains +16.5 to +19.0 pp; reverse-chronological training causes severe forgetting. Cross-jurisdictional pretraining on Swiss Judgment Prediction data improves absolute performance but does not reduce temporal degradation magnitude, confirming that temporal drift is an intrinsic property of legal language evolution. The dataset (428K decisions across three epochs) is publicly available as a LEXTREME contribution.

Climate emulation is an out-of-distribution (OOD) projection task. This is precisely the challenge where modern Machine Learning (ML) methods are most prone to failure. Consequently, while current ML emulators trained on present climate achieve high in-distribution performance, their future reliability under the inevitable distribution shifts of a changing climate remains a critical, poorly understood blind spot. Addressing this challenge requires a fundamental shift in how we understand, evaluate, and design climate emulators. In this work, we first confirm that climate change drives a statistically significant and progressively growing shift in atmospheric state distributions, rendering standard evaluation protocols insufficient. We empirically establish that seasonal variation serves as an effective proxy for these long-term climate shifts, providing access to $\textit{real-world}$ distribution shifts without recourse to heuristics like synthetic perturbations. Motivated by this link, we introduce a novel evaluation framework that leverages seasonal shifts as a rigorous, zero-overhead testbed for emulator robustness. Our systematic characterisation confirms that current state-of-the-art hybrid-ML emulators degrade significantly under these realistic shifts. Finally, we chart a path forward by identifying compositional generalisation, the ability to form novel combinations from observed elementary components, as a principled route towards robust climate emulation. We demonstrate that physically motivated decompositions substantially improve OOD performance with only modest trade-offs against in-distribution performance, providing an avenue towards ML-driven climate emulators robust to an unknown future.

Correlated-noise mechanisms are among the most promising approaches for improving the utility of differentially private model training, but rigorous guarantees require explicit, analyzable factorizations, and practical deployment requires memory efficiency. Recent works have developed banded inverse factorizations, which address both requirements by exploiting a banded structure in the correlation matrix. The bandwidth controls the size of the noise buffer used to correlate noise across iterations, and thus governs the tradeoff between utility and memory cost. Existing factorizations highlight this tradeoff: DP-$λ$CGD achieves high memory efficiency by using only a one-step noise buffer, but this limits its utility gains, while the banded inverse square root (BISR) factorization exploits larger correlation windows and is asymptotically optimal for large bandwidths but performs poorly at low bandwidths. We propose $γ$-BIFR, a unified generalization of both factorizations. In the low-memory, low-bandwidth regime, $γ$-BIFR significantly improves RMSE, amplified RMSE, and private training performance, while yielding tighter theoretical guarantees for multi-participation error in multi-epoch training.

The scaling laws guiding modern model training were calibrated for a single regime: data-rich, single-epoch pretraining. The dominant such scaling law form, Chinchilla's $L = E + A/N^α+ B/D^β$, has three structural limitations outside that regime: it diverges as unique data shrinks instead of saturating at the uninformed baseline; it cannot represent overfitting when capacity exceeds the data; and it conflates total examples seen with unique examples available. We propose a closed-form extension, $L(N, D, T) = E + (L_0 - E)\,h/(1+h)$ with $h = a/N^α+ b/T^β+ c\,N^γ/D^δ$, that decomposes loss into undercapacity, undertraining, and overfitting terms. It saturates between the irreducible loss $E$ and an uninformed baseline $L_0$ fixed by the loss type, and reduces to Chinchilla in the data-rich, single-epoch limit. We validate it on four multi-epoch experiments spanning four architecture families (MLPs, ResNets, Fourier neural operators, and transformers) across vision, scientific ML, and language domains, and refit it to five published LLM scaling-law grids. Extrapolating to higher compute and larger unique data than seen at fit time, our form achieves state-of-the-art RMSE on every published LLM grid we evaluate and on most cells of our constructed experiments. Once calibrated, the form admits a cost-aware allocation that recovers Chinchilla's optimum when data is free and shifts toward smaller corpora and more epochs as data grows expensive.

This revision updates a pop-to-jazz chord-generation rehearsal study. Best-epoch metrics still show that modest pop rehearsal preserves pop accuracy while improving jazz prediction, but v2 corrects released-checkpoint selection: the released F1 equals Phase 0, F2 had a transcription error, and ft-pop80-v2 restores a hash-distinct jazz-adapted F1 across 3 seeds.