Relaxed activation analysis of dataflow networks - A clock calculus for machine learning and real-time scheduling

As machine learning(ML) systems evolve to continual adaptation, each re-training cycle uses compute, annotation, and energy. We introduce TIMEGATE, a policy layer managing adaptation by budgeting time, labeling, training, and evaluation. TIMEGATE emits a metric-availability signal M for partial vs. full-evaluation decisions. We validate: (i) labeling outperforms training by 2.3x on Adult tabular; (ii) it transfers to LLaMA-3.1-8B + QLoRA on SST-2 (accuracy 0.80 to 0.96; M =1 in 35/36 runs); (iii) M is informative, 28-cell sensitivity shows M drops to 0.81 at tight thresholds; (iv) 100-cycle simulation achieves 66% evaluation-compute savings with no silent mis-promotions; (v) 10%-slice evaluation on LLaMA uses 89% less wall-clock and energy on a single H200 (ratios agree to 0.2%).

Semantic faults specific to the use of machine learning models are a common problem for machine learning developers, causing suboptimal predictions, high computational cost, or incorrect outputs. For example, one may erroneously use unscaled data to train a scale-sensitive model. Machine learning developers detect these faults after training their models and manually analyzing the results, making it an inefficient process. We propose a novel data-aware static analysis approach to detect semantic faults in machine learning code, allowing developers to reveal these bugs while writing code instead of after training the model. Our approach uses combined data and control flow analysis, and API contracts, enabling data-aware reasoning about machine learning code at a high level of abstraction. We highlight the potential of our solution by analyzing a sample of real-world machine learning notebooks, finding that we can detect faults that require a data-aware approach.

Grokking suggests that fitting the training data and learning a simple underlying rule may occur on different time scales. We formalize this phenomenon by separating the fast decay of the classification loss from the slower simplification of the learned representation, and we call the resulting pair of stopping times two training clocks. For deep linear networks, we show that a post-margin gap-growth or one-step tail-contraction condition reduces the cross-entropy loss to level epsilon on a logarithmic time scale. In contrast, when layerwise weight decay is present, the induced regularization on the end-to-end map can be expressed as a Schatten-type penalty; under a sharp late-time Kurdyka-Lojasiewicz tail, this structural energy closes on a polynomial time scale. The two clocks, therefore, separate fitting from representation simplification. We then explain how the same mechanism can appear in ReLU MLPs. In regions where the activation patterns on the training set remain fixed, the network reduces to a linear model in the active coordinates. In a two-layer ReLU embedding model, chain-rule estimates further show that the classifier head can receive larger effective gradients than the embedding block under controlled downstream norms. This supports a two-stage mechanism in which the classifier fits first, while the representation continues to simplify later. We use modular addition as the main experimental setting. The deep linear theory provides the rigorous core of the analysis. But the ReLU results are formulated as conditional reductions that account for empirical behavior without claiming a global proof for nonlinear training dynamics.