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Jose I. Mestre

Jose I. Mestre contributes to research discovery and scholarly infrastructure.

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Machine Learning Artificial Intelligence

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preprint2026arXiv

FedOUI: OUI-Guided Client Weighting for Federated Aggregation

Federated learning usually aggregates client updates using dataset size or gradient-level criteria, while overlooking internal signals about how each client model is organizing its input space during training. We introduce FedOUI, a simple aggregation rule based on the Overfitting-Underfitting Indicator (OUI), an activation-based and label-free metric. Each participating client sends its local update together with a OUI value computed on a fixed probe batch, and the server estimates the round-wise OUI distribution to assign lower weights to structurally atypical clients through a smooth reweighting rule. We evaluate FedOUI on CIFAR-10 under strong non-IID partitioning and noisy-client conditions, comparing it with FedAvg, FedProx, and a gradient-alignment baseline. The clearest gains appear under strong heterogeneity, where OUI-based weighting improves aggregation quality while remaining lightweight and interpretable. These results show that internal activation structure can provide useful information for federated aggregation beyond client size and gradient geometry.

preprint2026arXiv

OUI as a Structural Observable: Towards an Activation-Centric View of Neural Network Training

Activation functions are what make deep networks expressive: without them, the model collapses to a linear map. Yet we still evaluate training mostly from the outside, through loss, accuracy, return, or final calibration, while the internal structural evolution of the network remains largely unobserved. In this paper, we argue that the Overfitting--Underfitting Indicator (OUI) should be understood as a first practical observable of that internal structure. Across our recent results, OUI consistently appears as an early, label-free, activation-based signal that reveals whether a network is entering a poor or promising training regime before convergence. In supervised learning, it anticipates weight decay regimes; in reinforcement learning, it discriminates learning-rate regimes early in PPO actor--critic; and in online control, it can drive layer-wise weight decay adaptation. Read together with recent evidence that activation patterns tend to stabilize earlier than parameters, these results suggest a broader research direction: an activation-centric theory of training dynamics. OUI is becoming an empirical foothold toward this theory.

preprint2026arXiv

OUIDecay: Adaptive Layer-wise Weight Decay for CNNs Using Online Activation Patterns

Weight decay remains one of the most widely used regularization mechanisms for training convolutional neural networks, yet it is still commonly applied as a fixed coefficient shared by all layers throughout training. This uniform treatment ignores that different layers may follow different structural dynamics and therefore may require different regularization strengths. In this work, we propose OUIDecay, an adaptive layer-wise and time-dependent weight decay scheduler for CNNs driven by the Overfitting-Underfitting Indicator (OUI), an activation-based metric previously shown to provide early information about regularization quality. OUIDecay uses a lightweight batch-based formulation of OUI to monitor the structural behavior of each layer online and periodically rescales its weight decay relative to the other layers in the network. Unlike gradient-based adaptive decay methods, our approach relies on functional information extracted from activation patterns and does not require validation data. Experiments on EfficientNet-B0 with Stanford Cars, ResNet50 with Food101, DenseNet121 with CIFAR100, and MobileNetV2 with CIFAR10 show that OUIDecay achieves the best mean best-validation-loss in 7 out of 8 evaluated settings. These results indicate that activation-driven weight decay adaptation is a practical and effective alternative to fixed decay and gradient-based adaptive decay, while keeping the method lightweight and suitable for online use.

preprint2026arXiv

Refresh-Scaling the Memory of Balanced Adam

Recent evidence suggests that Adam performs robustly when its momentum parameters are tied, $β_1=β_2$, reducing the optimizer to a single remaining parameter. However, how this parameter should be set remains poorly understood. We argue that, in balanced Adam, $β$ should not be treated as a dimensionless constant: it defines a statistical memory horizon $H_β=(1-β)^{-1}$. In terms of the effective learning horizon $T_{\mathrm{ES}}$, estimated from the validation trajectory, we study the refresh count $R_β=(1-β)T_{\mathrm{ES}}$, which measures how many times Adam renews its internal statistics during the useful phase of training. Across 11 vision and language experiments, we find that choosing $β$ so that $R_β\approx1000$ selects different $β$ values depending on the training scale, yet improves robustness over the best fixed-beta baseline. Compared with the strongest fixed choice $β=0.944$, the refresh rule improves worst-case robustness, reducing the maximum relative gap in validation loss by 33.4\%, while bringing all 11 runs within 1\% of their validation oracle. These results suggest that the remaining hyperparameter of balanced Adam is more naturally viewed as a memory-scale variable than as a fixed constant. This provides a simple budget-aware perspective on optimizer scaling and opens a path toward treating Adam's momentum as part of the learning dynamics rather than as a static default.

preprint2026arXiv

StableGrad: Backward Scale Control without Batch Normalization

Training very deep neural networks requires controlling the propagation of magnitudes across depth. Without such control, activations and gradients may vanish, explode, or enter unstable regimes that make optimization fail. Modern architectures often mitigate this problem through Batch Normalization, residual connections, or other normalization layers, which repeatedly re-scale or bypass intermediate representations. However, these mechanisms are not always appropriate. In Physics-Informed Neural Networks (PINNs), the network represents a continuous physical field and its input derivatives define the training objective, making batch-dependent normalization problematic because it can introduce non-local dependencies into the predicted field and its derivatives. We propose StableGrad, an optimizer-level scale-control mechanism that corrects layer-wise weight-gradient imbalances without modifying the forward model. Because the normalization is applied only after backpropagation and before the optimizer update, the network output, its derivatives, and the physical residual remain unchanged. We analyze the effective training dynamics induced by this rescaling and evaluate StableGrad on deep PINNs as the target application, with BatchNorm-free convolutional networks serving as a diagnostic stress test. On PINN benchmarks, StableGrad improves matched-depth solution accuracy and makes deeper models more reliable under standard optimization. On ResNet and EfficientNet architectures, where removing Batch Normalization normally leads to training collapse, StableGrad stabilizes optimization without introducing any other architectural change. These results show that optimizer-level control of weight-gradient scale can provide a practical alternative when forward normalization is unavailable or undesirable.

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