Auto-Unrolled Proximal Gradient Descent: An AutoML Approach to Interpretable Waveform Optimization

Deep neural networks with repeated architectural blocks, such as transformers, often exhibit structured relationships across layers that emerge during training. Motivated by this observation, we introduce Depth-wise Gradient Augmentation, a general optimization paradigm in which the update applied to each layer is obtained by transforming the collection of block-wise optimizer updates along the depth dimension. Within this framework, we study Gradient Smoothing, a family of depth-wise smoothing methods, and instantiate it with a simple local Window Smoothing operator. The resulting method operates directly on block-wise updates produced by arbitrary base optimizers (e.g., SGD, Adam, Muon), incurs minimal computational overhead, and is compatible with existing optimization pipelines. We evaluate Gradient Smoothing across a diverse set of architectures and training regimes, including language model pretraining, RL post-training of LLMs for reasoning, diffusion modeling, and image classification with Vision Transformers. Across these settings, Gradient Smoothing consistently improves optimization and generalization performance without modifying model architectures or training objectives. We further show that it promotes more structured representation evolution across depth, consistent with its interpretation as a structured depth-wise preconditioning method. Together, these results establish Depth-wise Gradient Augmentation as a promising framework for exploiting cross-depth structure in optimization and demonstrate Gradient Smoothing as a simple and broadly applicable instantiation.

Efficient deep learning traditionally relies on static heuristics like weight magnitude or activation awareness (e.g., Wanda, RIA). While successful in unstructured settings, we observe a critical limitation when applying these metrics to the structural pruning of deep vision networks. These contemporary metrics suffer from a magnitude bias, failing to preserve critical functional pathways. To overcome this, we propose a decoupled kinetic paradigm inspired by Alternating Gradient Flow (AGF), utilizing an absolute feature-space Taylor expansion to accurately capture the network's structural "kinetic utility". First, we uncover a topological phase transition at extreme sparsity, where AGF successfully preserves baseline functionality and exhibits topological implicit regularization, avoiding the collapse seen in models trained from scratch. Second, transitioning to architectures without strict structural priors, we reveal a phenomenon of Sparsity Bottleneck in Vision Transformers (ViTs). Through a gradient-magnitude decoupling analysis, we discover that dynamic signals suffer from signal compression in converged models, rendering them suboptimal for real-time routing. Finally, driven by these empirical constraints, we design a hybrid routing framework that decouples AGF-guided offline structural search from online execution via zero-cost physical priors. We validate our paradigm on large-scale benchmarks: under a 75% compression stress test on ImageNet-1K, AGF effectively avoids the structural collapse where traditional metrics aggressively fall below random sampling. Furthermore, when systematically deployed for dynamic inference on ImageNet-100, our hybrid approach achieves Pareto-optimal efficiency. It reduces the usage of the heavy expert by approximately 50% (achieving an estimated overall cost of 0.92$\times$) without sacrificing the full-model accuracy.

Modern deep models are often pretrained on large-scale data with missing labels using composite objectives, where the relative weights of multiple loss terms act as hyperparameters. Tuning these weights with random search or Bayesian optimization is computationally expensive, as it requires many independent training runs. To address this, we propose a gradient-based bilevel method that learns pretraining loss weights online by aligning the composite pretraining gradient with a downstream objective. By exploiting the structure of the loss, the method avoids the multiple backward passes typically required by truncated backpropagation through the full model, reducing the overhead of hyperparameter tuning to approximately 30% above a single training run. We evaluate the approach on event-sequence modeling and self-supervised computer vision, where it matches or improves upon carefully tuned baselines while substantially reducing the cost of hyperparameter tuning compared to random or Bayesian search.