Systematic Evaluation of Learning Rate Scheduling Strategies Across Heterogeneous Architectures

The learning-rate schedule is a consequential choice in training deep networks, yet the policies in common use are heuristic, and published comparisons are hard to read, because architecture, dataset, and budget tend to vary alongside the schedule. We study BrachistoneLR, a schedule built by mapping the vertical coordinate of the brachistochrone, the curve of fastest descent under gravity, onto the range between a peak and a floor rate. Expanding the definition shows it to be cosine annealing with the half-period set to E - 1 instead of E, the configuration a standard implementation gives when its period argument is one less than the number of epochs. The rate therefore reaches its floor at the last epoch trained rather than one epoch later, and we show this difference decays as E^-2, making it a short-horizon effect. We then benchmark six schedules over 72 runs on three image classification datasets (MNIST, Fashion-MNIST, CIFAR-10) and four architecture families (fully connected, convolutional, recurrent, residual), fixing the optimizer, data pipeline, and evaluation protocol so that only the schedule varies. Schedules that fall smoothly from peak to floor beat the constant rate and calendar-based decay by margins that grow with task difficulty, reaching 2.5 points of dataset mean on CIFAR-10. Within that leading group, BrachistoneLR, cosine annealing, and warmup-cosine lie within 0.06 accuracy points and 0.17 of a mean rank, which one seed per configuration cannot separate. BrachistoneLR is best on both residual networks and has the highest CIFAR-10 mean, and it sets no milestones, decay factor, warmup length, or restart period. We conclude that the shape of a schedule matters more than its parameterization, that the choice of whether to use a smooth schedule matters more than the choice among them, and that the terminal-rate distinction is worth attention only over short horizons.

Learning rate scheduling has evolved from the single global fixed rate of early SGD to sophisticated layer-wise adaptive strategies. We systematize this evolution into five generations: (Gen1) global fixed learning rates, (Gen2) global scheduling, (Gen3) parameter-level adaptation, (Gen4) layer-level differentiation, and (Gen5) joint layer-time scheduling. We trace the fundamental motivation behind each transition, showing how the shift from one-size-fits-all to tailoring by layer and time addresses the impossible trinity of transfer learning: lower layers require small updates to preserve general knowledge while higher layers need large updates to adapt to new tasks. Building on this taxonomy, we propose Discriminative Adaptive Layer Scaling (DALS), a unified framework that integrates phase-adaptive cosine scheduling, depth-aware Grokfast gradient filtering, and LARS-style trust ratios into a single coherent optimizer. We benchmark 18 strategies including three DALS variants across all five generations on five datasets: synthetic, CIFAR-10 (from scratch), RTE, TREC-6, and IMDb (fine-tuning). On synthetic, DALS achieves the best accuracy at 98.0%, while DALS-Fast reaches 90% in just 3 epochs. The cross-dataset analysis reveals striking regime-dependent patterns -- no single strategy wins across all regimes. Critically, STLR+Discriminative, the ULMFiT champion, catastrophically fails on from-scratch tasks (43.6% on TREC-6 from scratch vs. 96.8% with RAdam), confirming that directional decay biases are harmful without pretrained features. DALS avoids either extreme, achieving the best synthetic result while maintaining competitive fine-tuning performance.

Introduce a MinHash-based similarity scheduling framework that constructs a progressive curriculum over neural architecture code for LLM-based neural architecture search (NAS). Using 128-permutation MinHash signatures over normalised 7-gram source code shingles, we partition the reference pool into similarity bands and present them in increasing architectural heterogeneity, with the best LoRA adapter from each stage merged cumulatively into the backbone. We evaluate the framework on OlympicCoder-7B within the LEMUR benchmark on CIFAR-10 image classification, generating N =15 candidate architectures per epoch across six progressive fine-tuning steps. The curriculum achieves 60% peak success rate at the high-similarity level without post-processing repair. A 2*2 ablation at the most diverse level curriculum versus base model, with versus without partial interface repair reveals that without repair the base model (47% peak SR) substantially outperforms the curriculum model (7% SR), while adding partial repair brings both to 53% SR. This pattern is consistent with merge-level weight drift progressively erasing evaluator-interface priors, and suggests that interface repair and curriculum scheduling target distinct failure modes. We further report a cross-dataset transfer observation on SVHN, where direct base-model generation without curriculum warmup yields 27% peak SR at substantially lower accuracy (60.5%) than the CIFAR-10 equivalent, consistent with the increased synthesis difficulty of the unq-family anchor architecture.