Learn&Drop: Fast Learning of CNNs based on Layer Dropping

End-to-end training with full-depth backpropagation remains the dominant paradigm for optimizing deep neural networks, but its efficiency deteriorates as models grow deeper. Since every block must be executed and differentiated under a single global objective, full-depth BP introduces substantial parameter redundancy, activation-memory cost, and training latency, especially when neighboring layers exhibit highly correlated learning patterns. Directly skipping or removing layers can reduce cost, but often weakens representation capacity or requires architecture-specific reuse designs. In this paper, we propose Replacement Learning (RepL), a training-time paradigm that reduces full-depth redundancy by replacing selected blocks rather than simply discarding them. For each removed block, RepL inserts a lightweight computing layer that synthesizes a surrogate operator from the parameters of its adjacent preceding and succeeding blocks through a learnable transformation, and applies the synthesized operator to the preceding activation. In this way, RepL preserves local contextual continuity while avoiding unnecessary full-layer computation. We instantiate RepL for CNNs and ViTs with tailored parameter-fusion blocks that handle convolutional channels, feature resolutions, and transformer submodules. Extensive experiments on CIFAR-10, SVHN, STL-10, ImageNet, COCO, and CityScapes show that RepL reduces trainable parameters, GPU memory usage, and training time while matching or surpassing standard end-to-end training across classification, detection, and segmentation. Additional results on WikiText-2, transfer learning, inference throughput, checkpointing, stochastic depth, and INT8 quantization further demonstrate its generality and compatibility.

Understanding and exploiting the training dynamics of overparameterized deep neural networks remains a central challenge in modern machine learning. Recent evidence on Neural Collapse (NC) shows that class representations and classifiers exhibit highly structured geometry, while the Tunnel Effect suggests that only a subset of layers is essential for feature extraction. We combine these two perspectives and propose an NC-inspired training framework for simplifying deep networks during training. Our method monitors representation dynamics through the Inverse Fisher Criterion, a stable and efficient proxy for the variability collapse behavior, to identify both the split point between feature extraction and classification and the training stage at which simplification becomes viable. We then replace the trailing layers with a lightweight classification head and continue training the reduced model. Experiments on image-classification benchmarks across MLP, VGG, and ResNet architectures show that the proposed method achieves substantial parameter reductions while maintaining accuracy comparable to that of the full model. Code to reproduce the experiments can be found at: https://github.com/LorenzoSciandra/NNS.

Common practice when training Convolutional Neural Networks (CNNs) is to use randomly shuffled mini-batches. This creates two limitations: slower convergence, and a diminishing learning signal, since many samples are quickly classified as easy during training. We address these inefficiencies with A*-Inspired Batch Selection (A*-BS), a lightweight, model-agnostic strategy that formulates mini-batch scheduling as a heuristic search problem. Each batch is treated as a node in a search space and ranked using an A*-like score combining a loss-based difficulty measure with a reuse penalty. This encourages informative gradient updates and batch diversity throughout training, without modifying network architectures or optimization algorithms, so it integrates seamlessly into existing pipelines. We evaluate A*-BS on the twelve 2D classification tasks of the MedMNIST-v2 benchmark, using a deliberately simple architecture of approximately 2.25x10^5 parameters, compared against the ResNet-18 and ResNet-50 baselines reported by the benchmark. On half of these tasks, the lightweight model with A*-BS reaches higher accuracy and AUC than both ResNet baselines, with relative gains of up to 15%. An ablation under identical architecture and hyperparameters shows A*-BS outperforms random batch shuffling on all twelve tasks. Wall-clock measurements further show the lightweight CNN with A*-BS trains substantially faster than ResNet-18 and ResNet-50 on identical hardware. These results indicate that intelligent batch ordering can partially compensate for reduced architectural complexity, offering a computationally efficient alternative to deeper models, with reliability reinforced by strong performance even against deeper, more sophisticated architectures.