In computer vision, the basic pipeline of most convolutional neural networks consists of multiple feature extraction layers, where the input signal is downsampled to a lower resolution in each subsequent layer. This downsampling process is commonly referred to as pooling, which is an essential operation in CNNs. Pooling improves robustness against transformations, reduces the number of trainable parameters, increases the receptive field, and lowers computation time. Since pooling is a lossy process but remains important for extracting high-level information from low-level representations, it is important to preserve the most prominent information from previous activations to improve network discriminability. Standard pooling is usually performed using dense pooling methods, such as max pooling or average pooling, or through strided convolutional kernels. In this paper, we propose a simple yet effective adaptive pooling method, called FlexPooling, which generalizes average pooling by learning a weighted average over activations jointly with the rest of the network. We further show that attaching Simple Auxiliary Classifiers (SAC) to the CNN improves performance and demonstrates the effectiveness of the proposed method compared with standard pooling methods. Experiments on multiple popular image classification datasets show that FlexPooling consistently outperforms baseline networks, achieving approximately 1 to 3 percent improvement in accuracy.
This paper proposes a new method to improve the training efficiency of deep convolutional neural networks. During training, the method evaluates scores to measure how much each layer's parameters change and whether the layer will continue learning or not. Based on these scores, the network is scaled down such that the number of parameters to be learned is reduced, yielding a speed up in training. Unlike state-of-the-art methods that try to compress the network to be used in the inference phase or to limit the number of operations performed in the backpropagation phase, the proposed method is novel in that it focuses on reducing the number of operations performed by the network in the forward propagation during training. The proposed training strategy has been validated on two widely used architecture families: VGG and ResNet. Experiments on MNIST, CIFAR-10 and Imagenette show that, with the proposed method, the training time of the models is more than halved without significantly impacting accuracy. The FLOPs reduction in the forward propagation during training ranges from 17.83% for VGG-11 to 83.74% for ResNet-152. These results demonstrate the effectiveness of the proposed technique in speeding up learning of CNNs. The technique will be especially useful in applications where fine-tuning or online training of convolutional models is required, for instance because data arrive sequentially.
Giorgio Cruciata, Luca Cruciata, Liliana Lo Presti +2
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.
Modern image classifiers widely adopt global average pooling (GAP) followed by a linear classification head. This linearity ensures that the image-level logits equal the average of logits obtained by applying the classification head pointwise to the feature grid prior to GAP. Consequently, standard classifiers may inherently retain spatial class evidence that remains recoverable even when the image-level prediction is incorrect. This structure naturally suggests a multiple-instance learning (MIL) interpretation, where an image is viewed as a bag of spatial instances. Within this formulation, we demonstrate that standard classifiers trained with a single label per image can still learn the intended classification task in multi-object scenes. We further exploit this property to decompose image-level logits into a prediction grid, providing a post-hoc diagnostic to extract spatial class evidence that GAP otherwise obscures. Our systematic evaluation reveals that off-the-shelf models consistently recover the ground-truth class within foreground regions. The MIL interpretation further suggests that common classifier failures reflect known limitations of mean aggregation.