Learnable polynomial, trigonometric, and tropical activations
- URL: http://arxiv.org/abs/2502.01247v1
- Date: Mon, 03 Feb 2025 11:13:58 GMT
- Title: Learnable polynomial, trigonometric, and tropical activations
- Authors: Ismail Khalfaoui-Hassani, Stefan Kesselheim,
- Abstract summary: This paper investigates scalable neural networks with learnable activation functions based on function bases and tropicals.
We propose a scheme that preserves unitary variance in transformers and convolutional networks, ensuring stable gradient flow even in deep architectures.
Experiments demonstrate that networks with Hermite, Fourier, and Tropical-based learnable activations significantly improve over GPT-2 and ConvNeXt networks in terms of accuracy and perplexity in train and test.
- Score: 1.534667887016089
- License:
- Abstract: This paper investigates scalable neural networks with learnable activation functions based on orthogonal function bases and tropical polynomials, targeting ImageNet-1K classification and next token prediction on OpenWebText. Traditional activations, such as ReLU, are static. In contrast, learnable activations enable the network to adapt dynamically during training. However, stability issues, such as vanishing or exploding gradients, arise with improper variance management in deeper networks. To remedy this, we propose an initialization scheme that single-handedly preserves unitary variance in transformers and convolutional networks, ensuring stable gradient flow even in deep architectures. Extensive experiments demonstrate that networks with Hermite, Fourier, and Tropical-based learnable activations significantly improve over GPT-2 and ConvNeXt networks in terms of accuracy and perplexity in train and test, highlighting the viability of learnable activations in large-scale tasks. The activation functions developed here are the subject of a library coded entirely in pure PyTorch: torchortho, available at https://github.com/K-H-Ismail/torchortho.
Related papers
- Features that Make a Difference: Leveraging Gradients for Improved Dictionary Learning [4.051777802443125]
Sparse Autoencoders (SAEs) are a promising approach for extracting neural network representations.
We introduce Gradient SAEs, which modify the $k$-sparse autoencoder architecture by augmenting the TopK activation function.
We find evidence that g-SAEs learn latents that are on average more effective at steering models in arbitrary contexts.
arXiv Detail & Related papers (2024-11-15T18:03:52Z) - Globally Optimal Training of Neural Networks with Threshold Activation
Functions [63.03759813952481]
We study weight decay regularized training problems of deep neural networks with threshold activations.
We derive a simplified convex optimization formulation when the dataset can be shattered at a certain layer of the network.
arXiv Detail & Related papers (2023-03-06T18:59:13Z) - Simple initialization and parametrization of sinusoidal networks via
their kernel bandwidth [92.25666446274188]
sinusoidal neural networks with activations have been proposed as an alternative to networks with traditional activation functions.
We first propose a simplified version of such sinusoidal neural networks, which allows both for easier practical implementation and simpler theoretical analysis.
We then analyze the behavior of these networks from the neural tangent kernel perspective and demonstrate that their kernel approximates a low-pass filter with an adjustable bandwidth.
arXiv Detail & Related papers (2022-11-26T07:41:48Z) - Dynamics-aware Adversarial Attack of Adaptive Neural Networks [75.50214601278455]
We investigate the dynamics-aware adversarial attack problem of adaptive neural networks.
We propose a Leaded Gradient Method (LGM) and show the significant effects of the lagged gradient.
Our LGM achieves impressive adversarial attack performance compared with the dynamic-unaware attack methods.
arXiv Detail & Related papers (2022-10-15T01:32:08Z) - Rapid training of deep neural networks without skip connections or
normalization layers using Deep Kernel Shaping [46.083745557823164]
We identify the main pathologies present in deep networks that prevent them from training fast and generalizing to unseen data.
We show how these can be avoided by carefully controlling the "shape" of the network's kernel function.
arXiv Detail & Related papers (2021-10-05T00:49:36Z) - Learning specialized activation functions with the Piecewise Linear Unit [7.820667552233989]
We propose a new activation function called Piecewise Linear Unit(PWLU), which incorporates a carefully designed formulation and learning method.
It can learn specialized activation functions and achieves SOTA performance on large-scale datasets like ImageNet and COCO.
PWLU is also easy to implement and efficient at inference, which can be widely applied in real-world applications.
arXiv Detail & Related papers (2021-04-08T11:29:11Z) - GradInit: Learning to Initialize Neural Networks for Stable and
Efficient Training [59.160154997555956]
We present GradInit, an automated and architecture method for initializing neural networks.
It is based on a simple agnostic; the variance of each network layer is adjusted so that a single step of SGD or Adam results in the smallest possible loss value.
It also enables training the original Post-LN Transformer for machine translation without learning rate warmup.
arXiv Detail & Related papers (2021-02-16T11:45:35Z) - A Use of Even Activation Functions in Neural Networks [0.35172332086962865]
We propose an alternative approach to integrate existing knowledge or hypotheses of data structure by constructing custom activation functions.
We show that using an even activation function in one of the fully connected layers improves neural network performance.
arXiv Detail & Related papers (2020-11-23T20:33:13Z) - Revisiting Initialization of Neural Networks [72.24615341588846]
We propose a rigorous estimation of the global curvature of weights across layers by approximating and controlling the norm of their Hessian matrix.
Our experiments on Word2Vec and the MNIST/CIFAR image classification tasks confirm that tracking the Hessian norm is a useful diagnostic tool.
arXiv Detail & Related papers (2020-04-20T18:12:56Z) - Large-Scale Gradient-Free Deep Learning with Recursive Local
Representation Alignment [84.57874289554839]
Training deep neural networks on large-scale datasets requires significant hardware resources.
Backpropagation, the workhorse for training these networks, is an inherently sequential process that is difficult to parallelize.
We propose a neuro-biologically-plausible alternative to backprop that can be used to train deep networks.
arXiv Detail & Related papers (2020-02-10T16:20:02Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.