Mish: Self Regularized
Non-Monotonic Activation Function

BMVC 2020 (Official Paper)

News/ Media Coverage:

• (02/2020): Podcast episode on Mish at Machine Learning Café is out now. Listen on:

• (02/2020): Talk on Mish and Non-Linear Dynamics at Sicara is out now. Watch on:

• (07/2020): CROWN: A comparison of morphology for Mish, Swish and ReLU produced in collaboration with Javier Ideami. Watch on:

• (08/2020): Talk on Mish and Non-Linear Dynamics at Computer Vision Talks. Watch on:

• (12/2020): Talk on From Smooth Activations to Robustness to Catastrophic Forgetting at Weights & Biases Salon is out now. Watch on:

• (12/2020) Weights & Biases integration is now added 🔥. Get started.

• (08/2021) Comprehensive hardware based computation performance benchmark for Mish has been conducted by Benjamin Warner. Blogpost.

MILA/ CIFAR 2020 DLRLSS (Click on arrow to view)

Mish:

Minimum of f(x) is observed to be ≈-0.30884 at x≈-1.1924
Mish has a parametric order of continuity of: C^∞

Derivative of Mish with respect to Swish and Δ(x) preconditioning:

Further simplifying:

Alternative derivative form:

where:

We hypothesize the Δ(x) to be exhibiting the properties of a pre-conditioner making the gradient more smoother. Further details are provided in the paper.

Loss Landscape:

To visit the interactive Loss Landscape visualizer, click here.

Loss landscape visualizations for a ResNet-20 for CIFAR 10 using ReLU, Mish and Swish (from L-R) for 200 epochs training:

Mish provides much better accuracy, overall lower loss, smoother and well conditioned easy-to-optimize loss landscape as compared to both Swish and ReLU. For all loss landscape visualizations please visit this readme.

We also investigate the output landscape of randomly initialized neural networks as shown below. Mish has a much smoother profile than ReLU.

ImageNet Scores:

For Installing DarkNet framework, please refer to darknet(Alexey AB)

For PyTorch based ImageNet scores, please refer to this readme

Results on CSPResNext-50:

Results on CSPResNet-50:

Results on CSPDarkNet-53:

Results on SpineNet-49:

MS-COCO:

For PyTorch based MS-COCO scores, please refer to this readme

Credits to AlexeyAB, Wong Kin-Yiu and Glenn Jocher for all the help with benchmarking MS-COCO and ImageNet.

Variation of Parameter Comparison:

MNIST:

To observe how increasing the number of layers in a network while maintaining other parameters constant affect the test accuracy, fully connected networks of varying depths on MNIST, with each layer having 500 neurons were trained. Residual Connections were not used because they enable the training of arbitrarily deep networks. BatchNorm was used to lessen the dependence on initialization along with a dropout of 25%. The network is optimized using SGD on a batch size of 128, and for fair comparison, the same learning rates for each activation function was maintained. In the experiments, all 3 activations maintained nearly the same test accuracy for 15 layered Network. Increasing number of layers from 15 gradually resulted in a sharp decrease in test accuracy for Swish and ReLU, however, Mish outperformed them both in large networks where optimization becomes difficult.

The consistency of Mish providing better test top-1 accuracy as compared to Swish and ReLU was also observed by increasing Batch Size for a ResNet v2-20 on CIFAR-10 for 50 epochs while keeping all other network parameters to be constant for fair comparison.

Gaussian Noise with varying standard deviation was added to the input in case of MNIST classification using a simple conv net to observe the trend in decreasing test top-1 accuracy for Mish and compare it to that of ReLU and Swish. Mish mostly maintained a consistent lead over that of Swish and ReLU (Less than ReLU in just 1 instance and less than Swish in 3 instance) as shown below. The trend for test loss was also observed following the same procedure. (Mish has better loss than both Swish and ReLU except in 1 instance)

CIFAR10:

Significance Level:

The P-values were computed for different activation functions in comparison to that of Mish on terms of Top-1 Testing Accuracy of a Squeeze Net Model on CIFAR-10 for 50 epochs for 23 runs using Adam Optimizer at a Learning Rate of 0.001 and Batch Size of 128. It was observed that Mish beats most of the activation functions at a high significance level in the 23 runs, specifically it beats ReLU at a high significance of P < 0.0001. Mish also had a comparatively lower standard deviation across 23 runs which proves the consistency of performance for Mish.

Values rounded up which might cause slight deviation in the statistical values reproduced from these tests

Results:

News: Ajay Arasanipalai recently submitted benchmark for CIFAR-10 training for the Stanford DAWN Benchmark using a Custom ResNet-9 + Mish which achieved 94.05% accuracy in just 10.7 seconds in 14 epochs on the HAL Computing Cluster. This is the current fastest training of CIFAR-10 in 4 GPUs and 2nd fastest training of CIFAR-10 overall in the world.

Summary of Results (Vision Tasks):

Comparison is done based on the high priority metric, for image classification the Top-1 Accuracy while for Generative Networks and Image Segmentation the Loss Metric. Therefore, for the latter, Mish > Baseline is indicative of better loss and vice versa. For Embeddings, the AUC metric is considered.

Summary of Results (Language Tasks):

Comparison is done based on the best metric score (Test accuracy) across 3 runs.

Try It!

Cite this work:

@article{misra2019mish,
  title={Mish: A self regularized non-monotonic neural activation function},
  author={Misra, Diganta},
  journal={arXiv preprint arXiv:1908.08681},
  year={2019}
}