[Paper Review] Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches

Yeming Wen, Paul Vicol+3 more|arXiv (Cornell University)|Mar 12, 2018

Advanced Neural Network Applications25 references175 citations

TL;DR

Flipout decorrelates gradient perturbations within a mini-batch, achieving near-ideal 1/N variance reduction for various architectures and enabling faster large-batch training and GPU-accelerated evolution strategies.

ABSTRACT

Stochastic neural net weights are used in a variety of contexts, including regularization, Bayesian neural nets, exploration in reinforcement learning, and evolution strategies. Unfortunately, due to the large number of weights, all the examples in a mini-batch typically share the same weight perturbation, thereby limiting the variance reduction effect of large mini-batches. We introduce flipout, an efficient method for decorrelating the gradients within a mini-batch by implicitly sampling pseudo-independent weight perturbations for each example. Empirically, flipout achieves the ideal linear variance reduction for fully connected networks, convolutional networks, and RNNs. We find significant speedups in training neural networks with multiplicative Gaussian perturbations. We show that flipout is effective at regularizing LSTMs, and outperforms previous methods. Flipout also enables us to vectorize evolution strategies: in our experiments, a single GPU with flipout can handle the same throughput as at least 40 CPU cores using existing methods, equivalent to a factor-of-4 cost reduction on Amazon Web Services.

Motivation & Objective

• Motivate the use of stochastic weight perturbations for regularization, Bayesian inference, exploration, and ES.
• Address inefficiency caused by shared perturbations across mini-batch examples.
• Introduce Flipout to decorrelate gradients while preserving unbiasedness.
• Provide an efficient vectorized implementation suitable for GPUs/TPUs.
• Demonstrate variance reduction, regularization benefits, and speedups across architectures.

Proposed method

• Assume perturbations are independent and symmetric about zero; show perturbation invariance under random sign flips.
• Define Flipout: per-example perturbations DeltaW_n = DeltaW_hat ∘ (r_n s_n^T) using random ±1 vectors r_n, s_n.
• Show unbiased gradient estimates despite decorrelation by proving distributional equivalence to shared perturbations.
• Provide a vectorized forward pass formulation Y = φ(XW̄ + ((X ∘ S) ΔŴ) ∘ R) to enable GPU-friendly computation.
• Analyze gradient variance with a decomposition into alpha, beta, gamma terms and prove Flipout reduces variance to the ideal 1/N scaling.
• Discuss applications to Gaussian perturbations, DropConnect, LSTMs, CNNs, and Evolution Strategies, including GPU-based speedups.

Experimental results

Research questions

• RQ1 Can per-example decorrelation via Flipout achieve unbiased gradient estimates while attaining the ideal 1/N variance reduction across network types (FC, CNN, RNN)?
• RQ2 How does Flipout affect training speed and efficiency in large-batch regimes and on GPU-accelerated ES implementations?
• RQ3 To what extent can Flipout regularize recurrent connections (LSTMs) and improve performance against dropout-based methods?
• RQ4 What are the computational overheads of Flipout and how do they compare to shared perturbations and local reparameterization tricks?

Key findings

• Flipout yields unbiased gradient estimates and achieves the ideal 1/N variance reduction across fully connected, convolutional, and LSTM architectures.
• Empirically, Flipout provides significant variance reduction in large mini-batch settings and speeds up training time.
• Flipout regularizes LSTMs more effectively than dropout-based methods in language modeling tasks.
• Flipout enables vectorized evolution strategies on GPUs, achieving comparable throughput to 40 CPU cores with reduced cost on cloud platforms.
• In large-batch Bayes by Backprop experiments, Flipout converges about 3x faster in iterations than shared perturbations, with roughly 1.5x overall speedup due to overheads.
• Across tasks, Flipout demonstrates faster convergence and effective regularization compared to prior perturbation and dropout-based methods.