[Paper Review] SoftAdapt: Techniques for Adaptive Loss Weighting of Neural Networks with Multi-Part Loss Functions

A. Ali Heydari, Craig A. Thompson+1 more|arXiv (Cornell University)|Dec 27, 2019

Advanced Neural Network ApplicationsComputer Science32 references65 citations

TL;DR

SoftAdapt introduces adaptive weighting of multi-part loss components using softmax-inspired schemes that depend on the recent rate of change of each loss part, improving convergence without manual tuning.

ABSTRACT

Adaptive loss function formulation is an active area of research and has gained a great deal of popularity in recent years, following the success of deep learning. However, existing frameworks of adaptive loss functions often suffer from slow convergence and poor choice of weights for the loss components. Traditionally, the elements of a multi-part loss function are weighted equally or their weights are determined through heuristic approaches that yield near-optimal (or sub-optimal) results. To address this problem, we propose a family of methods, called SoftAdapt, that dynamically change function weights for multi-part loss functions based on live performance statistics of the component losses. SoftAdapt is mathematically intuitive, computationally efficient and straightforward to implement. In this paper, we present the mathematical formulation and pseudocode for SoftAdapt, along with results from applying our methods to image reconstruction (Sparse Autoencoders) and synthetic data generation (Introspective Variational Autoencoders).

Motivation & Objective

• Motivate and tackle the challenge of balancing multiple loss components in neural networks.
• Propose a general, fast, and optimizer-compatible method to adapt weights of loss terms during training.
• Show that adaptive weighting can outperform fixed or heuristically chosen weights across tasks.
• Demonstrate applicability to autoencoders, VAEs, and gradient-descent optimization benchmarks.

Proposed method

• Formulate the multi-part loss as F(x)=sum_k f_k(x) and define a weighted gradient direction h^i = sum_k alpha_k^i grad f_k(x^i).
• Compute component-wise performance rates s_k^i as a short-horizon rate of change of each f_k.
• Compute weights alpha^i via SoftAdapt variants using softmax over s^i (Original).
• Enhance with Loss Weighted variant: alpha_k^i scaled by current loss f_k^i.
• Optionally normalize the rate vector to sharpen distinctions between components.
• Provide pseudocode for SoftAdapt and its variants ready for integration with any gradient-descent optimizer.

Experimental results

Research questions

• RQ1 Can adaptive weighting of loss components improve training efficiency and outcomes over fixed equal weights?
• RQ2 How do different SoftAdapt variants (Original, Loss Weighted, Normalized) affect convergence across tasks and loss scales?
• RQ3 Is SoftAdapt compatible with common optimizers and architectures without substantial overhead?
• RQ4 How does adaptive weighting impact performance in autoencoders and VAEs compared to fixed heuristics?

Key findings

• SoftAdapt can yield faster convergence than fixed weights on benchmark optimization problems like Rosenbrock and Beale’s functions.
• In IntroVAE experiments, SoftAdapt-adaptive weights improve SSIM and PSNR metrics versus fixed weights while preserving similar training time.
• In Sparse Autoencoder experiments, SoftAdapt dynamically adjusting lambda improves reconstruction quality and classification performance compared to a fixed optimal lambda found by grid search.
• Across tasks, the adaptive weighting approach reduces the need for prior hyperparameter tuning and grid searches.
• The method is compatible with Adam and other gradient-based optimizers and is simple to implement as an add-on.