ResNEsts and DenseNEsts: Block-based DNN Models with Improved Representation Guarantees
This work addresses a theoretical gap in understanding representation guarantees for deep neural networks, specifically for researchers in machine learning theory and architecture design, but it is incremental as it builds on existing ResNet and DenseNet frameworks.
The paper tackles the problem that theoretical models used to prove residual networks (ResNets) are better than linear predictors differ from standard ResNets, lacking nonlinearities at the final residual representation. They define ResNEsts by dropping these nonlinearities, show that wide ResNEsts with bottleneck blocks guarantee adding more blocks does not decrease performance, and propose DenseNEsts which inherently exhibit this property without architectural changes.
Models recently used in the literature proving residual networks (ResNets) are better than linear predictors are actually different from standard ResNets that have been widely used in computer vision. In addition to the assumptions such as scalar-valued output or single residual block, these models have no nonlinearities at the final residual representation that feeds into the final affine layer. To codify such a difference in nonlinearities and reveal a linear estimation property, we define ResNEsts, i.e., Residual Nonlinear Estimators, by simply dropping nonlinearities at the last residual representation from standard ResNets. We show that wide ResNEsts with bottleneck blocks can always guarantee a very desirable training property that standard ResNets aim to achieve, i.e., adding more blocks does not decrease performance given the same set of basis elements. To prove that, we first recognize ResNEsts are basis function models that are limited by a coupling problem in basis learning and linear prediction. Then, to decouple prediction weights from basis learning, we construct a special architecture termed augmented ResNEst (A-ResNEst) that always guarantees no worse performance with the addition of a block. As a result, such an A-ResNEst establishes empirical risk lower bounds for a ResNEst using corresponding bases. Our results demonstrate ResNEsts indeed have a problem of diminishing feature reuse; however, it can be avoided by sufficiently expanding or widening the input space, leading to the above-mentioned desirable property. Inspired by the DenseNets that have been shown to outperform ResNets, we also propose a corresponding new model called Densely connected Nonlinear Estimator (DenseNEst). We show that any DenseNEst can be represented as a wide ResNEst with bottleneck blocks. Unlike ResNEsts, DenseNEsts exhibit the desirable property without any special architectural re-design.