Multiplications are responsible for most of the computational cost involved in neural network training and inference. Recent research has thus looked for ways to reduce the cost associated with them. Inspired by Mogami (2020), we replace multiplication with a cheap piecewise affine approximation that is achieved by adding the bit representation of the floating point numbers together as integers. We show that transformers can be trained with the resulting modified matrix multiplications on both vision and language tasks with little to no performance impact, and without changes to the training hyperparameters. We further replace all non-linearities in the networks making them fully and jointly piecewise affine in both inputs and weights. Finally, we show that we can eliminate all multiplications in the entire training process, including operations in the forward pass, backward pass and optimizer update, demonstrating the first successful training of modern neural network architectures in a fully multiplication-free fashion.

We consider the problem of online learning in the presence of distribution shifts that occur at an unknown rate and of unknown intensity. We derive a new Bayesian online inference approach to simultaneously infer these distribution shifts and adapt the model to the detected changes by integrating ideas from change point detection, switching dynamical systems, and Bayesian online learning. Using a binary'change variable,' we construct an informative prior such that-if a change is detected-the model partially erases the information of past model updates by tempering to facilitate adaptation to the new data distribution. Furthermore, the approach uses beam search to track multiple change-point hypotheses and selects the most probable one in hindsight. Our proposed method is model-agnostic, applicable in both supervised and unsupervised learning settings, suitable for an environment of concept drifts or covariate drifts, and yields improvements over state-of-the-art Bayesian online learning approaches.

Segmentation of curvilinear structures such as vasculature and road networks is challenging due to relatively weak signals and complex geometry/topology.

This document supplements our main paper entitled Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks as follows: (i) Sec. S1 firsts gives some of the formal definitions and interpretations omitted from the main paper due to space limitations. Next, it involves a discussion and contrasts our dimension estimator against the commonly used ones. Finally, it provides additional details into the regularizer we devised in the main paper; (ii) we then provide the complement the experimental evaluations given in the main paper and present additional studies on our synthetic diffusion data.

Almost every single image restoration problem has a closely related parameter, such as the scale factor in super-resolution, the noise level in image denoising, and the quality factor in JPEG deblocking. Although recent studies on image restoration problems have achieved great success due to the development of deep neural networks, they handle the parameter involved in an unsophisticated way. Most previous researchers either treat problems with different parameter levels as independent tasks, and train a specific model for each parameter level; or simply ignore the parameter, and train a single model for all parameter levels. The two popular approaches have their own shortcomings. The former is inefficient in computing and the latter is ineffective in performance. In this work, we propose a novel system called functional neural network (FuncNet) to solve a parametric image restoration problem with a single model. Unlike a plain neural network, the smallest conceptual element of our FuncNet is no longer a floating-point variable, but a function of the parameter of the problem. This feature makes it both efficient and effective for a parametric problem.

We propose Conditional Adapter (CODA), a parameter-efficient transfer learning method that also improves inference efficiency. CODA generalizes beyond standard adapter approaches to enable a new way of balancing speed and accuracy using conditional computation. Starting with an existing dense pretrained model, CODA adds sparse activation together with a small number of new parameters and a light-weight training phase. Our experiments demonstrate that the CODA approach provides an unexpectedly efficient way to transfer knowledge. Across a variety of language, vision, and speech tasks, CODA achieves a 2x to 8x inference speed-up compared to the state-of-the-art Adapter approaches with moderate to no accuracy loss and the same parameter efficiency.