First, as R4 suggested, "symbolic35 tree" was more approachable for people in the ML community. Second, the symbolic tree is declared by the user using36 decorators and serves to represent high-level program constructs, which is different from the AST that represents all37 the syntactic structures for the program. For example, the full Python AST contains information about objects' class38 methods, whereas our symbolic representation does not.39 R4: "Second, most of their tool/language design could be summarized as adding some kind of non determinis-40 tic/parametric choice ... It's extension to ML does not introduce anything particularly new ..."41 We agree with R4 that symbolic programming and non-deterministic programming are well-studied topics in the PL42 community. However, we would like to emphasize that this work is the first to introduce such concepts to AutoML43 to significantly reduce engineering effort, which is a novel and useful contribution. For example, PyGlove leverages44 symbolic manipulation to decouple the search algorithm, search space and child program, which enabled us to unify45 the interface among search methods with and without weight sharing. To enable symbolic programming in Python,46 PyGlove implements an object model for maintaining the consistency of program state during symbolic manipulation.47 R4 "Provide the grammar in the main text"48 We understand the "grammar" here as a reference to the formal definition of the search space specification. We will49 revise current Appendix Table 3 into a formal definition, and add it to the "search space" sub-section.50

Language models employ a very large number of trainable parameters. Despite being highly overparameterized, these networks often achieve good out-of-sample test performance on the original task and easily fine-tune to related tasks. Recent observations involving, for example, intrinsic dimension of the objective landscape and the lottery ticket hypothesis, indicate that often training actively involves only a small fraction of the parameter space. Thus, a question remains how large a parameter space needs to be in the first place -- the evidence from recent work on model compression, parameter sharing, factorized representations, and knowledge distillation increasingly shows that models can be made much smaller and still perform well. Here, we focus on factorized representations of matrices that underpin dense, embedding, and self-attention layers. We use low-rank factorized representation of a reshaped and rearranged original matrix to achieve space efficient and expressive linear layers. We prove that stacking such low-rank layers increases their expressiveness, providing theoretical understanding for their effectiveness in deep networks. In Transformer models, our approach leads to more than tenfold reduction in the number of total trainable parameters, including embedding, attention, and feed-forward layers, with little degradation in on-task performance. The approach operates out-of-the-box, replacing each parameter matrix with its compact equivalent while maintaining the architecture of the network.

Meta-learning empowers data-hungry deep neural networks to rapidly learn from merely a few samples, which is especially appealing to tasks with small datasets. Critical in this context is the accumulated from related tasks. Existing meta-learning approaches typically rely on preselected priors, such as a Gaussian probability density function (pdf). The limited expressiveness of such priors however, hinders the enhanced performance of the trained model when dealing with tasks having exceedingly scarce data. Targeting improved expressiveness, this contribution introduces a prior that optimally fits the provided tasks using a novel non-injective change-of-variable (NCoV) model. Unlike preselected prior pdfs with fixed shapes, the advocated NCoV model can effectively approximate a considerably wide range of pdfs. Moreover, compared to conventional change-of-variable models, the introduced NCoV exhibits augmented expressiveness for pdf modeling, especially in high-dimensional spaces. Theoretical analysis underscores the appealing universal approximation capacity of the NCoV model. Numerical experiments conducted on three few-shot learning datasets validate the superiority of data-driven priors over the prespecified ones, showcasing its pronounced effectiveness when dealing with extremely limited data resources.

Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of nonstationary kernels.

Nuanced expressiveness, especially through detailed hand and facial expressions, is pivotal for enhancing the realism and vitality of digital human representations.In this work, we aim to learn expressive human avatars from a monocular RGB video; a setting that introduces new challenges in capturing and animating fine-grained details.To this end, we introduce EVA, a drivable human model that can recover fine details based on 3D Gaussians and an expressive parametric human model, SMPL-X.Focused on enhancing expressiveness, our work makes three key contributions.First, we highlight the importance of aligning the SMPL-X model with the video frames for effective avatar learning.Recognizing the limitations of current methods for estimating SMPL-X parameters from in-the-wild videos, we introduce a reconstruction module that significantly improves the image-model alignment.Second, we propose a context-aware adaptive density control strategy, which is adaptively adjusting the gradient thresholds to accommodate the varied granularity across body parts.Third, we develop a feedback mechanism that predicts per-pixel confidence to better guide the optimization of 3D Gaussians.Extensive experiments on two benchmarks demonstrate the superiority of our approach both quantitatively and qualitatively, especially on the fine-grained hand and facial details. We make our code available at the project website: https://evahuman.github.io.

The expressive power of neural networks is important for understanding deep learning. Most existing works consider this problem from the view of the depth of a network. In this paper, we study how width affects the expressiveness of neural networks. Classical results state that depth-bounded (e.g.

Critical in this context is the prior knowledge accumulated from related tasks.

However, such an approach is highly empirical and provides an indirect evaluation affected by external factors.