Empirical Evaluation and Theoretical Analysis for Representation Learning: A Survey

Representation learning enables us to automatically extract generic feature representations from a dataset to solve another machine learning task. Recently, extracted feature representations by a representation learning algorithm and a simple predictor have exhibited state-of-the-art performance on several machine learning tasks. Despite its remarkable progress, there exist various ways to evaluate representation learning algorithms depending on the application because of the flexibility of representation learning. To understand the current representation learning, we review evaluation methods of representation learning algorithms and theoretical analyses. On the basis of our evaluation survey, we also discuss the future direction of representation learning. Note that this survey is the extended version of Nozawa and Sato (2022).

Neural Lagrangian Schrödinger bridge

Population dynamics is the study of temporal and spatial variation in the size of populations of organisms and is a major part of population ecology. One of the main difficulties in analyzing population dynamics is that we can only obtain observation data with coarse time intervals from fixed-point observations due to experimental costs or other constraints. Recently, modeling population dynamics by using continuous normalizing flows (CNFs) and dynamic optimal transport has been proposed to infer the expected trajectory of samples from a fixed-point observed population. While the sample behavior in CNF is deterministic, the actual sample in biological systems moves in an essentially random yet directional manner. Moreover, when a sample moves from point A to point B in dynamical systems, its trajectory is such that the corresponding action has the smallest possible value, known as the principle of least action. To satisfy these requirements of the sample trajectories, we formulate the Lagrangian Schr\"odinger bridge (LSB) problem and propose to solve it approximately using neural SDE with regularization. We also develop a model architecture that enables faster computation. Our experiments show that our solution to the LSB problem can approximate the dynamics at the population level and that using the prior knowledge introduced by the Lagrangian enables us to estimate the trajectories of individual samples with stochastic behavior.

A Closer Look at Prototype Classifier for Few-shot Image Classification

The prototypical network is a prototype classifier based on meta-learning and is widely used for few-shot learning because it classifies unseen examples by constructing class-specific prototypes without adjusting hyper-parameters during meta-testing. Interestingly, recent research has attracted a lot of attention, showing that a linear classifier with fine-tuning, which does not use a meta-learning algorithm, performs comparably with the prototypical network. However, fine-tuning requires additional hyper-parameters when adapting a model to a new environment. In addition, although the purpose of few-shot learning is to enable the model to quickly adapt to a new environment, fine-tuning needs to be applied every time a new class appears, making fast adaptation difficult. In this paper, we analyze how a prototype classifier works equally well without fine-tuning and meta-learning. We experimentally found that directly using the feature vector extracted using standard pre-trained models to construct a prototype classifier in meta-testing does not perform as well as the prototypical network and linear classifiers with fine-tuning and feature vectors of pre-trained models. Thus, we derive a novel generalization bound for the prototypical network and show that focusing on the variance of the norm of a feature vector can improve performance. We experimentally investigated several normalization methods for minimizing the variance of the norm and found that the same performance can be obtained by using the L2 normalization and embedding space transformation without fine-tuning or meta-learning.

Disentanglement Analysis with Partial Information Decomposition

Given data generated from multiple factors of variation that cooperatively transform their appearance, disentangled representations aim at reversing the process by mapping data to multiple random variables that individually capture distinct generative factors. As the concept is intuitive but abstract, one needs to quantify it with disentanglement metrics to evaluate and compare the quality of disentangled representations between different models. Current disentanglement metrics are designed to measure the concentration, e.g., absolute deviation, variance, or entropy, of each variable conditioned by each generative factor, optionally offset by the concentration of its marginal distribution, and compare it among different variables. When representations consist of more than two variables, such metrics may fail to detect the interplay between them as they only measure pairwise interactions. In this work, we use the Partial Information Decomposition framework to evaluate information sharing between more than two variables, and build a framework, including a new disentanglement metric, for analyzing how the representations encode the generative factors distinctly, redundantly, and cooperatively. We establish an experimental protocol to assess how each metric evaluates increasingly entangled representations and confirm through artificial and realistic settings that the proposed metric correctly responds to entanglement. Our results are expected to promote information theoretic understanding of disentanglement and lead to further development of metrics as well as learning methods.

Loss function based second-order Jensen inequality and its application to particle variational inference

Bayesian model averaging, obtained as the expectation of a likelihood function by a posterior distribution, has been widely used for prediction, evaluation of uncertainty, and model selection. Various approaches have been developed to efficiently capture the information in the posterior distribution; one such approach is the optimization of a set of models simultaneously with interaction to ensure the diversity of the individual models in the same way as ensemble learning. A representative approach is particle variational inference (PVI), which uses an ensemble of models as an empirical approximation for the posterior distribution. PVI iteratively updates each model with a repulsion force to ensure the diversity of the optimized models. However, despite its promising performance, a theoretical understanding of this repulsion and its association with the generalization ability remains unclear. In this paper, we tackle this problem in light of PAC-Bayesian analysis. First, we provide a new second-order Jensen inequality, which has the repulsion term based on the loss function. Thanks to the repulsion term, it is tighter than the standard Jensen inequality. Then, we derive a novel generalization error bound and show that it can be reduced by enhancing the diversity of models. Finally, we derive a new PVI that optimizes the generalization error bound directly. Numerical experiments demonstrate that the performance of the proposed PVI compares favorably with existing methods in the experiment.

Toward Neural-Network-Guided Program Synthesis and Verification

We propose a novel framework of program and invariant synthesis called neural network-guided synthesis. We first show that, by suitably designing and training neural networks, we can extract logical formulas over integers from the weights and biases of the trained neural networks. Based on the idea, we have implemented a tool to synthesize formulas from positive/negative examples and implication constraints, and obtained promising experimental results. We also discuss two applications of our synthesis method. One is the use of our tool for qualifier discovery in the framework of ICE-learning-based CHC solving, which can in turn be applied to program verification and inductive invariant synthesis. Another application is to a new program development framework called oracle-based programming, which is a neural-network-guided variation of Solar-Lezama's program synthesis by sketching.

Abelian Neural Networks

We study the problem of modeling a binary operation that satisfies some algebraic requirements. We first construct a neural network architecture for Abelian group operations and derive a universal approximation property. Then, we extend it to Abelian semigroup operations using the characterization of associative symmetric polynomials. Both models take advantage of the analytic invertibility of invertible neural networks. For each case, by repeating the binary operations, we can represent a function for multiset input thanks to the algebraic structure. Naturally, our multiset architecture has size-generalization ability, which has not been obtained in existing methods. Further, we present modeling the Abelian group operation itself is useful in a word analogy task. We train our models over fixed word embeddings and demonstrate improved performance over the original word2vec and another naive learning method.

Understanding Negative Samples in Instance Discriminative Self-supervised Representation Learning

Instance discriminative self-supervised representation learning has been attracted attention thanks to its unsupervised nature and informative feature representation for downstream tasks. Self-supervised representation learning commonly uses more negative samples than the number of supervised classes in practice. However, there is an inconsistency in the existing analysis; theoretically, a large number of negative samples degrade supervised performance, while empirically, they improve the performance. We theoretically explain this empirical result regarding negative samples. We empirically confirm our analysis by conducting numerical experiments on CIFAR-10/100 datasets.