We propose the Hierarchical Flow (HF) model constrained by isometric regularizations for manifold learning that combines manifold learning goals such as dimensionality reduction, inference, sampling, projection and density estimation into one unified framework. Our proposed HF model is regularized to not only produce embeddings preserving the geometric structure of the manifold, but also project samples onto the manifold in a manner conforming to the rigorous definition of projection. Theoretical guarantees are provided for our HF model to satisfy the two desired properties. In order to detect the real dimensionality of the manifold, we also propose a two-stage dimensionality reduction algorithm, which is a time-efficient algorithm thanks to the hierarchical architecture design of our HF model. Experimental results justify our theoretical analysis, demonstrate the superiority of our dimensionality reduction algorithm in cost of training time, and verify the effect of the aforementioned properties in improving performances on downstream tasks such as anomaly detection.

Isometric Manifold Learning using Hierarchical Flow

The model identifiability is a considerable issue in the unsupervised learning of disentangled representations. The PCA inductive biases revealed recently for unsupervised disentangling in VAE-based models are shown to improve local alignment of latent dimensions with principal components of the data. In this paper, in additional to the PCA inductive biases, we propose novel geometric inductive biases from the manifold perspective for unsupervised disentangling, which induce the model to capture the global geometric properties of the data manifold with guaranteed model identifiability. We also propose a Geometric Disentangling Regularized AutoEncoder (GDRAE) that combines the PCA and the proposed geometric inductive biases in one unified framework. The experimental results show the usefulness of the geometric inductive biases in unsupervised disentangling and the effectiveness of our GDRAE in capturing the geometric inductive biases.

Geometric Inductive Biases for Identifiable Unsupervised Learning of Disentangled Representations

The information bottleneck (IB) method is a technique for extracting information that is relevant for predicting the target random variable from the source random variable, which is typically implemented by optimizing the IB Lagrangian that balances the compression and prediction terms. However, the IB Lagrangian is hard to optimize, and multiple trials for tuning values of Lagrangian multiplier are required. Moreover, we show that the prediction performance strictly decreases as the compression gets stronger during optimizing the IB Lagrangian. In this paper, we implement the IB method from the perspective of supervised disentangling. Specifically, we introduce Disentangled Information Bottleneck (DisenIB) that is consistent on compressing source maximally without target prediction performance loss (maximum compression). Theoretical and experimental results demonstrate that our method is consistent on maximum compression, and performs well in terms of generalization, robustness to adversarial attack, out-of-distribution detection, and supervised disentangling.

Disentangled Information Bottleneck

ML: Representation Learning

poster

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-23 is the Thirty-Seventh AAAI Conference on Artificial Intelligence. The theme of this conference is to create collaborative bridges within and beyond AI. Like previous AAAI conferences, AAAI-23 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and two new activities: a Bridge Program and a Lab Program. Many of these activities are tailored to the theme of bridges and all are selected according to the highest standards, with additional programs for students and young researchers. 
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AAAI 2023

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines.

Posters & Demos I

Main Track

technical paper

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

Ziqi Pan

3

SHORT BIO

Presentations

Isometric Manifold Learning using Hierarchical Flow

Geometric Inductive Biases for Identifiable Unsupervised Learning of Disentangled Representations

Disentangled Information Bottleneck

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