Relative representations enable zero-shot latent space communication (2209.15430v2)

Abstract: Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

• The paper introduces a novel method using relative representations to stabilize latent spaces without extra training.
• It employs cosine similarity with flexible anchor selection to achieve invariance across different neural network architectures.
• Empirical results demonstrate improved model interoperability and a strong performance proxy through latent similarity.

Summary of "Relative Representations Enable Zero-Shot Latent Space Communication"

The paper "Relative Representations Enable Zero-Shot Latent Space Communication" introduces a novel method to enhance the stability and interoperability of neural network models by utilizing relative representations in latent spaces. The authors address a significant limitation in current neural network training—namely, that latent spaces may become incoherent due to various sources of randomness like weight initialization and training hyperparameters. This incoherence impedes the reuse and comparison of neural network components.

Core Concept

The central concept revolves around creating relative representations based on the similarity between data samples and a fixed set of anchor points in the latent space. This approach shifts away from absolute representations to enforce invariance to transformations such as isometries or rescalings without requiring additional training.

Methodology

The paper outlines a methodology that focuses on the angles between encodings:

1. Relative Representations: The authors propose representing each data point in terms of its similarity to a set of anchor points using cosine similarity. This representation intrinsically encodes invariance to transformations that preserve angles.
2. Anchor Selection: Anchors can be chosen from within the training set or sourced from out-of-domain datasets. The choice of anchors is flexible but influenced by the specific task and domain.
3. Generalization Across Modalities: The paper empirically validates this representation approach using varied datasets (images, text, graphs) and tasks (classification, reconstruction).

Empirical Validation and Results

The authors present extensive experiments demonstrating the efficacy of the proposed representations:

• Zero-Shot Model Stitching: The framework allows for zero-shot integration of neural components from different trainings or architectures, demonstrated with AEs, VAEs, and transformers. This includes combinations over different stochastic situations, architectures, and datasets.
• Invariance and Stability: Empirical evidence shows the angles between latent space embeddings are preserved across different stochastic training settings. Relative representations lead to much better-aligned latent spaces compared to absolute representations.
• Latent Similarity and Performance Proxy: In node classification tasks, the paper showcases how similarity in relative latent spaces correlates strongly with model performance. This provides a differentiable metric that could enhance model evaluation during training.

Implications and Future Directions

The work's implications extend to building robust AI systems that can operate across varied environments and data distributions. There are several potential pathways for future research and applications:

• Invariance Exploration: Further exploration of alternative similarity functions that could account for more complex transformations or distortions.
• Optimization of Anchors: Delving deeper into anchor selection methods, adjusting the balance between computational efficiency and representation quality, and understanding how different anchors influence modeling effectiveness.
• Multi-Layer Stitching: Expanding the stitching concept across multiple neural network layers to develop reusable network components.

Overall, the proposed method marks a significant progression in addressing the issues of latent space stability, leading to promising developments in AI systems capable of seamless model integration and comparison.