Learning Flexible Multi-Modal Generative Models with Permutation-Invariant Encoders and Tighter Variational Bounds

Core Concepts

This paper proposes a new variational bound that can tightly approximate the multi-modal data log-likelihood, and develops more flexible aggregation schemes based on permutation-invariant neural networks to encode latent variables from different modality subsets.

Abstract

The paper addresses the problem of learning deep latent variable models for multi-modal data, where each sample has features from distinct sources. The authors consider a latent variable model setup, where the joint generative model factorizes as the product of the prior density and the decoding distributions for each modality. The key contributions are: A new variational bound that can tightly approximate the multi-modal data log-likelihood, avoiding the limitations of mixture-based bounds which may not provide tight lower bounds on the joint log-likelihood. New multi-modal aggregation schemes based on permutation-invariant neural networks, such as DeepSets and attention models, which yield more expressive multi-modal encoding distributions compared to previous Mixture-of-Experts (MoE) or Product-of-Experts (PoE) approaches. An information-theoretic perspective showing that the proposed variational objective can be interpreted as a relaxation of bounds on marginal and conditional mutual information. Experiments illustrating the trade-offs of different variational bounds and aggregation schemes, and demonstrating the benefits of tighter variational bounds and more flexible aggregation models when approximating the true joint distribution over observed modalities and latent variables.

Stats

The joint generative model factorizes as pθ(z, x) = pθ(z) Π_s pθ(xs|z), where z is the shared latent variable across modalities. The proposed variational bound L(x, θ, ϕ, β) = ∫ ρ(S) [LS(xS, θ, ϕ, β) + L\S(x, θ, ϕ, β)] dS, where LS and L\S are the marginal and conditional variational bounds. The permutation-invariant aggregation schemes, such as DeepSets and Set Transformers, allow for more flexible multi-modal encoding distributions compared to MoE or PoE.

Quotes

"Devising deep latent variable models for multi-modal data has been a long-standing theme in machine learning research." "To encode latent variables from different modality subsets, Product-of-Experts (PoE) or Mixture-of-Experts (MoE) aggregation schemes have been routinely used and shown to yield different trade-offs, for instance, regarding their generative quality or consistency across multiple modalities." "We develop more flexible aggregation schemes that generalize PoE or MoE approaches by combining encoded features from different modalities based on permutation-invariant neural networks."

Key Insights Distilled From

Learning multi-modal generative models with permutation-invariant encoders and tighter variational bounds

by Marcel Hirt,... at arxiv.org 04-22-2024

https://arxiv.org/pdf/2309.00380.pdf

Deeper Inquiries

How can the proposed permutation-invariant aggregation schemes be extended to handle private latent variables in addition to the shared latent variables

The proposed permutation-invariant aggregation schemes can be extended to handle private latent variables by incorporating permutation-equivariance into the encoding distribution. This extension ensures that the encoding distribution is invariant with respect to the ordering of the encoded features of each modality, including both shared and private latent variables. By enforcing permutation-equivariance, the encoding distribution approximates the posterior distribution in a way that is unaffected by the inputs from the private latent variables when encoding the shared latent variables. This approach allows for a more flexible and robust modeling of multi-modal data, where the private latent variables can be effectively integrated into the overall variational framework.

What are the potential challenges in optimizing the multi-modal variational objective, especially regarding initialization and training dynamics, and how can they be addressed

Optimizing the multi-modal variational objective poses several challenges, especially concerning initialization and training dynamics. One potential challenge is the optimization landscape, which can be complex due to the high-dimensional parameter space and the interplay between the different modalities. Addressing this challenge requires careful initialization strategies, such as using pre-trained models or initializing the parameters based on prior knowledge. Additionally, training dynamics can be unstable, leading to issues like vanishing or exploding gradients. Techniques like gradient clipping, batch normalization, and learning rate scheduling can help stabilize training and improve convergence. Regularization methods, such as dropout or weight decay, can also prevent overfitting and improve generalization performance. Monitoring training progress with appropriate metrics and visualization tools is essential for diagnosing issues and adjusting the training process accordingly.

Can the insights from this work on tighter variational bounds and flexible aggregation models be applied to other multi-modal learning tasks beyond generative modeling, such as multi-task learning or cross-modal retrieval

The insights from this work on tighter variational bounds and flexible aggregation models can be applied to various other multi-modal learning tasks beyond generative modeling. For example, in multi-task learning, the concept of tighter variational bounds can help in jointly optimizing multiple tasks while ensuring a balance between task-specific performance and shared representation learning. The flexible aggregation models can be beneficial in tasks like cross-modal retrieval, where information from different modalities needs to be effectively integrated to retrieve relevant and coherent results. By incorporating permutation-invariant neural networks and variational bounds, these tasks can benefit from improved model interpretability, generalization, and performance across diverse modalities.