Attentive Neural Processes (1901.05761v2)

Abstract: Neural Processes (NPs) (Garnelo et al 2018a;b) approach regression by learning to map a context set of observed input-output pairs to a distribution over regression functions. Each function models the distribution of the output given an input, conditioned on the context. NPs have the benefit of fitting observed data efficiently with linear complexity in the number of context input-output pairs, and can learn a wide family of conditional distributions; they learn predictive distributions conditioned on context sets of arbitrary size. Nonetheless, we show that NPs suffer a fundamental drawback of underfitting, giving inaccurate predictions at the inputs of the observed data they condition on. We address this issue by incorporating attention into NPs, allowing each input location to attend to the relevant context points for the prediction. We show that this greatly improves the accuracy of predictions, results in noticeably faster training, and expands the range of functions that can be modelled.

• The paper demonstrates that incorporating attention in Neural Processes significantly reduces underfitting by enabling target-specific contextual focus.
• The ANP model enhances prediction accuracy and accelerates training, as evidenced by improved outcomes in both 1D and 2D regression experiments.
• ANPs maintain permutation invariance and scalability, opening avenues for advanced applications in few-shot learning, image inpainting, and generative modeling.

Attentive Neural Processes: An Analytical Overview

Introduction

This paper presents the Attentive Neural Processes (ANPs), a significant enhancement over traditional Neural Processes (NPs) by incorporating attention mechanisms. NPs, a regression model, map observed input-output pairs to a distribution over functions with linear complexity regarding the context set size. However, NPs have been identified to suffer from underfitting, yielding inaccurate predictions at the inputs of their context sets. ANPs address this issue by allowing each input location to attend specifically to the relevant context points for the prediction.

Neural Processes and Their Limitations

NPs model a distribution over functions, conditioned on a context set, possessing characteristics such as scalability, flexibility, and permutation invariance. Despite these features, NPs consistently underfit their context sets, producing inaccurate predictive means and overestimated variances.

The authors hypothesize that the cause of underfitting lies in the mean-aggregation step in the encoder. This step acts as a bottleneck because it gives equal weight to each context point, complicating the decoder's ability to discern which points provide pertinent information for particular target predictions.

Incorporating Attention

Inspired by Gaussian Processes, which utilize kernels to determine input similarity, ANPs use attention mechanisms to improve prediction accuracy. By allowing each target input to attend to its relevant context points, ANPs effectively expand the range of functions that can be modeled and accelerate training.

The attention mechanism introduced in ANPs preserves the permutation invariance inherent to NPs and involves two main steps: self-attention and cross-attention. The self-attention mechanism interprets interactions between context points, while cross-attention allows target inputs to focus sharply on related contexts.

Experimental Results and Observations

The paper evaluates the efficacy of ANPs through several experiments on synthetic 1D Gaussian Process data and 2D image regression using MNIST and CelebA datasets.

• 1D Regression Experiments: ANPs displayed rapid decreases in reconstruction error and reduced iteration needs compared to NPs. Utilization of different attention mechanisms revealed that dot-product and multihead attention provided notable gains, with multihead attention offering smoother prediction curves.
• 2D Image Regression: On MNIST and CelebA datasets, ANPs demonstrated an improved ability to reconstruct image data from context points and achieve better inpainting results than NPs. The use of multihead and stacked self-attention enhanced the network's capability to produce globally coherent and sharp predictions.

Implications and Future Directions

The introduction of attention into Neural Processes enriches the model's expressiveness and scalability, potentially influencing applications such as Bayesian optimization. The ability to attend to relevant contexts also provides insights into possible enhancements in machine learning tasks requiring few-shot learning and in areas like visual navigation.

Future work may explore extending attention mechanisms further into latent variable paths, which could broaden context understanding in regression settings. Additionally, implementing ANPs in text data applications could enable advanced tasks such as sophisticated text inpainting. The parallels between ANPs and the Image Transformer suggest potential for cross-pollination of ideas between these frameworks, driving forward improvements in sequence-to-sequence learning and autoregressive models.

ANPs stand as a robust model for handling complex data relationships and highlight the power of attention in overcoming inherent limitations of earlier neural process-based models. This paper sets a foundation for further exploration and refinement of attention-based models in the broader landscape of generative and predictive modeling.