Interpretable Transformations with Encoder-Decoder Networks (1710.07307v1)

Abstract: Deep feature spaces have the capacity to encode complex transformations of their input data. However, understanding the relative feature-space relationship between two transformed encoded images is difficult. For instance, what is the relative feature space relationship between two rotated images? What is decoded when we interpolate in feature space? Ideally, we want to disentangle confounding factors, such as pose, appearance, and illumination, from object identity. Disentangling these is difficult because they interact in very nonlinear ways. We propose a simple method to construct a deep feature space, with explicitly disentangled representations of several known transformations. A person or algorithm can then manipulate the disentangled representation, for example, to re-render an image with explicit control over parameterized degrees of freedom. The feature space is constructed using a transforming encoder-decoder network with a custom feature transform layer, acting on the hidden representations. We demonstrate the advantages of explicit disentangling on a variety of datasets and transformations, and as an aid for traditional tasks, such as classification.

Overview of Interpretable Transformations with Encoder-Decoder Networks

The paper "Interpretable Transformations with Encoder-Decoder Networks" addresses a key challenge in the application of deep learning: the disentanglement of transformations in feature spaces. This work proposes a novel approach for constructing deep feature spaces that are explicitly interpretable with respect to several known transformations, enabling enhanced manipulation and control over image synthesis tasks.

Deep feature spaces encode complex, nonlinear transformations, making it difficult to understand the relationships between encoded inputs and their transformations such as rotation, scaling, and lighting. The paper introduces a method to disentangle these transformations using a transforming encoder-decoder network, facilitated by a custom feature transform layer. The layer enforces equivariance, allowing the feature space representation of transformations to be explicitly known and interpreted. This approach enhances both the interpretability and control of transformed image renderings.

Methodology

The authors propose an architecture centered around a transforming encoder-decoder network. The key component is the feature transform layer, which encodes transformations through linear transformations on feature vectors. This allows for both interpretable equivariance and invariance, achieved by employing transformation matrices with homomorphism properties. The homomorphism property ensures that transformation sequences in image space translate equivalently to the feature space, supporting a form of structural preservation between input and feature representations.

Feature Transform Layer

The feature transform layer applies linear transformations, often using rotation matrices, to the feature vectors. These transformations maintain the norm of the feature vectors, allowing for transformation invariance through the L2-norm. This is pivotal for providing a direct, interpretable link between input transformation parameters and their feature-space analogs. The construction allows for relative phases of sub-vector groups as invariants, offering an avenue for discriminative tasks.

Experimental Results

The approach's efficacy is demonstrated on multiple datasets including MNIST and the Basel Face Dataset. For MNIST, the network disentangles 2D transformations such as scaling and rotation, facilitating clear control over reconstructions. In the more complex Basel Face Dataset, the model demonstrates the ability to infer and manipulate 3D transformations like out-of-plane rotation and lighting, translating 2D images back into consistent 3D pseudorepresentations with reasonable fidelity.

Quantitatively, the method enhances classification accuracy on tasks such as the MNIST-rot, showcasing the benefit of interpreting and leveraging transformation equivariance. The integration of feature transform layers enables the extraction of invariant representations that improve performance on standard recognition benchmarks.

Implications and Future Directions

The implications of this research are profound for tasks that require interpretable AI, such as image synthesis, 3D reconstruction, and computer vision applications where transformation control is critical. This work opens up possibilities for developing more robust models that can generalize across views by encoding transformations directly into the network’s architecture.

Future research could explore extending this method to more complex transformations and higher-dimensional feature manipulations. Additionally, investigating other neural network architectures like transformers might yield further enhancements in disentangling and interpreting transformations. Furthermore, advancing unsupervised disentanglement using this interpretable framework could lead to significant advancements in understanding intrinsic variabilities within data.

This paper lays groundwork for bridging the interpretability gap in deep learning paradigms, enabling a closer inspection and more controllable manipulation of learned representations, thereby fostering developments in AI that are both powerful and comprehensible.