A Disentangling Invertible Interpretation Network for Explaining Latent Representations

1. Introduction

• Distributed coding spreads semantic concepts across many neurons, hindering attribution of meaning to individual hidden units.Constraining architectures to localize concepts can alter the network and typically deteriorate performance.Source: §1 · pp. 1–2
• The proposed invertible translation maps hidden representations to human-comprehensible semantic concepts while allowing modifications to map back to the original representation.It is designed to sit on top of arbitrary existing networks without altering them.Source: §1 · p. 2
• Two sketches showing a change in a concept can define semantic factors, avoiding large annotated training sets for each concept.The approach derives concept invariances and synthesizes training data; it also offers an unsupervised strategy for disentangling concepts.Source: §1 · p. 2
• Interpretable factors can expose concepts explaining dataset structure and variability, and support semantically meaningful image modifications through inverse translation.The modified representation can be decoded back into the image domain.Source: §1 · p. 2
• The method applies to existing autoencoder representations without altering or retraining them, and interpretation can help analyze classifier invariance and robustness.The paper contrasts this with existing disentangled image synthesis approaches [34] [8] [32] [7].Source: §1 · p. 2

2. Interpretability

• Interpretation is a translation between domains that lets concepts in one domain be understood through concepts in another.Here the target concepts are human-understandable representations such as text, visual attributes, or images.Source: §2 · p. 2
• Approaches that modify network architectures or training losses can trade performance for interpretability, while invertible transformations augment existing models without information loss.The passage contrasts augmentation with approaches that modify architectures, which it says involve an interpretability-performance tradeoff.Source: §2 · p. 2
• Visualization methods often assume fixed neurons, although semantic concepts are distributed across multiple neurons and individual neurons can participate in different concepts.The proposed response is a nonlinear transformation from distributed to concept-specific factors.Source: §2 · p. 3
• Latent attribute-vector methods are limited to representations with linear structure, whereas the proposed interpretable space supports semantic factors and linear operations for arbitrary representations.Invertibility maps modified interpretable representations back to the original space.Source: §2 · p. 3

3.1. Interpreting Hidden Representations

• An invertible transformation T maps a network’s flattened hidden representation z to factors and maps modified factors back to the original representation.The network can be placed on an existing model without restricting the model architecture.Source: §3.1 · p. 3
• Independent factors with normal distributions support separate analysis, sampling, and interpolation within each concept.The factor distributions are specified to make samples and paths between samples useful for examining variation.Source: §3.1 · pp. 3–4
• Training image pairs define semantic factors by concept similarity, while a residual factor captures variability not represented by the specified concepts.Each concept factor is intended to vary with that concept and remain invariant to other variations.Source: §3.1 · p. 4

3.2. Obtaining Semantic Concepts

• Factor dimensionality is estimated from representation-component correlations under a joint-Gaussian assumption; the table reports a smaller color factor for a color-invariant classifier than for an autoencoder.The remaining dimensions are assigned to the residual factor.Source: §3.2 · pp. 4–5, Table 1 · p. 5
• Linear walks in the interpreted space map back to nonlinear encoder-space walks that decode to meaningful images, unlike encoder-space linear walks with ghosting artifacts.This supports exploring representations with vector arithmetic.Source: Figure 4 · p. 5, §3.2 · p. 6
• Two sketches can specify a concept change, which style transfer uses to synthesize image pairs for training.The sketches demonstrate opposite concept states, such as round versus angular contours.Source: §3.2 · p. 5, Figure 3 · p. 5
• Without concept-change examples, marginal-likelihood training produces independent transformed components that users can interpret after training.The approach minimizes the negative log-likelihood of the marginal distribution of hidden representations.Source: §3.2 · p. 5
• Factor swapping transfers digit, color, or animal class from a source image while retaining the target’s other factors, such as gaze direction in the AnimalFaces example.The ColorMNIST example swaps digit type, color, and residual factors.Source: Figure 2 · p. 4, Figure 5 · p. 6

4.1. Interpretation of Autoencoder-Frameworks

• Factor swaps separate animal category from gaze on AnimalFaces, extend to pose-guided synthesis of articulated people on DeepFashion, and disentangle digit, color, and residual on ColorMNIST.On AnimalFaces, the decoded animal class follows the class factor while gaze follows the residual factor.Source: §4.1 · p. 6
• For unsupervised autoencoders, normally distributed interpreted representations can be sampled, inverted to the autoencoder’s latent space, and decoded into images.Semantic axes can also be formed after training from examples with and without an attribute, supporting semantic interpolation.Source: §4.1 · pp. 6–7
• Using an autoencoder architecture based on, trained on the same datasets with losses as in, the approach significantly improves over the state-of-the-art FID reported in.FID means and standard deviations were reported over three trials with 10K generated images.Source: §4.1 · p. 7, Table 2 · p. 7
• Linear walks in the interpreted space decode to meaningful images on the data manifold, unlike walks in the encoder’s hidden space, which show ghosting artifacts.The paper visualizes a 2D submanifold on CelebA.Source: §4.1 · p. 7, Figure 7 · p. 7
• Interpolations increase beardiness or decrease smiling, while beard-related changes also reflect the strong gender correlation in the original data.The figure illustrates that some semantic attributes in the data are correlated rather than independent.Source: Figure 8 · p. 7, §4.1 · p. 7

4.2. Interpretation of Classifiers

• On ColorMNIST, changing the color factor leaves classifier outputs mostly insensitive, while changing the digit factor alters them; inverse-mapped color walks stay within digit clusters.The experiment uses a digit classifier and examines both log-softmax values and predicted classes.Source: §4.2 · p. 8, Figure 10 · p. 8
• For ResNet-50 on AnimalFaces, the interpreted factors indicate invariance to grayscale value but not to roundness.The factors are grayscale value, roundness, and a residual.Source: §4.2 · p. 8

5. Conclusion

• Latent representations of black-box models can be translated into interpretable representations whose disentangled factors represent semantic concepts.The translation is presented as lossless, leaving an equivalent representation for the original model.Source: §5 · p. 8
• The approach provides interpretable representations equivalent to those used internally by arbitrary models, supporting analysis of models and data as seen by a model.The conclusion states that the translation does not lose information.Source: §5 · p. 8
• Invertibility enables semantic modifications and the approach produces state-of-the-art autoencoder-based generative models.Source: §5 · p. 8

A.1. Invertible Interpretation Network

• The network applies multiple invertible blocks and then splits its output into interpretable factors.Each block is a sequence of coupling, actnorm, and shuffling layers.Source: §A.1 · p. 11
• Shuffling uses a fixed random channel permutation, while actnorm learns per-channel shift and scale initialized for zero mean and unit variance.These layers are among the three invertible layers used to build a block.Source: §A.1 · p. 11
• Coupling blocks split their input evenly along channels and use fully connected networks for the s_i and t_i transformations.Source: §A.1 · p. 11
• The appendix defines Conv2d and ConvT2d as convolution operators and Linear as a vector mapping from R^cin to R^cout.Conv2d and ConvT2d use square kernels; their notation includes stride and padding.Source: §A.1 · p. 11

A.2. Autoencoder Architecture

• The autoencoder architecture is based on, replaces batch normalization with act normalization, and removes the highest fully connected layer to reduce model size.The patch discriminator used for adversarial loss has a 70-pixel receptive field.Source: §A.2 · p. 11
• The architecture assumes square images, with height equal to width for an image of size c × h × w.Source: Table 3 · p. 12
• The parameter-count table compares the described autoencoding architectures in millions; the [4] count in its last row is calculated from that architecture but was not used in their experiments.Source: Table 4 · p. 12

A.3. Classifier Architecture

• The classifier experiments use an encoder-based model with a fully connected layer and a ResNet-50 whose feature extractor ends at the last convolutional layer.The remaining ResNet-50 layers produce class scores.Source: §A.3 · p. 12

A.4. Details on Sketch Based Description of Semantic Concepts

• Style transfer [40] turns two sketches demonstrating a concept change into paired stylized training examples.The pairs are (x, xa), (x, xb), and (xa, xb).Source: §A.4 · p. 12
• A realism-prior loss uses a discriminator to distinguish real images from stylized images and is weighted by λg = 1.0.The discriminator architecture matches that used in the autoencoder experiments.Source: §A.4 · p. 12
• The sketch-based concept-description experiments train on AnimalFaces content images and Wikiart style images [20].Source: §A.4 · p. 12

A.5. Training Hyperparameters

• Training uses batch size 25, Adam learning rate 10−4, and σab = 0.9 to allow some stochasticity in training pairs.σab = 0.0 denotes uncorrelated examples, while σab = 1.0 denotes perfect correlation.Source: §A.5 · p. 12
• The transformer configuration specifies the number of flow blocks nflow and the hidden-layer dimensionality H and depth D of subnetworks si and ti.Source: §A.5 · p. 13
• The experiments’ transformer hyperparameter configurations are listed in Table 6.Source: §A.5 · p. 13, Table 6 · p. 13

• On ColorMNIST, the embedding shows independent factors ˜z1 and ˜z2; on CelebA, a missing top-left region corresponds to absent training examples of women with beards.The embedding colors represent digit class for ColorMNIST and gender for CelebA.Source: B. Additional Results · p. 14, Figure 13 · p. 14, Figure 14 · p. 15
• Semantic modifications that are linear in ˜z map to complex paths in the autoencoder latent space z before decoding to modified images.The pipeline modifies a factor in ˜z, applies the inverse translation, and decodes the resulting representation.Source: B. Additional Results · p. 14
• On ColorMNIST, changing the color factor leaves classifier predictions unchanged, whereas changing the digit factor varies predictions.The analysis changes one factor at a time with a random walk in transformed space.Source: B. Additional Results · p. 15, Figure 17 · p. 17
• For an AnimalFaces ResNet-50 classifier, changing greyscale does not affect predictions, while changing roundness often changes the predicted class.The response suggests the classifier relies to some degree on contour shape.Source: B. Additional Results · p. 15, Figure 18 · p. 17
• DeepFashion results demonstrate sampling an appearance factor while keeping the top image’s residual factor fixed.This samples a factor instead of swapping disentangled factors between images.Source: B. Additional Results · p. 15, Figure 15 · p. 16
• A 2D UMAP visualization shows variation within clusters of the AnimalFaces classifier’s hidden code as factors change.The visualized changes include residual, roundness, and grayness.Source: B. Additional Results · p. 16, Figure 19 · p. 17
• Samples from ˜z-space yield more structured and coherent images than samples from latent space z.The figures compare autoencoder-prior and transformer-prior samples on CelebA, CIFAR-10, and FashionMNIST.Source: B. Additional Results · p. 16, Figure 20 · p. 18, Figure 21 · p. 19