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The geometry of efficient codes: How rate-distortion trade-offs distort the latent representations of generative models

Fig 10

Comparison of the latent representations of the baseline model and the hybrid model E2M4.

The E2M4 model is assigned a multiclass classification task. The possible positions of each corridor are grouped into 5 bins (as explained in Section 2.4) resulting in a partition of input images into 25 possible classes. ( A, F) 2D projections of the 5D embeddings learned by the baseline model at high ( nats) and low ( nats) capacity, respectively. ( C, H) 2D projections of the 5D embeddings learned by the hybrid E2M4 model trained at high ( nats) and low ( nats) capacity, respectively. ( B, G) Activation patterns of the 5 latent channels of the baseline model at high and low capacity, respectively. Each of the five heat-maps is computed as in Section 4.4. ( D, I) Activation patterns of the 5 latent channels of the E2M4 model at high and low capacity, respectively. Each heat-map is computed as in Section 4.4. ( E, J) Measure of distortions in the latent representations of the hybrid E2M4 model compared to the baseline model at high and low capacity, respectively. ( K) Measure of distortions in the latent representation of the baseline model induced by the reduction of the encoding capacity from high to low. ( L) Measure of distortions in the latent representation of the E2M4 model induced by the reduction of the encoding capacity from high to low. Distortion matrices are computed as described in Section 4.3.

doi: https://doi.org/10.1371/journal.pcbi.1012952.g010