Activation Analysis

This wiki page contains information about the analysis of activations of our models.

Baseline ResNet

Layer Overview

#	Name	Shape	Size	Description
0	act0_raw_input	64x64x3	12,288
1	act1_processed_imgs	64x64x3	12,288
2	act2_first_conv	64x64x64	262,144
3	act3_block1	64x64x64	262,144
4	act4_block2	32x32x128	131,072
5	act5_block3	16x16x256	65,536
6	act6_block4	8x8x512	32,768
7	act7_block4_postact	8x8x512	32,768
8	act8_global_avg	512	512
9	act9_logits	200	200

ALP ResNet

Layer Overview

#	Name	Shape	Size	Description
1	act1_input	64x64x3	12,288	Input images
2	act2_first_conv	16x16x64	16,384
3	act3_block1	8x8x256	16,384
4	act4_block2	4x4x512	8,192
5	act5_block3	2x2x1024	4,096
6	act6_block4	2x2x2048	8,192
7	act7_norm	2x2x2048	8,192
8	act8_pool	200		Logits

Compression Effects

Compression of the activations after layer xxx (1) disabled, (2) with a random matrix, (3) a matrix computed using PCA. The PCA was computed on the training data.

Preceeding layer	Axis	Matrix shape	Mode	Validation accuracy [%]
-	-	-	(1)	72.04
act2_first_conv	Channels	64x64	(2)	72.04
act2_first_conv	Channels	64x63	(2)	72.60
act2_first_conv	Channels	64x62	(2)	61.68
act2_first_conv	Channels	64x61	(2)	61.72
act2_first_conv	Channels	64x64	(3)	72.04
act2_first_conv	Channels	64x63	(3)	60.88
act5_block3	All	4096x4096	(3)	72.04
act5_block3	All	4096x3968	(3)	71.54 71.65
act5_block3	All	4096x3840	(3)	70.71 71.47
act5_block3	All	4096x3584	(3)	68.72 70.00
act5_block3	All	4096x3328	(3)	67.64
act5_block3	All	4096x3072	(3)	65.87
act5_block3	All	4096x2048	(3)	47.40 46.60
act5_block3	All	4096x1024	(3)	7.12
act4_block2	All	8192x7680	(3)	70.08
act4_block2	All	8192x7168	(3)	67.23
act4_block2	All	8192x4096	(3)	21.51
act4_block2	All	8192x2048	(3)	2.31
act4_block2	All	8192x1024	(3)	0.75

Explanations: Italic accuracies are expected to match the baseline (1).

Fig.: Plot of the table above. As can be seen, the earlier layer (closer to the input) is more sensitive to PCA compression.

Cosine Similarity

Tiny ImageNet contains samples labeled with 200 different classes. We store the activations induced by 74,246 correctly classified training samples and compute the cosine similarity between those vectors and a single activation chosen from this matrix.

Fig.: Activations taken from the layer act5_block3 in this commit. The unimodal distribution shows where the cosine similarities are in general. The red histogram shows the similarity of labels of the same class as the sample that is being compared to the activations. It can be seen that samples of the same class tend to induce activation vectors with higher cosine similarities among each other.

Fig.: Zoomed version of the histogram above.

We did the same type of analysis for all layers (with 20,000 training samples, minus misclassified ones). The resulting histograms can be seen in the following figure:

Fig.: The histograms clearly show the gain of "classification information" with increasing depth. Samples of the same class tend to be closer to each other, the closer to the output.

Cosine Distance for Compressed Activations

Compressing the activations of the layer act5_block3 with a PCA and computing the same histogram as above (for different compression levels).

Fig.: The layer output vector size is 4096. Here we compare the cosine similarity of a randomly chosen sample from the dataset with all other vectors after applying a PCA reducing to the named dimensionality (4096, 2048, 1024, ..., 8). In can be seen that the similarity of samples of the same class still holds for compression levels up down to 32.