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We train many NNs with different running conditions described in Fig. For example, by comparing Bregman Occlusion and Bar Occlusion to Normal networks, we can see how much occluded images matter to the effect. The Random Labels n c and Random Labels networks may learn representations i. Random Labels has access to more variety of images to extract features from than Random Labels n c. Shuffled Pixels networks cannot learn good representations, nor can they generalize.

Psychology

However, they are different from White Noise networks, as they have access to some statistics of natural images e. We train each condition with convolutional layers and fully-connected layer only FC-only networks. We first train a number of simple networks with which we can iterate quickly. We test the closure effect at a wide range of element sizes, and at each layer of the network. These layers are either convolutional or fully-connected layers only network FC-only network. For convolutional networks, we iterate between convolutional and max-pooling layers n l times to predict n c classes.

For FC-only network, we first flatten the input image, then add n l FC layers. The training dataset was prepared with standard data augmentation: feature-wise normalization, linear translation 0. This network was trained on 1. Experimental results relating to each hypothesis are presented, followed by discussion. Reporting significance and multiple runs Each run produces one significance testing for each element size for each layer.

To reduce the clutter, we only report the significance of the largest element size for each layer. Some plots show multiple runs , arbitrarily chosen to ensure consistency. When multiple runs are present, we report the significance results for a randomly chosen run.

PY2025 - Lecture 02 - Perception (2017)

We also confirm similar patterns in Inception Fig. Despite some evidence for an association between generalization and a closure effect, readers may wonder about somewhat odd observations: the closure effect in Untrained and the two NNs trained on random labels. Discussion 1: Why do Untrained networks have the closure effect?


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When we intentionally decrease features extraction ability e. We believe this has to do with a network trying to fit the random noise and thus unlearning any useful features it may previously have had more on this in H3. Discussion 2: Why does a network trained with random labels have the closure effect?

We conjecture that this is because even though the model cannot truly generalize as labels are randomly assigned to each image , it can still achieve a very low training error, and in order to do so, it has to use its parameters efficiently. One way to do so is to organize the first layers of the model such that they extract representations that capture what is most commonly seen in the training images, irrespective of their assigned labels. Therefore, we see more closure effect was shown when the network saw more images Random Labels than less Random Labels n c.

References

This probably gives rise to the observed closure effect in hidden representations. What we observe here is that a network that is able to generalize e. Results: Higher layers close to the prediction layer in convolutional networks typically show more of the closure effect than lower layers Fig. Interestingly, each network seems to have a threshold layer after which all the above layers are statistically significant.

In Fig. The more layers a networks has, the more pre-final layers show significance and therefore, the closure effect. Interestingly, studies using brain recordings in primates also discovered a discrepancy between visual area V1-V5. However, recordings from an area one level higher V2 of the monkey visual cortex found illusory stimuli responses in about one third of the recorded neurons.

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They also found response signals get weaker as element size decreases. Results: We hypothesized that the closure effect would increase during training and will converge, similar to a typical validation accuracy curve. This varies depending on the layer. In Normal network, the closure effect reaches its peak earlier in the iteration, then fluctuates as it learns, then forgets the effect slightly as it converges in both simple network and Inception Fig.

This is typically observed in higher layers e. In lower layers e. On the other hand, networks trained with degenerate training data e. However the closure effect drops immediately and stays close to zero in the duration of training. The fluctuation during learning before convergence is an interesting symptom, and may benefit from further study.

This hints that the closure effect may reflect a prediction-related signal that can be useful e. In this section, we try to invalidate a hypothesis that a seemingly meaningless input manipulation on the training data e. Results: There is no strong pattern between closure effects and brightness of the training images Fig. Discussion: Note that the variance in each run reflects the amount of information lost by multiplying or dividing each pixel and saturating them e.

Naturally in conditions with no strong closure effect e. Results: As shown in Fig. Discussion: In hindsight, perhaps H1 and this hypothesis cannot coexist. Motivated by this, we trained networks with two types of intentionally occluded training data: 1 randomly chosen number of vertical black bars with random width are drawn in images 2 Bregman B. Bregman, type of occlusion added to images Fig. Results: Convolutional networks trained with occlusion rarely exhibit more closure effects than normally trained networks. However, in the FC-only case, closure effects do appear to increase when the network is trained with occluded data.

Discussion It may be surprising that training with occlusions does not have a strong effect on our results. One explanation for these results is that the types of occlusions we trained on may not match with the stimuli that we tested on. For example, the stimuli we used does not resemble black bars. In addition, the occlusions we tried in this work are artificial; the Bregman pattern or the vertical bars would rarely occur in real world. Results: While both Normal convolutional networks and FC-only networks exhibit the closure effect, it is typically stronger in convolutional networks Fig.

Discussion: Interestingly, in the Untrained condition, we do not observe the closure effect in FC-only networks. Layer-wise patterns are another interesting thing to notice in this experiment. Instead, other layers may exhibit the most closure effect depending on n c and n l. Note that FC-only networks naturally have much lower accuracy than the convolutional networks, which could be a confounding factor.

Humans have been studying humans for a long time. The field of psychology has developed useful tools and insights to study human brains— tools that we may be able to borrow to analyze artificial neural networks. In this work, we use one of these tools to study NNs, to gain insights on how similarly or differently they see the world from us. We test for a particular phenomenon, the law of closure, and show that under proper circumstances neural nets also exhibit this effect.

The work here is just one step along a much longer path. We believe that exploring other Gestalt laws—and more generally, other psychophysical phenomena—in the context of neural networks is a promising area for future research. Understanding where humans and neural networks differ will be helpful for research on interpretability by enlightening the fundamental differences between the two interesrting species.

Do Neural Networks Show Gestalt Phenomena? An Exploration of the Law of Closure

Pixels are shuffled across channels. White Noise with random white noise images. The volume is divided into three main parts: Gestalt and perceptual organisation, attention aftereffects and illusions, and color vision and art perception. Themes covered in the book include: - a historical review of Gestalt theory and its relevance in modern-day neuroscience - the relationship between perceptive and receptive fields - a critical analysis of spatiotemporal unity of perception - the role of Gestalt principles in perceptual organization - self-organizing properties of the visual field - the role of attention and perceptual grouping in forming non-retinotopic representations - figural distortions following adaptation to spatial patterns - illusory changes of brightness in spatial patterns - the function of motion illusions as a tool to study Gestalt principles in vision - conflicting theories of color vision and the neural basis of it - the role of color in figure-ground segmentation - chromatic assimilation in visual art and perception - the phenomena of colored shadows.

Including contributions from experts in the field, this book will provide an essential overview of current research and theory on visual perception and Gestalt. It will be key reading for researchers and academics in the field of visual perception and neuroscience.

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