Perception and the Efficient Coding of Universal Law of Generalization

 

Science  11 May 2018: Vol. 360, Issue 6389, pp. 652-656

Efficient coding explains the universal law of generalization in human perception

Chris R. Sims

Department of Cognitive Science, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.

[paraphrase]

Perceptual generalization and discrimination are fundamental cognitive abilities. Here, I challenge existing theoretical explanations for the universal law and offer an alternative account based on the principle of efficient coding. I show that the universal law emerges inevitably from any information processing system (whether biological or artificial) that minimizes the cost of perceptual error subject to constraints on the ability to process or transmit information.

Adaptive behavior requires perceptual generalization and discrimination abilities that are finely calibrated to the costs of perceptual error. This is true not just for predator–prey relationships, but is equally important for expert-level human performance in domains such as medicine. Not surprisingly, the theoretical study of generalization is also central to progress in artificial intelligence and machine learning.

Here, I offer a qualitatively different explanation for the origins of the universal law in human perception, based on the principle of efficient coding, or the idea that biological information processing should seek to maximize performance subject to constraints on information processing capacity.

Critically, the proposed approach also generates unique predictions that distinguish it from competing explanations for the universal law. These include predictions that relate the slope of the generalization gradient to information-theoretic quantities, asymmetric generalization gradients in situations where there are asymmetric costs for perceptual error, and the finding that artificial systems (such as the JPEG image compression algorithm) can also produce an exponential generalization gradient. The result is a revised universal law of perceptual generalization.

The approach uses results from the field of rate-distortion theory, a subdiscipline within information theory concerned with the design and analysis of optimal, but capacity-limited, information channels. Previous work has shown that rate-distortion theory offers a compelling account of human visual working memory limitations.

The current results can be concisely stated as follows: Perceptual generalization in any efficient communication system will necessarily follow an exponential function of the cost of perceptual error. In this framework, the emergence of the universal law is the signature of an organism that seeks to perceive the world as best as possible, according to some utility measure, subject to available resource limitations.

Notably, several of the properties (such as a “bias to the mean effect”) are also predicted by Bayesian models of perception. As both are rational or optimal models of cognition, this is not surprising. Whereas Bayesian models of perception often make atheoretic assumptions about the nature of “internal noise” within a perceptual channel, rate-distortion theory instead gives sensory processing limitations a strong theoretical interpretation in terms of constructs from information theory. Hence, rate-distortion theory can be viewed as a special case of the more general class of Bayesian models of perception.

The steepness of the generalization gradient should be monotonically related to the information rate of the perceptual channel. Specifically, when plotted on a logarithmic axis, exponential curves will appear as straight lines with slope s. Rate-distortion theory uniquely provides a strong theoretical interpretation for the slope, which is the rate-distortion curve for the channel.

Rate-distortion theory predicts that exponential generalization gradients should not be limited to biological information processing, but rather should be exhibited by any communication system that operates efficiently in the rate-distortion sense, whether natural or artificial. An example is the JPEG image compression algorithm. Since JPEG is a form of lossy compression, the encoded images will almost certainly introduce perceptual “confusions” — an input pixel replaced by a somewhat different pixel at the output stage. A confusion matrix is obtained by collecting the joint statistics of input and JPEG-encoded pixels. JPEG has the useful feature that the objective for perceptual coding is obtainable by inspection of its algorithm. In brief, JPEG performs a discrete cosine transform (DCT) on an input image and scales the coefficients by a weight matrix that emphasizes coding accuracy for low spatial frequencies. This weighted DCT representation is essentially the “psychological space” for JPEG encoding, which conforms to the universal law of generalization.

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