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February 26, 2024

Representation of stimuli is logarithmic

By EVA PEKLE | October 18, 2012

Researchers have presented a model for information processing and sensory perception that reveals some particularities of the human brain.

Findings suggest that logarithmic representation is the optimal representation for sensory systems. The study was lead by Lav Raj Varshney and colleagues from the Signal Transformation Information Representation as well as Grace Wang, a neurophysiologist at the Massachusetts Eye and Ear Infirmary.

“The question of how the external world is represented internally is the central question in psychophysics; one of the most robust findings, dating back to the work of Weber in 1846, is that perception is logarithmic in stimulus intensity. Although there have been other proposed explanations in the interceding century and a half, they have not been tied to the purpose of perception,” Lav Raj Varshney wrote in an email to The News-Letter.

Sun and Goyal previously worked on data compression using the expected relative error, and on how the sensory system perceives it. Data compression of video and audio was designed to match the perception process in the brain.

Absolute error is the difference in magnitude between the exact value and the approximation. Relative error is the absolute error divided by the exact value.

“Adopting the optimization approach to biology, we argued that this phenomenon and other related experimental findings in psychophysics are explained by a simple unified information-theoretic principle.  Namely, that the brain optimizes signal representation fidelity for natural stimuli under neurobiological information flow constraints,” Varshney wrote.

The brain was shown to be more sensitive to the expected relative error rather than the absolute error. This seems logical, since being off by three is more relevant when you are differentiating between three and six, than when you are differentiating between 47 and 50.

Perception was found to follow a Bayesian framework. “What it means for something to be ‘Bayes optimal’ is that it fully takes into account the likelihoods of things appearing in the environment. Hence something ‘Bayes optimal’ is well-adapted,” Varshney wrote.

The main advantage of a ‘Bayes optimal’ nervous system is that it limits relative error. The brain, as hypothesized, computes information to minimize the expected relative error in representing a stimulus. This has been shown to be the case in two different situations.

The first situation concerns memory storage. Storing data in our brain using compressed representations seems to be more efficient during situations where neural communication and storage are costly. The second situation is when the stimuli presented are statistically distributed.

The model was tested with natural sounds, including animal sounds and human speech. The ability to optimally process this information is essential to survival.

Results from stimulating humans with human speech show that a bell shaped curve best represents the empirical distribution of stimulus intensities. This is only possible if the representation were logarithmic. The researchers also showed that the expected relative error was minimized.

In addition, the data illustrated that it is harder to process data at the edges of the stimuli intensities.

Our nervous system is capable of a great degree of plasticity when it comes to perception. The model could also be used to determine how experience can re-shape the already implemented circuits of our brain.

“The hypothesis we have put forth implies several novel experimental tests that can be used to support or falsify,” Varshney wrote.

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