Intrinsic noise

Biological systems carry appreciable amounts of internal noise. The magnitude of this noise source can be estimated by presenting the human observer with two identical sequences of noisy stimuli, and measuring the "consistency" with which the observer responds to the two repeated presentations (Fig. 1). If the observer were noiseless, it would behave like a deterministic device and generate identical response sequences on the two presentations of the same stimulus sequence. Real observers, however, often respond differently to repeated identical stimuli (at threshold they do so about every 4 trials); this inconsistent behaviour reflects internally generated randomness, and can be used to estimate the magnitude of internal noise.

Figure 1 Signal detection devices map external sensory stimuli (A) onto the space of the decisional variable (x axis in B), generating two internal distributions associated with "target" and "non-target" stimulus configurations. These distributions consist of two components: a deterministic component mapped by the perceptual circuitry (black in B,D), and a stimulus-decoupled component (internal noise) that is intrinsic to the system (red in B,D). When the internal variables across repeated passes of the same stimulus sequence (D) are converted into binary psychophysical responses (C), discrepancies between the two response sequences for the two passes (differences between red traces in C) reflect the magnitude of the internally generated noise source.

We have exploited this double-pass paradigm to estimate internal noise across a wide range of tasks, stimuli and observers (Neri 2010), including language processing (Diependaele et al 2012). Collectively, the magnitude of the internal noise source stands at roughly 1.4 times the magnitude of the variability induced by the external noise source (Fig. 2). This is huge: it essentially means that the response generated by the human observer depends more on stimulus-decoupled processes going on in her/his brain than it does on what the experimenter presents on the screen.

Figure 2 Internal noise (>400 independent estimates) is on average (green arrow) ~1.3X greater than the stimulus-driven component of the decision variable (indicated by orange vertical line), and the distribution of its magnitude across different stimuli/tasks/observers is log-normal. It is uncorrelated with sensitivity (plotted on y axis).

We have also characterized the distribution of the internal noise source, which had previously been assumed Gaussian. We have found that it is more kurtotic than Gaussian (Fig. 3), closer to a Laplacian distribution (Neri 2013).

Figure 3 The distribution of the internal noise source is typically assumed Gaussian (orange). We have demonstrated that this assumption is incorrect for a range of sensory mappings between stimulus and decision variable (from linear to nonlinear, black to red). The underlying distribution is better described by the Laplacian characteristic.

In recent theoretical work (Neri 2020), we have used calculus of variations to demonstrate the counter-intuitive result that ideal templates for signal detection/discrimination depend on internal noise intensity for some plausible constraints (Fig. 4H-I). We find empirical evidence to support the theoretical expectation when internal noise is compared across participants (but not within each participant), indicating that implicit knowledge about internal variability in different individuals is reflected by their detection templates (Fig. 4K).

Figure 4 Ideal templates depend on internal noise. The detection device is asked to identify which of two stimuli contains a smooth signal (A) added to a white noise source (C versus G). In the absence of internal noise, the ideal template is the signal itself (E). In the presence of internal noise (F), the ideal template is a clipped version of the signal (red dashed line in H) rescaled to lie within the 0-1 range (red solid line). The clipping point (indicated by red horizontal arrow in H) is a monotonically decreasing function of internal noise intensity (I) specified by a transcendental equation (Neri 2020). Red elements illustrate the case of internal noise intensity equal to 2. The theoretical prediction in H is empirically supported when different human participants are classified as carrying either low (black) or high (red) noise via median split across participants (K), but not when different blocks from the same participant are classified as carrying either low (black) or high (red) noise via median split across blocks (J).

We have also demonstrated that similar approaches can be exploited to estimate behavioural internal noise in other species (Spilioti et al 2016), allowing for a common metric within which to compare intrinsic variability across different animals.

Relevant publications:

• Neri P Optimal templates for signal extraction by noisy ideal detectors and human observers 2020 Journal of Computational Neuroscience in press

• Spilioti M, Vargesson N, Neri P Quantitative assessment of intrinsic noise for visually guided behaviour in zebrafish 2016 Vision Research 127 104-114

• Neri P The statistical distribution of noisy transmission in human sensors 2013 Journal of Neural Engineering 10 016014

• Diependaele K, Brysbaert M, Neri P How noisy is lexical decision? 2012 Frontiers in Language Sciences 3 348

• Hasan BAS, Joosten ERM, Neri P Estimation of internal noise using double passes: does it matter how the second pass is delivered? 2012 Vision Research 69 1-9

• Neri P How inherently noisy is human sensory processing? 2010 Psychonomic Bulletin & Review 17 802-808