The cost of correcting for error during sensorimotor adaptation

Learning from error is often a slow process. In machine learning, the learning rate depends on a loss function that specifies a cost for error. Here, we hypothesized that during motor learning, error carries an implicit cost for the brain because the act of correcting for error consumes time and energy. Thus, if this implicit cost could be increased, it may robustly alter how the brain learns from error. To vary the implicit cost of error, we designed a task that combined saccade adaptation with motion discrimination: movement errors resulted in corrective saccades, but those corrections took time away from acquiring information in the discrimination task. We then modulated error cost using coherence of the discrimination task and found that when error cost was large, pupil diameter increased and the brain learned more from error. However, when error cost was small, the pupil constricted and the brain learned less from the same error. Thus, during sensorimotor adaptation, the act of correcting for error carries an implicit cost for the brain. Modulating this cost affects how much the brain learns from error.

Maximal prime gaps bounds

This paper presents research results, pertinent to the maximal prime gaps bounds. Four distinct bounds are presented: Upper bound, Infimum, Supremum and finally the Lower bound. Although the Upper and Lower bounds incur a relatively high estimation error cost, the functions representing them are quite simple. This ensures, that the computation of those bounds will be straightforward and efficient. The Lower bound is essential, to address the issue of the value of the lower bound implicit constant C, in the work of Ford et al (Ford, 2016). The concluding Corollary in this paper shows, that the value of the constant C does diverge, although very slowly. The constant C, will eventually take any arbitrary value, providing that a large enough N (for p <= N) is considered. The Infimum/Supremum bounds on the other hand are computationally very demanding. Their evaluation entails computations at an extreme level of precision. In return however, we obtain bounds, which provide an extremely close approximation of the maximal prime gaps. The Infimum/Supremum estimation error gradually increases over the range of p and attains at p = 18361375334787046697 approximately the value of 0.03.

The cost of correcting for error during sensorimotor adaptation

Learning from error is often a slow process. To accelerate learning, previous motor adaptation studies have focused on explicit factors such as reward or punishment, but the results have been inconsistent. Here, we considered the idea that a movement error carries an implicit cost for the organism because the act of correcting for error consumes time and energy. If this implicit cost could be modulated, it may robustly alter how the brain learns from error. To vary the cost of error, we considered a simple saccade adaptation task but combined it with motion discrimination: movement errors resulted in corrective saccades, but those corrections took time away from acquiring information in the discrimination task. We then modulated error cost using coherence of the discrimination task and found that when error cost was large, pupil diameter increased, and the brain learned more from error. However, when error cost was small, the pupil constricted, and the brain learned less from the same error. Thus, during sensorimotor adaptation, the act of correcting for error carried an implicit cost for the brain. Modulating this cost affects how the brain learns from error.

The cost of correcting for error during sensorimotor adaptation

Learning from error is often a slow process. To accelerate learning, previous motor adaptation studies have focused on explicit factors such as reward or punishment, but the results have been inconsistent. Here, we considered the idea that a movement error carries an implicit cost for the organism because the act of correcting for error consumes time and energy. If this implicit cost could be modulated, it may robustly alter how the brain learns from error. To vary the cost of error, we considered a simple saccade adaptation task but combined it with motion discrimination: movement errors resulted in corrective saccades, but those corrections took time away from acquiring information in the discrimination task. We then modulated error cost using coherence of the discrimination task and found that when error cost was large, pupil diameter increased, and the brain learned more from error. However, when error cost was small, the pupil constricted, and the brain learned less from the same error. Thus, during sensorimotor adaptation, the act of correcting for error carried an implicit cost for the brain. Modulating this cost affects how the brain learns from error.