The ability to discriminate between large and small quantities is a core aspect of basic numerical competence in both humans and animals. In this work, we examine the extent to which the state-of-the-art neural networks designed for vision exhibit this basic ability. Motivated by studies in animal and infant numerical cognition, we use the numerical bisection procedure to test number discrimination in different families of neural architectures. Our results suggest that vision-specific inductive biases are helpful in numerosity discrimination, as models with such biases have lowest test errors on the task, and often have psychometric curves that qualitatively resemble those of humans and animals performing the task. However, even the strongest models, as measured on standard metrics of performance, fail to discriminate quantities in transfer experiments with differing training and testing conditions, indicating that such inductive biases might not be sufficient.

Stimulus arrays are inevitably presented at different positions on the retina in visual tasks, even those that nominally require fixation.

Stimulus arrays are inevitably presented at different positions on the retina in visual tasks, even those that nominally require fixation. In particular, this applies to many perceptual learning tasks. We show that perceptual inference or discrimination in the face of positional variance has a structurally different quality from inference about fixed position stimuli, involving a particular, quadratic, non-linearity rather than a purely linear discrimination. We show the advantage taking this non-linearity into account has for discrimination, and suggest it as a role for recurrent connections in area VI, by demonstrating the superior discrimination performance of a recurrent network. We propose that learning the feedforward and recurrent neural connections for these tasks corresponds to the fast and slow components of learning observed in perceptual learning tasks. 1 Introduction The field of perceptual learning in simple, but high precision, visual tasks (such as vernier acuity tasks) has produced many surprising results whose import for models has yet to be fully felt.

Stimulus arrays are inevitably presented at different positions on the retina in visual tasks, even those that nominally require fixation. In particular, this applies to many perceptual learning tasks. We show that perceptual inference or discrimination in the face of positional variance has a structurally different quality from inference about fixed position stimuli, involving a particular, quadratic, non-linearity rather than a purely linear discrimination. We show the advantage taking this non-linearity into account has for discrimination, and suggest it as a role for recurrent connections in area VI, by demonstrating the superior discrimination performance of a recurrent network. We propose that learning the feedforward and recurrent neural connections for these tasks corresponds to the fast and slow components of learning observed in perceptual learning tasks. 1 Introduction The field of perceptual learning in simple, but high precision, visual tasks (such as vernier acuity tasks) has produced many surprising results whose import for models has yet to be fully felt.