Autism as an impairment in detecting invariants Norbert Michael Mayer 1 and Ian Fasel 2 1 National Chung Cheng University, Min-Hsiung, Chia-Yi, Taiwan 2 University of Arizona, Tucson, USA Abstract—Individuals with Autism Spectrum Disorders (ASD) show a variety of atypical behavioral and perceptual patterns which seem to lack a common underlying cause. We hypothesize that there may be a general impairment of the autistic brain char- acterized by a restriction on the class of connectivity patterns, i.e. features, that can be utilized for learning perceptual and cognitive tasks. In particular, we suggest that the autistic brain may not make proper use of features which pool information over larger areas of the input space, which would otherwise allow them to make use of symmetries and develop invariants to permutations. I. I NTRODUCTION It has been proposed that artificial intelligence and devel- opmental robotics may provide a useful tool for developing a theoretical understanding of ASD, and may perhaps be useful in proposing possible treatments (e.g. [1]). Many of the problems of autistic children are social ones. The CDC list of diagnostic criteria [2] describes a total of 8 possible symptoms of ASD with regard to social and communication impairments, such as lack of speech, a lack of spontaneous seeking to share enjoyment, interests, or achievements with other people, and others. However, psychological symptoms go beyond problems of social interaction and communication, as autistic individuals also tend to have very unusual interests and interacitons with objects and overall structure in the real world, such as (taken from the same list as above): Restricted repetitive and stereotyped patterns of behaviour, interests, and activities, ... and restricted patterns of interest that is abnormal either in intensity or focus; apparently inflexible adherence to specific, non-functional routines or rituals; stereotyped and repetitive motor manners and, persistent preoccupation with parts of objects. It is hard to distinguish between perceptive impairments that result in unusual behaviors, versus unusual behaviors due to impaired perception. From a set of EEG [3] experiments, Ramachandran [4] emphasized the fact that one very essential defect lays in the mirror neuron system. Previously it has been suggested that the behavioural problems may be caused by a ”weak central coherence” (WCC) in perception (for a review see [5]), which goes on to suggest that all phenomena related to ASD might be understood under a single paradigm of an essential functional impairment that can be modeled. The basic hypothesis of WCC is that due to enhanced perception of or focus on small details, the autistic individual is not able to perceive the ‘big picture’, which ultimately lies at the heart of all behavioral problems of autistic children. That is, autistic individuals “cannot see the woods for the trees.” If the WCC idea is considered as a general theory of perception in ASD, it could perhaps be extended to understand deficits in social interaction, imitation, and the mirror neuron system. Thus, rather than focusing on initial behavioral im- pairments, it might make sense to focus first on understanding potential sensory deficits, with pathological behaviors of ASD then viewed as a secondary effect of the underlying sensory problems. Following this idea, we propose in this paper that a major element of ASD may be general impairment in the ability to detect perceptual invariants. Real-world invariants may often be hard to detect, be- cause they are hidden behind several stages of processing. The problem here is quite similar to that of dimensionality reduction in machine learning: knowledge of symmetries and other invariants allows one to reduce the search space and is a basic element of “imagination” and planning, and is thus essential in real-world intelligent agents. Precisely how these invariants come about or where they come from is an open question (and a topic of deep discussion in the literature, see for example [6]). Lack of proper invariants can render even the most powerful machine learning algorithms ineffective, thus designing the right set of features is critical for learning methods applied to real-world tasks. In some sense mirror neurons and imitation also fit into the context of invariants. The knowledge of which actions of others are equivalent to one’s own actions (thus invariance to self vs. other) may be considered necessary to perform imitation and may be seen as a very complicated perceptual invariant – body parts of the other person have to be identified with one’s own body parts, etc. Many of these invariants seem to come online even very early in life [7]. II. MODEL To illustrate this idea, in this paper we will develop a simu- lation to examine the computational benefits (and costs) when a symmetry constraint is implemented (the “non-autistic” ver- sion), and compare this to the case when the same symmetry constraint is not implemented (“autistic” version). One way to measure the computational cost is to find the number of neurons that are necessary to perform a discrimination task. For this study we use a two layer neural network model. These are connectionist units, thus the interpretation of the nodes should not be as real biological neurons but rather as functional entities that serve our task. The first layer is a set of model neurons with fixed random receptive fields. Each neuron i has the activation function: A i,t = tanh(I t · R i ), (1)