The lawful mind : active inference and projective geometry in perception, imagination, action programming and self-awareness

Orateur : David RUDRAUF (GIN)

We aim at understanding and rendering explicit the global, formal structure of the human mind and subjective consciousness. We propose a unifying mathematical theory rendering explicit essential laws of the embodied mind, which provides formal foundations for psychology, neuroscience and artificial intelligence. In the theory, the mind is construed as a virtual, supramodal global workspace with two main components. The first component is active inference : the embodied mind is an active inference machine. Variational-energy-based predictive coding provides a formal framework for understanding and modeling active inference in autonomous systems. The second component on which active inference operates is projective geometry. We show that the subjective frame is a projective frame in projective 3-space, and that the global workspace is ruled by the projective linear group, a non-euclidean geometry. The system uses simultaneous and sequential multi-view reconstruction to abstract, infer and populate the workspace based on sense modalities and priors, in a manner that regularizes the inverse problem of inferring 3D projective representations from sense data sampling (often on 2D sensors, e.g. the retina) and a world model in construction in memory. All senses contribute opportunistically to the space for spatial inferences. Perception corresponds to a specific "perception subgroup" of the projective linear group, constrained by body locations and axes, as well as calibration parameters : it reduces the search space for inferring projective representations based on sense data. Imagination corresponds to the full projective group including the perception group (for anticipation of perception states). The weight of sense data in inference versus prior beliefs about transformations determines the difference between perception and imagination, the former being more dependent on the physics of inertia than the latter, which can project representations that are freer from physical constraints to explore options before acting. Action programming can be performed using the imagination group since all parameters of motions are contained in the corresponding transformation matrices, assuming ongoing calibration between the projective frame and the Euclidean ambient space it represents. A virtual body avatar (e.g proprioception, phantom limbs) is modeled in the space for self-representation. Projective geometry also acts as an attentional filter implementing an attentional beam as it down-weights the importance of distant objects, and thus provides natural error metrics in a space of intuitive shapes for comparison between representations in perception and imagination. The global projective workspace thus provides a natural control space for embodied autonomous agents (biological or robotic). Based on this theory we can qualitatively and quantitatively explain in a unified framework a variety of perceptual and cognitive phenomena, but also classical paradoxes in the philosophy of mind ; which have generally been considered independently from each other in psychology and cognitive sciences. This includes : perceptual illusions such as the Necker cube ; phenomena of heautoscopy and out-of-body experience induced in specific experimental contexts ; as well as a range of drug-induced and mystical experiences (e.g. near death experiences). It also allows us to make sense of the ill-defined concept of pre-reflective self-awareness, reducing customary paradoxes. Following neurophenomenological principles, neurocomputational hypotheses can be derived from the theory : the brain is predicted to incorporate an active inference engine (relying on homeostasis, emotion, memory and language), which is expected to encompass fronto-temporal limbic and non-limbic associations cortices and subcortical structures ; and a projective geometry engine (relying on multisensory integration and motor programming), which is expected to encompass parietal systems and modal occipito-temporo-parietal systems, and frontal premotor regions, for the real-time construction of the global projective workspace. The two systems are coupled via long-range fasciculi, emotion-related processing and language that we conceive of as a system of network keys. The thalamus and DMN are predicted to arbiter the switch between perception-mode and imagination-mode. The cerebellum and basal ganglia play a role in the calibration of the projective frame with respect to the underlying ambient locally Euclidean world. We predict that hippocampal grid cells may implement a local projective frame. Likewise, a system design perspective can be adopted. Autonomous artificial agents and robots can be designed based on the theory, in a very direct manner, which would process information and act according to the same laws as those the projective model implies to be at the center of the mind. The machines that would result from this design would act based on imaginary inferences used as models of possible perceptual states to drive action and information integration based on priors implementing a specific utility function. The theory offers a formal model of enaction and embodiment. Optimal inference speaks to the minimization of complexity by appealing to a projective geometry, which provides the simplest explanation for the statistical structure of our sensorium. The theory thus also satisfies Occam’s razor. A future formal psychological science may consist of exploring the solutions of projective spaces in the context of active inference

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