Kun Xie - Brain Computation Is Organized via Power-of-Two-Based Permutation Logic (2016)

Context

Learned in this study

Things to explore

Overview

Notes

• Layer 2/3: random-connectivity strategy
  • Encodes specific and low-combinatorial features, projects inter-cortically
  • Ideal for maximizing cross-modality novel pattern-extraction, pattern-discrimination and pattern-categorization using sparse code
• Layer 5/6: nonrandom organizations
  • Ideal for feedback-control of motivation, emotion, consciousness and behaviors

Introduction

• We reasoned that the essence of intelligence lies in the brain's ability to discover specific features and generalized knowledge from a world full of uncertainties and infinite possibilities; therefore, our search for the brain's computational logic can be reduced to the question of how neurons should be connected in such a way that would inherently afford the brain to discover various patterns and conceptual knowledge
• Cell assembly: the supposed computational building block or computational primitive in the brain

The Theory of Connectivity and its Predictions: A permutation-Based Wiring Logic To Cover Every Possibility

• The Theory of Connectivity: a rather simple mathematical rule in organizing the microarchitecture of cell assemblies into the specific-to-general computational primitives that would readily enable knowledge and adaptive behaviors to emerge in the brain
• The theory specifies that within each computational building block, termed "functional connectivity motif" (FCM), the total number of principal projection-cell cliques with distinct inputs should follow the power-of-two-based permutation equation of $N = 2^i - 1$ (N is the number of distinct neural cliques, i is the number of distinct information inputs)
• An FCM is made of neural-clique assemblies arranged from specific input-coding principal cell assemblies to sub-combinatorial and to general responsive cell assemblies
• The specific neural cliques extract unique features about perspective stimuli
• The sub-general and general neural cliques categorically extract all possible combinational patterns
• Specific and sub-general cell cliques encode specific memories or actions for pattern-discrimination and categorization respectively, whereas higher combinational or generalized neural cliques discover general patterns for pattern-generalization corresponding to semantic memories, categorical knowledge, general intent and motor instruction
• The power-of-two-based permutation logic intrinsically enables each FCM to cover every mathematical possibility or connectivity patterns in a specific-to-general manner
• The theory predicts that by providing four distinct stimulus inputs, one should observe all 15 excitatory cell cliques in relevant brain regions that exhibit specific-to-general coding properties
• Six testable predictions
  1. Cognitive universality - This power-of-two-based computational logic should be used to process various cognitions across a wider range of modalities—including appetitive, emotional and social information
     1.Anatomical prevalence - This logic should be prevalent across many cortical and subcortical circuits, regardless of their macroscopic and microscopic variations
  2. Modulatory neurons, such as dopamine (DA) neurons, use a different logic
  3. The specific-to-general organization should be developmentally preconfigured, rather than to be formed after learning in adulthood
  4. This computational logic is implemented in the cortex vertically via the differential assignment of specific-to-general cliques to distinct laminar layers. This vertically implemented FCM has the advantage to be readily replicated via horizontal surface expansion (rather than via expansion of cortical thickness)
  5. Species conservancy - The proposed computational logic is evolutionarily conserved across the brains of different animal species

Brain Computation and Its Evolutionary Logic

• In the early stages of evolution with animals began to appear 500-600 million years ago, the random connectivity strategy may be initially used to execute this power-of-two permutation-based mathematical logic by constructing a simple circuitry node for rudimentary pattern-separation and pattern-generalization
• Through evolution as more neurons became available, the brain evolved with a greater capacity to expand the "power-of-two"-permutation-based permutation wiring and consequently, to extract more relational patterns, thereby leading to higher abstraction of categorical knowledge and more intelligent behaviors
• Over time, when the random connectivity strategy may no longer be sufficient and efficient to ensure the desired outcome, evolution exerts its selection force to develop nonrandom organization to execute this power-of-two-based permutation logic to efficiently deal with environments in which animals lived
• One this cortical FCM was in place, evolution can seamlessly implement this power-of-two-based permutation logic via expanding its surface size horizontally. This is supported by the examination of 30 different animal species showing that cortical surface area varied by a factor larger than 10000, whereas the thickness of the cortical layers varied only by a factor of 10
• Our results suggest that specific memory and generalized knowledge are generated via a coherent cell-assembly logic and should emerge simultaneously

The Power-of-Two-Based Permutation Logic Helps Explain Many Results in the Literature

• There is a general agreement that information processing in the brain is hierarchical - that is, simple features in the primary sensory cortex are somehow transformed into complex features in the next-stage cortex, and so on and so forth

Power-of-Two-Based Logic and its Constraints on Biological Brains

• The power-of-two-based permutation logic imposes biological boundary on the computational limitation of circuits
• For example, due to the exponential growth in input numbers i, the cost (in terms of cell resources) can quickly become prohibitive
• In order to cover all possible patterns for processing 40 distinct perceptual inputs, a single FCM would require over a trillion neurons ($10^{12}$)
• Every neurons in the human brain ($8.6 \times 10^{10}$ neurons) would be inadequate to afford this exponential coverage
• The best and necessary solution is to employ modular approaches, or a divide-and-conquer strategy, to segregate or stream information inputs through distinct sensory domains or pathways

See also

References

Xie, Kun, et al. "Brain Computation Is Organized via Power-of-Two-Based Permutation Logic." Frontiers in Systems Neuroscience 10 (2016).