Development of the core hyperdimensional computing infrastructure for neural-symbolic integration including implementation of HDC-Glue for combining neural networks and basic symbolic operations. This foundation will enable the efficient representation and manipulation of both neural network outputs and symbolic rules in hyperdimensional space. Construct scientific methods for design and testing of HDC enabled neuro-symbolic DNNs.

Literature review suitable for peer reviewed publication of current neuro-symbolic DNNs in relation to experiential rule vs higher-order reasoning abilities with comparative analysis of explainability learning efficiency (data operations) structured learning application as well as a comparative analysis of scalability challenges and technical details between logic based rule systems. We will describe and motivate with prior literature two approaches that can be achieved with HDC. First that HDC can act as a symbolic-reasoning engine to rule based systems to bridge the gap between data-driven and symbolic reasoning models. Secondly an approach to a novel neruo-symbolic model using HDC. Performance benchmarking framework/methods for benchmarking efficiency including tracking amount of learning operations per data unit as well as design of analysis methods of in depth capabilities of the system for logic rule embedding POC designs for integrating KANs AIRIS and PyNeurologic with metrics plan for higher order reasoning and efficiency improvements of current methods Documentation of existing and possible solutions using HDC as a core symbolic engine for rule-based systems POC design for a new neuro-symbolic DNN using HDC cable of experiential learning and higher-order reasoning

$20,000 USD

Submission of literature review to peer reviewed journal Documentation of POC designs for using HDC as the symbolic reasoning engine to enable logic rule based systems for AIRIS, KANs, and PyNeurologic reviewed by AIRIS, KANs, PyNeurologic, and HDC experts Benchmark analysis tools and report framework template Documentation of POC design for novel HDC model data-driven and symbolic reasoning model

Development of the interface layer between PyNeuraLogic and the HDC core enabling the translation of differentiable logic programming constructs into hyperdimensional representations. This includes mechanisms for encoding logical rules and their gradients in hypervector space.

PyNeuraLogic-HDC interface library Logic rule encoding modules Gradient translation mechanisms Integration test suite Documentation on technical and practical use of the model Example implementations

$15,000 USD

Demo of the POC Code and tools for the POC Documentation of the POC including graphics and tutorials Benchmarks reported Reviewed by PyNeurologic expert

Implementation of the HDC integration layer for Kolmogorov Arnold Networks focusing on representing continuous functions in hyperdimensional space while preserving KANs' mathematical properties and learning capabilities.

KANs-HDC interface library Continuous function encoding modules Learning rule translation layer Comprehensive test suite Integration examples Technical documentation

$15,000 USD

Demo of the POC Code and tools for the POC Documentation of the POC including graphics and tutorials Benchmarks reported Reviewed by KAN expert

Implementation of the HDC integration layer for AIRIS system focusing on representing higher-order reasoning in hyperdimensional space while preserving efficiency and probabilistic causality rule based learning.

AIRIS-HDC interface library Rule based embedding layer A-priori knowledge synthesis layer Integration examples Technical documentation

$15,000 USD

Demo of the POC Code and tools for the POC Documentation of the POC including graphics and tutorials Benchmarks reported Reviewed by AIRIS expert

Final integration of all components into a cohesive neural-symbolic framework including comprehensive testing optimization and documentation of the complete system. POC of new HDC based DNN demonstrating both experiential and higher-order reasoning learning.

Complete integrated system Performance analysis and tools User documentation Integration guides Benchmark results Comparative analysis of HDC approaches Hyperon integration roadmap plan

$15,000 USD

Demo of the POC Code and tools for the POC Documentation of the POC including graphics and tutorials Benchmarks reported Report on the POCs in relation to HDCs role in challenges and opportunities in neuro-symbolic DNNs Roadmap for how HDC can be useful in Hyperon with a plan of integration verified by Hyperon team