This milestone will establish the core architecture of the proposed neuro-symbolic system. It focuses on implementing a working version of Kolmogorov–Arnold Networks (KANs) for function approximation tasks and designing a robust interoperability framework that allows seamless translation of KAN-learned structures into logic representations interpretable by PyNeuraLogic. Early experiments will validate the feasibility of symbolic rule extraction from neural outputs. Work will include: Deploying and adapting KAN libraries for targeted cognitive learning tasks. Building the scaffolding for the logic interface layer to encode and interpret KAN outputs. Designing data pipelines and learning structures for symbolic translation and reasoning.

A working implementation of KANs with real-world function approximation examples. An initial interface module that transforms KAN-learned outputs into logical forms compatible with PyNeuraLogic (e.g., predicate logic encoding). Internal documentation detailing architecture and translation methodology. Early test logs showing symbolic structure emergence from KAN representations. All deliverables will be version-controlled and released under the MIT license on a public GitHub repository.

$20,000 USD

Verified KAN module training on sample function decomposition tasks with high generalization accuracy. Functional translation interface producing logical expressions from at least 3 KAN model outputs. Demonstration of PyNeuraLogic accepting and reasoning over the translated outputs. Internal testing benchmarks achieving explainable rule outputs and symbolic inference from learned neural representations. All results and code must be reproducible on standard hardware.

This milestone establishes the bidirectional feedback loop between neural learning (KAN) and symbolic reasoning (PyNeuraLogic). It will focus on creating a dynamic exchange layer that refines neural predictions through symbolic reasoning cycles, enabling the architecture to perform context-sensitive updates and recursive logic-grounded refinement of neural outputs. Tasks will include: Building the logic feedback interface and context encoder. Implementing mutual learning protocols for knowledge refinement. Creating test cases involving real-world inference tasks (e.g., commonsense reasoning, simple causal chains).

A functional bi-directional communication layer enabling feedback from PyNeuraLogic into the KAN system. Demonstrations of mutual learning cycles where symbolic logic is used to retrain or guide the KAN structure. Case study: reasoning through multi-step logic involving probabilistic and symbolic inferences. Full technical documentation of the loop protocol and update mechanism. All deliverables will be available under the MIT license in the shared repository, with reproducible Jupyter notebooks or scripts for demonstration

$15,000 USD

At least two test cases completed showing accurate symbolic reasoning that modifies or refines KAN outputs. Latency measurements showing efficient loop communication within defined performance thresholds. Measurable improvement (≥10%) in inference task performance after applying feedback loop. Validation logs demonstrating explainable symbolic tracebacks from updated KAN reasoning paths.

The final milestone focuses on integrating the hybrid neuro-symbolic architecture into the PRIMUS/Hyperon ecosystem, showcasing adaptive behavior in an autonomous agent. The deliverables will demonstrate the system's ability to perform logical planning, experiential learning, and abstract reasoning using both sub-symbolic and symbolic tools in harmony. Key focus areas: Wrapping the hybrid system into a Hyperon-compatible agent module. Demonstrating dynamic goal adaptation, memory-based learning, and context-aware behavior. Full test run of the agent in a realistic simulation or task (e.g., puzzle solving, scenario navigation).

A deployable module that plugs into PRIMUS/Hyperon with API support for receiving tasks and returning symbolic/neural decisions. Recorded demonstration of the agent completing a non-trivial task requiring both learning and reasoning. Live dashboard/visualization of the neuro-symbolic reasoning pipeline. Final whitepaper detailing architecture, performance metrics, and potential extensions. Deliverables will include Docker containers or setup scripts for reproducibility and demo videos for review.

$15,000 USD

Successful execution of an adaptive agent on at least one integrated real-world or simulated task. System is fully containerized and reproducible on external hardware. Verified symbolic-neural co-decision processes traceable through logs or UI. Whitepaper peer-reviewed by 1–2 external collaborators with positive feedback on clarity and utility.