Neural-symbolic DNN architectures

Explore and demonstrate the use of different neural-symbolic DNN architectures (e.g PyNeuraLogic, Kolmogorov Arnold Networks (KANs)) for experiential learning and/or...

SingularityNET April 14, 2025

Type

SingularityNET RFP

Total RFP Funding

$160,000 USD

Proposals

Awarded Projects

Completed & Awarded

The community and public are invited to view the full proposals and give feedback. During this time the RFP committee will doing their formal selection process to award winning proposals.

View Awarded Projects

Overview

Proposal Winners
Multiple
Max Funding / Proposal
$100,000 USD

Awarded Funding History

AWARDED PROJECTS	FUNDING AWARDED	ACTION
Hetzerk: a logical language of AI and Physics	$ 40000 USD	View

Short summary

This RFP invites proposals to explore and demonstrate the use of neural-symbolic deep neural networks (DNNs), such as PyNeuraLogic and Kolmogorov Arnold Networks (KANs), for experiential learning and/or higher-order reasoning. The goal is to investigate how these architectures can embed logic rules derived from experiential systems like AIRIS or user-supplied higher-order logic, and apply them to improve reasoning in graph neural networks (GNNs), LLMs, or other DNNs. Bids are expected to range from $40,000 - $100,000.

Main purpose

The purpose of this RFP is to explore how neural-symbolic DNN architectures can be integrated within the PRIMUS cognitive architecture to enhance both experiential learning and/or higher-order reasoning. By embedding logic rules — whether derived from agent-based learning systems like AIRIS or user-defined complex rules — into architectures like GNNs or LLMs, the research aims to advance AI’s ability to reason dynamically over complex systems across multiple spatio-temporal scales. Additional questions that should be highlighted are in what ways and how can different neural-symbolic DNN architectures:

Improve human interpretability and explainability of AI systems;
Can learn from small data using symbolic knowledge and reasoning;
Bridge the gap between data-driven and symbolic reasoning;
Could solve problems in domains in which structured learning is critical (e.g. medical ontologies).

Long description

SingularityNET Foundation, in collaboration with other partners such as the OpenCog Foundation and TrueAGI, is working toward a scalable implementation of the Hyperon AGI framework running on decentralized infrastructure, and toward implementation of the advanced cognitive frameworks. PRIMUS is a hybrid neural-symbolic AGI architecture designed to integrate and ingest various deep neural network (DNN) architectures. Due to the self-similar structures observed at multiple spatio-temporal scales in complex systems, and informed by recent neuroscience research, this RFP aims to explore how neural-symbolic DNNs can be embedded within the PRIMUS system. By embedding logic rules within DNNs, we seek to advance both experiential learning and/or higher-order reasoning across dynamic systems. The focus of this RFP is to investigate the use of neural-symbolic DNN architectures for embedding logic rules, which can be derived from two key sources:

Experiential Learning: Rules generated by agents exploring and interacting with their environment, such as in the AIRIS system, where agents autonomously generate and adapt logic rules based on sensory inputs and actions.
Higher-Order Reasoning: More complex logic rules provided by human users, allowing systems to engage in abstract or hierarchical reasoning tasks.

AIRIS (Autonomous Intelligent Reinforcement Interpreted Symbolism) is an AI system designed to generate and adapt symbolic rules through experiential learning. It operates by allowing agents to explore and learn about their environments, using sensory inputs to autonomously create symbolic rules that can then be applied to different contexts. This system emphasizes transparency and adaptability, where rules can be traced, interpreted, and adjusted in real-time. AIRIS is domain-agnostic, meaning the learned rules are not tied to a specific domain and can coexist across multiple environments, making it versatile for diverse AI applications. PyNeuraLogic is a neural-symbolic AI framework that combines differentiable logic programming with deep learning models, particularly graph neural networks (GNNs). It allows symbolic logic to be embedded into neural networks, enabling systems to perform reasoning tasks while maintaining the flexibility and scalability of DNNs. PyNeuraLogic focuses on using logic-based rules in tasks involving structured data, such as graphs, and integrates these rules with the learning capacity of neural networks. This hybrid architecture supports probabilistic reasoning and can be used for various AI tasks, including knowledge representation, graph reasoning, and decision-making These logic rules can be embedded into diverse DNN architectures, such as GNNs, LLMs, or other neural architectures. The goal is to demonstrate how these embeddings enhance the system’s reasoning capabilities, making it possible for AI systems to operate more flexibly in dynamic environments. For example, by embedding rules from AIRIS into PyNeuraLogic, a system could process learned rules in the form of GNNs or LLMs, which would then be capable of reasoning over the outputs of these neural structures. Kolmogorov-Arnold Networks (KANs) are networks inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). In place of fixed activation functions with learnable weights over nodes ("neurons"), KANs have learnable activation functions on edges ("weights") with a fixed unweighted sum over nodes. This exploration will involve:

A comprehensive survey and analysis of current neural-symbolic DNN architectures capable of embedding logic rules. Researchers are expected to evaluate the strengths and limitations of each architecture, particularly with respect to handling dynamic system behaviors across spatio-temporal scales.
Proof of Concept (POC). We can easily see two ideas for POCs:
1. Use PyNeuraLogic to demonstrate how logic rules can be embedded within a chosen DNN architecture. For example, simple logic rules derived from AIRIS could be embedded into GNNs using PyNeuraLogic, allowing the system to reason over the outputs of those GNNs, or LLMs. This POC would show how such architectures improve both experiential learning and/or higher-order reasoning.
2. As detailed in “KAN: Kolmogorov–Arnold Networks”, KANs operate quite differently than does PyNeuraLogic. KANs are quite interesting in their own right and appear to be more effective at representing certain types of functions, especially those of interest to the mathematical physics community, than do MLPs. Being built upon continuous splines, KANs can help bridge the discrete-continuous divide. They can also provide excellent human interpretability, yet sometimes rely on post-processing by either an automated symbolic regression step or, alternatively, human interaction to do so. One idea for a POC involving KANS would be to explore how well KANs could be used to ingest accurate and explainable DNNs in Hyperon. As one example, perhaps one could use KANs to create a predictive model for real-time energy consumption in a smart grid. The goal could then be to demonstrate how KANs could improve accuracy and explainability of the model, particularly in handling dynamic continuous data (e.g. fluctuating energy usage) alongside discrete events (e.g. switching energy sources). Another possibility could involve market predictions.

For all proposals, researchers are encouraged to demonstrate how their approach can drive complex system dynamics, potentially applying these methods to real-world AI tasks such as AI planning, natural language understanding, or decision-making systems. Expected Outcomes:

Comprehensive Survey and Evaluation: A detailed evaluation of different neural-symbolic architectures, including PyNeuraLogic, KANs, and others, with a focus on their ability to embed logic rules and enhance reasoning capabilities.
Architectural Comparisons: A comparison of how these architectures perform in embedding rules, addressing challenges in scalability, flexibility, and integration with complex systems across multiple spatio-temporal scales.
Proof of Concept (POC): A POC in the MeTTa language that demonstrates the feasibility of embedding logic rules into DNNs and applying reasoning over their outputs, using systems like AIRIS or user-supplied rules.
System Dynamics Demonstration: Evidence that the approach can drive interesting dynamics across multiple scales, showing improvements in reasoning and decision-making in dynamic environments.
Explainability: Explain how different architectures improve human interpretability and explainability of AI systems.
Learning from Small Data: Compare how different architectures can learn from small data using symbolic knowledge and reasoning.
Multiparadigmality: Bridge the gap between data-driven and symbolic reasoning.
Structured Learning: Evaluate how different architecturea can solve problems in domains in which structured learning is critical (e.g. medical ontologies).

Background & experience: A significant part of reviewing proposals goes into evaluating the ability of a team to execute the work. Please answer in as much detail as possible about related experience and accolades, and provide links to anything we can read such as published work, github, etc.

Functional Requirements

Must Have

Neural-Symbolic DNN Integration: This applies equally to both experiential learning (using AIRIS or similar systems to generate simple rules) and higher-order reasoning (embedding user-defined, abstract rules). In both cases, PyNeuraLogic or KANs will be used to implement these rules within GNNs, LLMs, or other DNNs.
Logic Rule Inclusion:
- For experiential learning, the rules will likely be generated through interaction with the environment and evolve over time.
- For higher-order reasoning, these rules may involve more complex, symbolic logic provided externally, guiding abstract reasoning or hierarchical decision-making.
Proof of Concept (POC): The POC will demonstrate the application of the embedded rules in either experiential learning (how well the system adapts over time) or higher-order reasoning (the system’s ability to handle abstract concepts).

Should Have

Comparative Analysis: Whether the project focuses on experiential learning or higher-order reasoning, comparing neural-symbolic architectures remains crucial. The analysis will focus on how well the system handles different types of rules (simple experiential rules vs. abstract higher-order logic).
Complex System Dynamics:
- In experiential learning, this would relate to how the system learns and adapts rules over time and across multiple environments.
- For higher-order reasoning, this would focus on the system's ability to reason across complex, hierarchical structures and solve problems requiring abstract thought.
Demonstration Tools: Regardless of the focus, clear visualizations or demonstration tools will be needed to show how embedded rules improve reasoning or decision-making. These could show real-time adaptation (experiential) or advanced reasoning pathways (higher-order).

Could Have

Hybrid Architectures: Combining both approaches—using experiential learning for foundational rule generation and applying higher-order reasoning for more complex tasks—could be beneficial for exploring hybrid solutions.
Novel Use Cases: Depending on the focus (experiential learning or higher-order reasoning), novel applications could include adaptive systems (for experiential learning) or advanced reasoning in fields like AI planning and problem-solving (for higher-order reasoning).

Non-functional Requirements

Programming language: The system should be implemented in languages compatible with Hyperon (preferably in MeTTa, but Python, Rust or C++ are also acceptable).
Architecture: Integrate neural-symbolic DNNs like PyNeuraLogic or Kolmogorov Arnold Networks (KANs), allowing the embedding of rules from AIRIS (experiential learning) or higher-order logic. The system should support reasoning tasks in GNNs, LLMs, or other architectures, with flexibility for handling dynamic system behaviors.
Performance: Focus on the accuracy and depth of reasoning. The system should efficiently handle rule embedding, processing logic from experiential learning (AIRIS) or complex, user-defined reasoning rules. Batch or incremental processing is acceptable, prioritizing reasoning quality over real-time performance.
Reproducibility: Ensure full reproducibility with clear documentation of methodologies, system configuration, and datasets. All experiments should be replicable, allowing other researchers to verify results.
Scalability: The system should be capable of scaling with increasing complexity in both experiential learning and higher-order reasoning tasks, managing more complex rules and larger datasets over time. While not production-level, it should demonstrate the capacity to expand reasoning capabilities as demands grow.
Documentation: Provide thorough documentation that explains system architecture, logic embedding processes, and experimental methods. This should include how to replicate, extend, or adapt the research for further exploration.
Data Requirements: Capable of handling moderate-to-large datasets, with sufficient computational resources to manage logic rule embeddings without compromising system functionality.

Main evaluation criteria

Alignment with requirements and objective

Does the proposal meet the requirements and advances the objectives of the RFP.

Pre-existing R&D

Has the team previously done similar or related research or development work in other platforms / languages / contexts?

Team Competence

Does the team have relevant skills?

Cost

Does the proposal offer good value for money?

Timeline

Does the proposal include a set of clearly defined milestones?
We highly recommend submitting proposals with project milestones along the lines of the following:
- Milestone 1: Submit a thorough research plan outlining and detailing the approach and work to be done. Deliverables: detailed research plan, agile breakdown of tasks with timeline, and framework design. 20% of grant
- Milestone 2: Complete initial development of the framework definitively showing implementation of the conceptual underpinnings of the RFP along with preliminary testing. Deliverables: draft implementation, initial testing results, and analysis against standard benchmarks. 40% of grant
- Milestone 3: Submit all final materials as committed to in the grant proposal. Deliverables (as applicable): final report with performance analysis, code, framework demonstration, documentation, recommendations, websites, etc. 40% of grant

Other resources

Hyperon and related AI-platforms are quickly evolving! This is a bit of a moving target, but the internal SingularityNET team will be available for help and expert advice, where needed. Also included:

SingularityNET technology links
PyNeuraLogic Github
AIRIS Github
Educational materials and resources for learning MeTTa
SingularityNET holds MeTTa study group calls every other week. Proposers are welcome to attend for support from our researchers and community.
Recurring Hyperon study group calls for community are currently being planned. These will cover MOSES, ECAN, PLN, and other key components of the OpenCog and PRIMUS Hyperon cognitive architectures.
Access to the SingularityNET World Mattermost server, with a dedicated channel for discussion and support among the RFP-winning teams and SingularityNET resources.