hermes-brain/projects/passepartout/architecture/ann-neuromorphic-symbolic-comparison.org

ANN vs Neuromorphic vs Symbolic — When Each Mathematics Fits

ANN vs Neuromorphic vs Symbolic

Core insight

The gap between ANNs and biology is not substrate (binary vs analog). Both are continuous mathematics running on discrete hardware. The real differences are architectural:

1. Memory-binding: ANNs store weights separately from compute (von Neumann bottleneck). Biology co-locates weight and signal at the synapse.
2. Local vs global learning: ANNs need a global error signal backpropagated through every layer. Biology uses purely local plasticity (STDP) — each synapse adjusts based on its own pre/post partners.
3. Time: Biology is asynchronous, continuous, with rich temporal dynamics. ANNs are synchronous — everything computed in lockstep. Recurrence is an awkward addition.
4. One substrate, many functions: A biological synapse does memory, signal propagation, temporal integration, and plasticity in one structure. ANNs separate these across different passes and optimizers.

When each mathematics is appropriate

Mathematics

Naturally good at

Awkward at

——————————-————

ANN / gradient descent	Smooth function approximation, interpolation, pattern completion from dense data	Symbolic reasoning, exact constraints, sparse data, multi-step verification
Neuromorphic / spiking dynamics	Temporal pattern recognition, event-driven control, low-power always-on sensing	Complex multi-step planning, precise arithmetic, storing large lookup tables
Symbolic / deduction	Exact reasoning, proof, constraint satisfaction, verifiable behavior	Learning from raw data, generalization, handling noisy inputs

How Passepartout uses all three

• LLM (ANN on GPU) handles the noisy real world — language, vision, imperfect input
• Screamer (symbolic constraint search on CPU) handles combinatorial reasoning — "find valid configuration"
• ACL2 (deductive proof) handles the verifiable kernel — "prove this decision follows from rules"
• P150 (RISC-V parallel accelerator, in-between arch) handles ambient awareness, parallel dispatch, anomaly detection

Each mathematics where it belongs. The failure mode of both pure ANN and pure symbolic approaches is forcing one mathematics to do what the other is better at.

The neuromorphic opportunity

A neuromorphic chip (Loihi-level) would add unsupervised temporal learning — learning daily rhythms, behavioral patterns, and detecting deviations without training, labels, or LLM involvement. This is the difference between responding to commands and anticipating needs.

But the P150 gets 80% there with programmable cores controlled directly, without waiting for neuromorphic hardware to mature.