What you will learn
Follow the project ladder alongside prerequisite parts; each project needs evidence, not a completion click.
Before you begin: Foundations: matter, mathematics & computation
Build a sequence of evidence
The project ladder progresses from one neuron to sparse networks, vision, connectome data and embodied simulation. Each step should produce a small artifact you can inspect: a voltage trace, a graph conversion, a confusion table or a controller log. More neurons are not a substitute for better tests.
Specify before scaling
Write the goal, model assumptions, units, dataset provenance, expected observations and a baseline. Keep experiment code, tests, configuration and results distinct. Use a manifest to identify data and versions. A benchmark without the parameters and inputs needed to rerun it is not yet a reproducible experiment.
Neural-network perspective
Connectivity storage is one scaling cost among several. Membrane state, delay queues, gradients and framework overhead can exceed the edge-array estimate. Measure a small model and extrapolate cautiously. Faster C++, CUDA, Rust or hardware implementations should be checked against a simple numerical reference before their outputs are trusted.
SEE THE RELATIONSHIPS
From structure to behavior.
MAKE THE IDEA PRECISE
The mathematics.
| Symbol | Meaning |
|---|---|
| N | Number of neurons |
| d | Chosen average outgoing degree |
| M | Number of directed edges |
| b_edge | Illustrative bytes per stored edge |
| b_weight | Bytes per dense weight |
Build the equation, step by step
- For N nodes with average outgoing degree d, the number of directed edge records is N d when d is calculated over the same graph.
- Multiply M by bytes per edge record for a sparse payload estimate. Multiply N squared by bytes per weight for the dense payload estimate.
- These estimates omit allocator, index, metadata and runtime-state overhead unless included explicitly. Sparse storage reduces payload when M is small, but runtime speed also depends on access patterns and hardware.
WORK THROUGH THE NUMBERS
Worked example
For 1000 neurons with average degree 10, there are 10,000 edges. At an illustrative 8 bytes per edge, the edge payload is about 78.1 KiB. A float32 dense matrix uses about 3.8 MiB. Neither number includes all runtime overhead.
A small Python experiment.
Python 3 · Standard library only · Synthetic educational example. Run this in your own notebook or a local file.
N, degree = 1000, 10
sparse = N*degree*8
dense = N*N*4
print(f"edge payload = {sparse/1024:.1f} KiB; dense = {dense/1024**2:.1f} MiB")Expected output
edge payload = 78.1 KiB; dense = 3.8 MiB
Change one quantity, predict the result, and then run the code again. Explain any difference before adding complexity.
Test your understanding.
Try it: Include one float32 membrane value per neuron and estimate the extra storage. What other arrays would a trained SNN require?
Self-check: Does a smaller sparse representation always execute faster?
No. Irregular indexing and scattered memory access can outweigh fewer arithmetic operations, while dense kernels can exploit specialized hardware. Measure representative workloads and include conversion costs; a storage estimate is not a speed benchmark.
Where this model stops: The example estimates storage, not throughput or end-to-end simulator memory.
A research question: Which optimization changes runtime while preserving the numerical behavior you care about?
Record evidence in your mastery worksheet →THE NEXT LAYER
Chapter depth map.
This introduction provides a first model. The following chapters are outlines for deeper future editions; their full treatments have not yet been published.
Build the foundations
24.1 Neurons and synthetic sensing · Outline
- 24.1.1 Project 1: single LIF neuron
- 24.1.2 Project 2: 100-neuron SNN
- 24.1.3 Project 3: motion detector
- 24.1.4 Project 4: looming detector
- 24.1.5 Unit tests, traces and simple baselines
24.2 Sensors and connectivity · Outline
- 24.2.1 Project 5: camera to SNN
- 24.2.2 Project 6: event camera to SNN
- 24.2.3 Project 7: fly-inspired collision avoidance
- 24.2.4 Project 8: connectome graph explorer
- 24.2.5 Dataset provenance and transformation tests
Build research evidence
24.3 Simulation and learning · Outline
- 24.3.1 Project 9: real Drosophila subcircuit simulation
- 24.3.2 Project 10: simulated rover
- 24.3.3 Project 11: simulated drone
- 24.3.4 Project 12: hybrid YOLO plus SNN system
- 24.3.5 Project 13: SNN plus reinforcement learning
24.4 Deployment and original research · Outline
- 24.4.1 Project 14: neuromorphic deployment study
- 24.4.2 Project 15: connectome-derived Physical AI architecture
- 24.4.3 Project 16: original research submission
- 24.4.4 Goal, theory, math, data, code, tests and benchmark template
- 24.4.5 Failure cases, experiments, expected observations and extensions
Read with the original sources.
These readings support the concepts and deeper investigation. The worked numbers and illustrations above are teaching examples.
Author-hosted textbook
Neuronal Dynamics — Gerstner, Kistler, Naud & Paninski (2014) ↗
Use for neuron-model prerequisites and notation; this site provides an original curriculum, not a reproduction of the textbook.
Official engineering documentation
PX4 — official simulation guide ↗
Begin with simulation and versioned interfaces. Simulation success alone does not establish hardware flight readiness.
Official hardware research resource
Intel — neuromorphic computing research ↗
Study event processing, memory and mapping constraints. Do not assume public hardware access or transfer platform-specific energy claims to a new task.