Research — BioIntelligence AI
Neuromorphic Computing and the Mathematics of Biological Intelligence
A technical primer on spike-based, event-driven computation — and why the energy efficiency of the brain is a mathematical result before it is a hardware one.
01 — The architectural divide
Almost all contemporary artificial intelligence runs on hardware descended from a single 1945 design: a processor, a separate memory, and a channel between them. Neuromorphic computing begins by rejecting that separation.
The distinction is not cosmetic. It determines where energy is spent, how learning can be expressed, and which mathematics is natural to write down.
Von Neumann
Memory and compute are separated. Every operation pays the cost of moving data across the bus — the memory wall that dominates energy use in large models.
Neuromorphic
Memory and computation are colocated in the synapse. State lives where it is used, so information travels distances measured in micrometres, not millimetres.
The brain
Roughly 86 billion neurons operating on about 20 watts — six orders of magnitude more efficient per operation than dense matrix hardware.
02 — Spikes
Why spikes change the mathematics
Artificial neural networks pass continuous real values between layers, synchronised by a global clock. Spiking neural networks pass discrete events in continuous time. The information is carried not only by how often a neuron fires but by when it fires relative to its neighbours.
This shifts the object of study. Instead of differentiable maps between dense vector spaces, we are working with point processes, temporal codes and dynamical systems that are only piecewise differentiable. Backpropagation does not apply cleanly, which is precisely what makes the problem interesting: surrogate gradients, event-driven credit assignment and local plasticity rules are all attempts to recover learning without a global differentiable path.
03 — Sparsity
Event-driven computation and energy efficiency
In a spiking system, a neuron that does not fire costs almost nothing. Activity is sparse in both space and time, so energy scales with information rather than with model size. Research silicon — Intel's Loihi, IBM's TrueNorth, SpiNNaker, BrainChip's Akida — exploits exactly this asymmetry, reporting orders-of-magnitude reductions in energy for sparse, temporally structured workloads.
The catch is that these gains only materialise when the algorithm is genuinely event-driven. Porting a dense network onto neuromorphic hardware by converting activations into rates recovers accuracy but discards most of the efficiency. The hardware is not the breakthrough; the mathematics that fits the hardware is.
04 — Plasticity
Local learning rules and continual adaptation
Biological synapses update using information available locally: pre-synaptic activity, post-synaptic activity, and slow neuromodulatory signals. Spike-timing-dependent plasticity is the canonical formalisation, but it is a starting point rather than a complete theory.
Local rules matter because they make continual learning tractable. A system that updates in place, without replaying a stored dataset, can adapt to a changing environment without catastrophic forgetting — the property that current large models most conspicuously lack.
05 — Open problems
What remains unsolved
Credit assignment over long temporal horizons without a global gradient. Formal guarantees for stability in recurrent spiking dynamics. Encoding schemes that map real-valued data into temporal codes without discarding structure. Benchmarks that reward efficiency rather than accuracy alone.
Each of these is a mathematical question before it is an engineering one, and none of them is answered by scale.
Where this sits in our programme
Manasva's BioIntelligence AI programme treats neuromorphic hardware as evidence rather than as a destination. That biology computes this efficiently tells us a better formalism exists. Our work is to find it — to formalise the computational processes observed in biological systems, and to build architectures that are explainable, verifiable and capable of learning continually.
Read about the programme