feat: vendor midstream and sublinear-time-solver libraries

Add ruvnet/midstream (AIMDS real-time inference) and ruvnet/sublinear-time-solver (sublinear optimization algorithms) as vendored dependencies under vendor/. Co-Authored-By: claude-flow <ruv@ruv.net>
2026-08-06 19:51:43 +00:00 · 2026-03-02 23:32:45 -05:00
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+# Neuromorphic Computing for Ultra-Low Power Linear Solvers
+
+## Executive Summary
+
+Neuromorphic computing mimics neural structures for massive parallelism and ultra-low power consumption. By encoding linear systems as spiking neural networks (SNNs), we can achieve 1000x energy efficiency improvements while maintaining sublinear complexity.
+
+## Core Concepts
+
+### 1. Spiking Neural Networks for Linear Systems
+
+**Key Innovation**: Encode Ax=b as energy minimization in SNN
+- Neurons represent solution variables
+- Synapses encode matrix entries
+- Spike timing represents values
+
+### 2. Memristive Crossbar Arrays
+
+Physical implementation of matrix operations:
+- **O(1) matrix-vector multiply** in analog domain
+- 10,000x lower power than digital
+- Natural sparsity handling
+
+### 3. Event-Driven Computation
+
+Only compute when changes occur:
+- Asynchronous updates
+- Natural sublinear behavior
+- Perfect for streaming/online problems
+
+## Research Frontiers
+
+### Intel Loihi 2 Implementation
+
+```python
+class LoihiLinearSolver:
+    """
+    Map linear system to Loihi 2 neuromorphic chip
+    """
+    def __init__(self, matrix):
+        self.setup_neural_encoding(matrix)
+        self.configure_learning_rules()
+
+    def neural_encoding(self, A, b):
+        """
+        Encode as energy function E = ||Ax - b||²
+        Neurons minimize via spike-timing dependent plasticity
+        """
+        # Each neuron represents x[i]
+        neurons = self.create_neurons(len(b))
+
+        # Synapses encode A[i,j]
+        for i, j, val in sparse_entries(A):
+            self.connect(neurons[i], neurons[j], weight=val)
+
+        # Inject current proportional to b
+        self.inject_bias(neurons, b)
+
+        return neurons
+```
+
+### IBM TrueNorth Mapping
+
+- 1 million neurons, 256 million synapses per chip
+- 70 mW power consumption
+- **Application**: Solve 1M×1M sparse systems at 0.01W
+
+### Memristor Crossbar Architecture
+
+```
+     x₁  x₂  x₃ ... xₙ
+   ┌───┬───┬───┬─────┐
+y₁ │ G₁₁│ G₁₂│ G₁₃│ ... │ → Σ → b₁
+   ├───┼───┼───┼─────┤
+y₂ │ G₂₁│ G₂₂│ G₂₃│ ... │ → Σ → b₂
+   ├───┼───┼───┼─────┤
+y₃ │ G₃₁│ G₃₂│ G₃₃│ ... │ → Σ → b₃
+   └───┴───┴───┴─────┘
+
+Gᵢⱼ = conductance = matrix element
+O(1) analog computation!
+```
+
+## Cutting-Edge Papers
+
+1. **Davies et al. (2021)**: "Advancing Neuromorphic Computing With Loihi"
+   - Intel's neuromorphic ecosystem
+   - doi:10.1109/MICRO50266.2020.00027
+
+2. **Xia & Yang (2019)**: "Memristive crossbar arrays for brain-inspired computing"
+   - Nature Materials review
+   - doi:10.1038/s41563-019-0291-x
+
+3. **Schuman et al. (2022)**: "Neuromorphic computing for scientific applications"
+   - Oak Ridge National Lab
+   - arXiv:2207.07951
+
+4. **Mostafa et al. (2018)**: "Deep learning with spiking neurons"
+   - Equilibrium propagation
+   - arXiv:1610.02583
+
+5. **Kendall et al. (2020)**: "Training End-to-End Analog Neural Networks"
+   - Analog backpropagation
+   - arXiv:2006.07981
+
+## Performance Projections
+
+### Power Efficiency Comparison
+
+| Platform | 1000×1000 Solve | Power | Energy/Op |
+|----------|----------------|-------|-----------|
+| CPU (x86) | 40ms | 100W | 4J |
+| GPU (V100) | 2ms | 250W | 0.5J |
+| FPGA | 5ms | 30W | 0.15J |
+| **Neuromorphic** | 10ms | 0.1W | **0.001J** |
+
+**4000x energy efficiency gain!**
+
+### Latency Analysis
+
+- Setup: 100μs (one-time)
+- Convergence: 1-10ms (depends on κ)
+- Readout: 10μs
+- **Total**: ~10ms with 0.001J energy
+
+## Novel Algorithms
+
+### 1. Oscillatory Neural Solver
+
+```python
+def oscillatory_solver(A, b):
+    """
+    Use coupled oscillators to solve Ax=b
+    Phase encodes solution values
+    """
+    # Create oscillator network
+    oscillators = [Oscillator(freq=1.0) for _ in range(len(b))]
+
+    # Couple based on matrix
+    for i, j, val in sparse_entries(A):
+        couple(oscillators[i], oscillators[j], strength=val)
+
+    # Drive with b
+    for i, val in enumerate(b):
+        oscillators[i].drive(val)
+
+    # Wait for phase lock
+    wait_sync()
+
+    # Read phases as solution
+    return [osc.phase for osc in oscillators]
+```
+
+### 2. Stochastic Spiking Solver
+
+Exploit noise for faster convergence:
+- Add controlled noise to escape local minima
+- Similar to simulated annealing
+- Natural in neuromorphic hardware
+
+### 3. Reservoir Computing Approach
+
+Use random recurrent network:
+- Fixed random connections
+- Train only output weights
+- **O(n) training for n×n system**
+
+## Hardware Platforms
+
+### Current Generation
+1. **Intel Loihi 2**: 128 cores, 1M neurons
+2. **IBM TrueNorth**: 4096 cores, 1M neurons
+3. **BrainChip Akida**: Commercial edge AI
+4. **SpiNNaker 2**: 1M cores (coming 2024)
+
+### Emerging Technologies
+1. **Photonic neuromorphic**: Speed of light computation
+2. **Quantum-neuromorphic hybrid**: Best of both worlds
+3. **DNA computing**: Molecular-scale parallelism
+
+## Implementation Roadmap
+
+### Phase 1: Simulation (Q4 2024)
+- NEST simulator for algorithm development
+- Brian2 for rapid prototyping
+- Benchmark vs classical
+
+### Phase 2: FPGA Prototype (Q1 2025)
+- Implement on Xilinx Zynq
+- Custom spiking accelerator
+- Real-time performance testing
+
+### Phase 3: Neuromorphic Chip (Q2 2025)
+- Port to Intel Loihi 2
+- Test on IBM TrueNorth
+- Energy efficiency validation
+
+### Phase 4: Custom ASIC (Q4 2025)
+- Design specialized neuromorphic solver chip
+- Target 10,000x efficiency gain
+- Production feasibility study
+
+## Code Example: Brian2 Simulation
+
+```python
+from brian2 import *
+
+def neuromorphic_solve(A, b, dt=0.1*ms, duration=10*ms):
+    """
+    Solve Ax=b using spiking neural network
+    """
+    n = len(b)
+
+    # Define neuron model (leaky integrate-and-fire)
+    eqs = '''
+    dv/dt = (I_ext + I_syn - v)/tau : volt
+    I_syn : volt
+    I_ext : volt
+    '''
+
+    # Create neuron group
+    neurons = NeuronGroup(n, eqs, threshold='v > 1*mV',
+                         reset='v = 0*mV', method='exact')
+
+    # Initialize with random values
+    neurons.v = 'rand() * mV'
+
+    # External input from b
+    neurons.I_ext = b * mV
+
+    # Synaptic connections from A
+    S = Synapses(neurons, neurons, 'w : volt', on_pre='I_syn += w')
+    for i, j, val in sparse_entries(A):
+        S.connect(i=i, j=j)
+        S.w[i, j] = val * mV
+
+    # Record solution
+    M = StateMonitor(neurons, 'v', record=True)
+
+    # Run simulation
+    run(duration)
+
+    # Extract solution from final voltages
+    return M.v[:, -1] / mV
+```
+
+## Advantages
+
+1. **Energy Efficiency**: 1000-10,000x lower power
+2. **Natural Parallelism**: All neurons compute simultaneously
+3. **Fault Tolerance**: Graceful degradation
+4. **Online Learning**: Adapt to changing matrices
+5. **Asynchronous**: No global clock needed
+
+## Challenges
+
+1. **Precision**: Currently limited to 8-16 bits
+2. **Programming Model**: Different from von Neumann
+3. **Hardware Access**: Limited availability
+4. **Noise**: Can help or hurt convergence
+
+## Conclusion
+
+Neuromorphic computing offers a paradigm shift for linear solvers, trading precision for massive energy efficiency and parallelism. Perfect for edge computing, IoT, and battery-powered applications where approximate solutions suffice.