Autoassociative Memory: Sensor Fault Recovery
April 3, 2026 ยท View on GitHub
Scenario
Imagine a facility monitored by 256 sensors -- temperature, pressure, vibration, flow rate -- spread across a plant floor. The network has learned 20 known-good operating profiles.
When sensors fail or return garbage, the network uses the remaining good readings to reconstruct what the faulty sensors should be reporting. This is content-addressable error correction: the partial input is enough to recall the whole.
| Parameter | Value |
|---|---|
| DIM | 8 |
| Sensors (N) | 256 |
| Stored profiles | 20 |
| Update mode | Sync |
Test 1: Gaussian Noise on All Sensors
Every sensor drifts from its true value by a random amount. Noise level is the standard deviation of the drift relative to signal values in [-1, 1]. Higher noise means more corruption.
| Noise | Similarity Before | Similarity After | Sweeps | Result |
|---|---|---|---|---|
| 0.5 | 0.7389 | 1.0000 | 2 | RECOVERED |
| 1.0 | 0.4506 | 1.0000 | 2 | RECOVERED |
| 1.5 | 0.3124 | 1.0000 | 3 | RECOVERED |
| 2.0 | 0.2662 | 1.0000 | 3 | RECOVERED |
| 3.0 | 0.1666 | 1.0000 | 3 | RECOVERED |
| 5.0 | 0.0514 | 0.0397 | 3 | FAILED |
The network recovers perfectly up to noise = 3.0. At that level, the input similarity to the true profile is already very low (0.17) -- yet the attractor basin pulls it back completely. Beyond that threshold, the corrupted state lands in the wrong basin and converges to a different attractor.
Test 2: Sensor Dropout (Dead Sensors Reporting Zero)
A percentage of sensors go completely dead, reporting 0.0 instead of their true values. The network must infer the missing readings from the survivors alone.
| Dead % | Dead Sensors | Similarity Before | Similarity After | Sweeps | Result |
|---|---|---|---|---|---|
| 10% | 25 | 0.9562 | 1.0000 | 2 | RECOVERED |
| 30% | 76 | 0.8129 | 1.0000 | 2 | RECOVERED |
| 50% | 128 | 0.6933 | 1.0000 | 2 | RECOVERED |
| 70% | 179 | 0.5396 | 1.0000 | 2 | RECOVERED |
| 90% | 230 | 0.3184 | 1.0000 | 3 | RECOVERED |
Even with 90% of sensors dead, the network reconstructs the full profile perfectly. The surviving sensors provide enough context to identify which stored profile matches, and the Hopfield dynamics fill in every missing value.
Takeaway
This is the practical value of associative memory: partial information is sufficient for complete reconstruction, as long as the input falls within the correct attractor basin.
With 20 stored profiles on a 256-vertex hypercube, the network tolerates extreme corruption (noise sigma up to 3.0, three times the [-1, 1] signal amplitude) and extreme data loss (90% of sensors dead) while still recovering the original profile in 2-3 sweeps.