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PING tolerates 80% dropped spikes but collapses on added noise#

The trained networks this entry uses are produced once in the shared training hub, exp022 (Training), and reused here rather than retrained.

Abstract#

Perturbs the hidden spike stream of trained PING and COBA networks at inference (drop spikes, add spikes) to ask whether the PING rate floor is dynamical or informational. PING tolerates dropping ≈ 80% of its emitted spikes (accuracy 85% at that level, from 91% unperturbed) yet collapses once added Poisson noise passes ≈ 81% of its own baseline rate. COBA is roughly flat to both, holding 89% across the whole add sweep (which reaches only ≈ 22% of its far higher baseline). The asymmetry, drops forgiven while adds break the gating, is the gamma cycle made visible: a structural feature of the architecture, not a readout-side trade-off.

Method#

The PING and COBA baseline definitions and training recipe are in exp025, where the rate-floor mechanism is also worked out. This entry tests whether the floor is dynamical (locked by the cycle period) or informational (locked by the readout’s spike-count requirement) by perturbing the hidden spike stream of the trained networks at inference.

The perturbation. A per-step callback on the COBANet’s _hidden_perturb_fn slot fires every timestep of every trial, with no warm-up, schedule, or exclusion. Trials are $𝑇=200$ ms at $\mathrm{\Delta }𝑡=0.1$ ms → 2000 fires per trial, applied across the held-out test set against the same trained network. At each timestep $𝑡$:

1. update conductances from the previous step’s spikes: ${𝑔}_{𝑒}^{\left(𝑡\right)}\leftarrow {𝑔}_{𝑒}^{\left(𝑡-1\right)}\cdot {𝑑}_{\text{AMPA}}+{\widetilde{𝒔}}^{𝐸,\left(𝑡-1\right)}{𝑊}_{𝑒𝑒}+{\text{input}}^{\left(𝑡\right)}{𝑊}_{\text{in}}$, with the analogous update for ${𝑔}_{𝑖}^{\left(𝑡\right)}$ from ${\widetilde{𝒔}}^{𝐼,\left(𝑡-1\right)}{𝑊}_{𝑖𝑒}$ and the E→I conductance from ${\widetilde{𝒔}}^{𝐸,\left(𝑡-1\right)}{𝑊}_{𝑒𝑖}$;
2. LIF step integrates ${𝑉}^{\left(𝑡\right)}$ and emits raw spike vectors ${𝒔}^{𝐸,\left(𝑡\right)}\in {\left\{0,1\right\}}^{𝐵\times {𝑁}_{𝐸}}$, ${𝒔}^{𝐼,\left(𝑡\right)}\in {\left\{0,1\right\}}^{𝐵\times {𝑁}_{𝐼}}$;
3. perturbation callback rewrites the raw vectors → ${\widetilde{𝒔}}^{𝐸,\left(𝑡\right)},{\widetilde{𝒔}}^{𝐼,\left(𝑡\right)}$;
4. record the perturbed vectors into the spike buffer;
5. readout accumulator adds ${\widetilde{𝒔}}^{𝐸,\left(𝑡\right)}{𝑊}_{\text{out}}$ to the mem-mean integrator.

Step 1 of timestep $𝑡+1$ consumes the perturbed spikes through ${𝑊}_{𝑒𝑒},{𝑊}_{𝑒𝑖},{𝑊}_{𝑖𝑒}$: a dropped E spike fails to drive I next step and contributes nothing to the readout; an injected I spike adds inhibition next step and counts in the rate metric. E and I get the same mode and level with independent draws.

Drop mode. For each (batch, neuron, timestep) slot $𝑖$, draw ${𝑢}_{𝑖}\sim \text{Uniform}\left(0,1\right)$ i.i.d. and keep each emitted spike with probability $1-{𝑝}_{\text{drop}}$:

Drop thins the count fed to both the readout and the next-step conductance update while leaving the E→I→E loop intact. Sweep ${𝑝}_{\text{drop}}\in \left\{0.0,0.1,\dots ,1.0\right\}$, 11 levels.

Add mode. For each slot draw ${𝑢}_{𝑖}\sim \text{Uniform}\left(0,1\right)$ i.i.d. and flip silent slots on at Poisson statistics, phase-independent:

Sweep ${𝑟}_{\text{add}}\in \left\{0,2,\dots ,40\right\}$ Hz per neuron, 21 levels, applied equally to E and I. Because the two architectures sit at very different baselines (COBA ≈ 181 Hz per E cell versus PING ≈ 12 Hz, a factor of ≈ 15), a fixed added rate is a much larger relative insult to PING than to COBA, so the right panel of Figure 1 expresses the added rate as a percentage of each model’s own baseline E rate (the architecture-fair view). The per-step RNG is seeded separately from the input encoder, so the Poisson input stream matches the unperturbed baseline. Total: 2 models × (11 drop + 21 add) = 64 forward passes.

Results#