Adaptive-Threshold IF — Source Fidelity

This page records exactly which parts of the primary literature the maintained AdaptiveThresholdIFNeuron implements, which parts it does not, and the executed evidence behind every claim.

Primary-source boundary

Two primary sources define the model's identity:

• Mihalas & Niebur (2009), A generalized linear integrate-and-fire neural model produces diverse spiking behaviors, Neural Computation 21(3), 704–718, DOI 10.1162/neco.2008.12-07-680. The source threshold equation is dΘ/dt = a(V - E_L) - b(Θ - Θ∞). Setting the voltage coupling to zero (a = 0) yields the maintained threshold decay dθ/dt = -(θ - θ_rest)/τ_θ.
• Platkiewicz & Brette (2010), A threshold equation for action potential initiation, PLoS Computational Biology 6(7), e1000850, DOI 10.1371/journal.pcbi.1000850. The source derives that "the spike threshold increases by a fixed amount after each spike" — the maintained post-spike shift θ ← θ + Δθ.

The model is therefore an explicitly composite reduced adaptive-threshold LIF, not an exact instance of either source:

• The Platkiewicz–Brette central mechanism — a voltage-dependent threshold equilibrium θ∞(V) through sodium-channel inactivation — is outside this model.
• The Mihalas–Niebur voltage-coupling term a(V - E_L) and its adaptation currents are outside this model.
• All defaults (theta_rest=-50 mV, delta_theta=5 mV, tau_m=10 ms, tau_theta=50 ms, dt=0.1 ms) are catalogue/model-family choices, not source-derived parameters.

An earlier revision of the model docstring named "Platkiewicz & Bhatt 2010" (a typographical error) and the descriptor recorded integration.method = "euler" while production always used the exact constant-input relaxation. Both are corrected findings, not harmless prose; the identity above replaces them.

Exact relaxation and the event convention

Both state equations are linear with piecewise-constant input, so the maintained step is the exact closed-form flow, never an Euler step:

Text Only

v'     = (v_rest + I) + (v - (v_rest + I)) * exp(-dt / tau_m)
theta' = theta_rest   + (theta - theta_rest) * exp(-dt / tau_theta)
spike  = (v' >= theta')
on spike: v <- v_reset; theta <- theta' + delta_theta

The event is detected on the post-update candidates at maintained step boundaries; no within-step root localisation is claimed.

Independent reference evidence

The committed reference trace reference_trace_data/adaptive_threshold_if_tonic_adaptation_doi.json is reproduced by an independent re-derivation (no production step code): tonic drive I = 20.0, 160 steps of dt = 0.1, one spike at step 138 with the threshold jumping from -50 toward -45 and decaying back. Every feature (spike count, first spike step, and final/min/max/mean of both states) matches at 1e-12 absolute.

Numerical and atomic contract

• Invalid input, invalid configuration, and non-finite candidates are rejected before any state mutation in every maintained lane.
• reset() restores only the documented state (v = v_rest, theta = theta_rest) and preserves the complete configuration.
• The batch contract returns complete v/theta/spikes trajectories plus final-state and spike-count receipts; the dispatcher validator re-checks the reset and the fixed threshold shift on every spike.

Executable parity matrix

Lane	Evidence	Result
Python golden	tests/test_model_adaptive_threshold_if.py	exact reference
Rust engine (PyO3)	tests/test_adaptive_threshold_if_parity.py	complete traces within 1e-12
Standalone Rust safety	tests/test_adaptive_threshold_if_rust_parity.py	complete traces within 2e-15
Julia (juliacall)	tests/test_adaptive_threshold_if_julia_parity.py	within 1e-12; typed buffer failures atomic
Go (C ABI)	tests/test_adaptive_threshold_if_go_parity.py, tests/test_adaptive_threshold_if_native_abi.py	within 1e-12; all overlap/null/status classes rejected without writes
Mojo (C ABI)	tests/test_adaptive_threshold_if_mojo_parity.py, tests/test_adaptive_threshold_if_native_abi.py	within 1e-10; identical ABI classes
Dispatch contracts	tests/test_adaptive_threshold_if_{input_validation,backend_selection,result_validation,c_facade}.py	input bounds, selection/reload, result validation, C-facade status boundaries

Paired schema and Q32.32 co-simulation

The TOML and JSON schema models are structurally identical and preserve the hand model's exact relaxation within 5e-12 over a varied 256-step drive, in both the subthreshold and the spiking regimes (6/6 events).

Generated Q32.32 SystemVerilog is validated at the enrolled grid-exact operating point (tau_m = tau_theta = 0.8, dt = 0.1, so both exponential arguments land exactly on the 0.125-step lookup grid):

• measured maximum state error over the 256-step sign-changing drive: v: 1.22e-8, theta: 2.65e-9 (declared envelope 0.01 mV);
• the complete 256-entry event vector is identical to the Python golden;
• every RTL spike resets v to v_reset and shifts theta by exactly delta_theta;
• a depth-4 Z3 bounded job proves reset safety only (hdl/formal/catalogue/sc_adaptive_threshold_if.sby, PASS);
• Yosys synth completes the generated module.

The enrolled default configuration (tau_m = 10, tau_theta = 50) is not claimed for the generated RTL: its exponential arguments do not lie on the lookup grid, and a grid-quantised envelope is not presented as fidelity. No formal equivalence, synthesis timing, device, or PPA claim is made; the silicon tier is H1.

Controlled benchmark

benchmarks/results/bench_adaptive_threshold_if.json records the five-runtime 200,000-step batch (22.0 + 6.0*sin(i*0.037) + 1.5*cos(i*0.011) drive, non-default initial state) measured with five repeats on one pinned logical CPU, with host load, tool versions, source and binary SHA-256 hashes, and run order recorded. All five lanes return matching events, final states, and trace digests within the declared tolerances. This is local regression evidence only; no production speed claim is made.

Boundaries

• No voltage-dependent threshold equilibrium, voltage coupling, adaptation current, refractory period, or synaptic conductance.
• Defaults are model-family choices, not source parameters.
• The benchmark is non-exclusive single-CPU evidence, not an isolated production measurement.

Reproduction

Bash

rustc --edition 2021 --test \
  src/sc_neurocore/accel/rust/safety/adaptive_threshold_if.rs -o /tmp/atif && /tmp/atif
python -m pytest \
  tests/test_model_adaptive_threshold_if.py \
  tests/test_adaptive_threshold_if_dynamics.py \
  tests/test_adaptive_threshold_if_backends.py \
  tests/test_adaptive_threshold_if_parity.py \
  tests/test_adaptive_threshold_if_rust_parity.py \
  tests/test_adaptive_threshold_if_julia_parity.py \
  tests/test_adaptive_threshold_if_go_parity.py \
  tests/test_adaptive_threshold_if_mojo_parity.py \
  tests/test_adaptive_threshold_if_native_abi.py \
  tests/test_adaptive_threshold_if_input_validation.py \
  tests/test_adaptive_threshold_if_backend_selection.py \
  tests/test_adaptive_threshold_if_result_validation.py \
  tests/test_adaptive_threshold_if_c_facade.py \
  tests/test_cosim_adaptive_threshold_if.py \
  tests/test_reference_adaptive_threshold_if.py \
  tests/test_bench_adaptive_threshold_if.py -q
cd hdl/formal/catalogue && sby -f sc_adaptive_threshold_if.sby
taskset -c 0 env PYTHONPATH=$WHEEL_SITE:src:. python \
  benchmarks/bench_model_adaptive_threshold_if.py