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F.M. Quintana Velazquez committed 2026-02-27 17:48:38 +01:00
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neuron_models/fhn/fhn/index.html
+251 -61
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@@ -1564,7 +1564,7 @@ span.linenos.special { color: #000000; background-color: #ffffc0; padding-left:
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="jp-InputPrompt jp-InputArea-prompt">In [2]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class="zeroclipboard-container">
<clipboard-copy ,="" aria-label="Copy to Clipboard" for="cell-1">
@@ -1583,9 +1583,8 @@ span.linenos.special { color: #000000; background-color: #ffffc0; padding-left:
<span class="kn">import</span><span class="w"> </span><span class="nn">jax.random</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jrand</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">mpl</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">eventpropjax.evnn</span><span class="w"> </span><span class="kn">import</span> <span class="n">FFEvNN</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">felice.neuron_models</span><span class="w"> </span><span class="kn">import</span> <span class="n">FHN</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">felice.neuron_models</span><span class="w"> </span><span class="kn">import</span> <span class="n">FHNRS</span>
</pre></div>
<div class="clipboard-copy-txt" id="cell-1">import diffrax as dfx
import jax
@@ -1593,9 +1592,8 @@ import jax.numpy as jnp
import jax.random as jrand
import matplotlib as mpl
import matplotlib.pyplot as plt
from eventpropjax.evnn import FFEvNN
from felice.neuron_models import FHN</div>
from felice.neuron_models import FHNRS</div>
</div>
</div>
</div>
@@ -1607,7 +1605,7 @@ from felice.neuron_models import FHN</div>
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In [2]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="jp-InputPrompt jp-InputArea-prompt">In [23]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class="zeroclipboard-container">
<clipboard-copy ,="" aria-label="Copy to Clipboard" for="cell-2">
@@ -1623,32 +1621,64 @@ from felice.neuron_models import FHN</div>
<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">key</span> <span class="o">=</span> <span class="n">jrand</span><span class="o">.</span><span class="n">key</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">max_time</span> <span class="o">=</span> <span class="mi">200</span>
<span class="n">snn</span> <span class="o">=</span> <span class="n">FFEvNN</span><span class="p">(</span>
<span class="n">layers</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
<span class="n">in_size</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="n">neuron_model</span><span class="o">=</span><span class="n">FHN</span><span class="p">,</span>
<span class="n">solver</span><span class="o">=</span><span class="n">dfx</span><span class="o">.</span><span class="n">Dopri5</span><span class="p">(),</span>
<span class="n">max_solver_time</span><span class="o">=</span><span class="n">max_time</span><span class="p">,</span>
<span class="n">key</span><span class="o">=</span><span class="n">key</span><span class="p">,</span>
<span class="n">max_event_steps</span><span class="o">=</span><span class="mi">1000000</span><span class="p">,</span>
<span class="n">solver_stepsize</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span>
<span class="n">init_weights</span><span class="o">=</span><span class="mf">2.0</span><span class="p">,</span>
<span class="n">neuron_model</span> <span class="o">=</span> <span class="n">FHNRS</span><span class="p">(</span>
<span class="n">gmax_pasive</span><span class="o">=</span><span class="mf">2.0</span><span class="p">,</span>
<span class="n">Erev_pasive</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span>
<span class="n">a_fast</span><span class="o">=-</span><span class="mf">2.0</span><span class="p">,</span>
<span class="n">voff_fast</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span>
<span class="n">tau_fast</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span>
<span class="n">a_slow</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span>
<span class="n">voff_slow</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span>
<span class="n">tau_slow</span><span class="o">=</span><span class="mf">50.0</span><span class="p">,</span>
<span class="n">vthr</span><span class="o">=</span><span class="n">jnp</span><span class="o">.</span><span class="n">inf</span><span class="p">,</span>
<span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">state_at_t</span><span class="p">(</span><span class="n">comp_times</span><span class="p">):</span>
<span class="n">sol</span> <span class="o">=</span> <span class="n">dfx</span><span class="o">.</span><span class="n">diffeqsolve</span><span class="p">(</span>
<span class="n">terms</span><span class="o">=</span><span class="n">dfx</span><span class="o">.</span><span class="n">ODETerm</span><span class="p">(</span><span class="n">neuron_model</span><span class="o">.</span><span class="n">dynamics</span><span class="p">),</span>
<span class="n">solver</span><span class="o">=</span><span class="n">dfx</span><span class="o">.</span><span class="n">Tsit5</span><span class="p">(),</span>
<span class="n">t0</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span>
<span class="n">t1</span><span class="o">=</span><span class="n">max_time</span><span class="p">,</span>
<span class="n">dt0</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span>
<span class="n">y0</span><span class="o">=</span><span class="n">neuron_model</span><span class="o">.</span><span class="n">init_state</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="o">+</span> <span class="n">jrand</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="n">minval</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">maxval</span><span class="o">=</span><span class="mf">0.5</span><span class="p">),</span>
<span class="n">saveat</span><span class="o">=</span><span class="n">dfx</span><span class="o">.</span><span class="n">SaveAt</span><span class="p">(</span><span class="n">ts</span><span class="o">=</span><span class="n">comp_times</span><span class="p">),</span>
<span class="n">max_steps</span><span class="o">=</span><span class="mi">200000</span><span class="p">,</span>
<span class="p">)</span>
<span class="k">return</span> <span class="n">sol</span><span class="o">.</span><span class="n">ts</span><span class="p">,</span> <span class="n">sol</span><span class="o">.</span><span class="n">ys</span>
</pre></div>
<div class="clipboard-copy-txt" id="cell-2">key = jrand.key(0)
max_time = 200
snn = FFEvNN(
layers=[1],
in_size=1,
neuron_model=FHN,
solver=dfx.Dopri5(),
max_solver_time=max_time,
key=key,
max_event_steps=1000000,
solver_stepsize=0.1,
init_weights=2.0,
)</div>
neuron_model = FHNRS(
gmax_pasive=2.0,
Erev_pasive=0.0,
a_fast=-2.0,
voff_fast=0.0,
tau_fast=0.0,
a_slow=0.5,
voff_slow=1.0,
tau_slow=50.0,
vthr=jnp.inf,
)
def state_at_t(comp_times):
sol = dfx.diffeqsolve(
terms=dfx.ODETerm(neuron_model.dynamics),
solver=dfx.Tsit5(),
t0=0.0,
t1=max_time,
dt0=1e-3,
y0=neuron_model.init_state(1)
+ jrand.uniform(key, shape=(1, 3), minval=0.1, maxval=0.5),
saveat=dfx.SaveAt(ts=comp_times),
max_steps=200000,
)
return sol.ts, sol.ys</div>
</div>
</div>
</div>
@@ -1660,7 +1690,7 @@ snn = FFEvNN(
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In [3]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="jp-InputPrompt jp-InputArea-prompt">In [24]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class="zeroclipboard-container">
<clipboard-copy ,="" aria-label="Copy to Clipboard" for="cell-3">
@@ -1674,9 +1704,9 @@ snn = FFEvNN(
</clipboard-copy>
</div>
<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">v_range</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mf">3.1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
<span class="n">VI_inst</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">vmap</span><span class="p">(</span><span class="n">snn</span><span class="o">.</span><span class="n">neuron_model</span><span class="o">.</span><span class="n">IV_inst</span><span class="p">)(</span><span class="n">v_range</span><span class="p">)</span>
<span class="n">VI_fast</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">vmap</span><span class="p">(</span><span class="n">snn</span><span class="o">.</span><span class="n">neuron_model</span><span class="o">.</span><span class="n">IV_fast</span><span class="p">)(</span><span class="n">v_range</span><span class="p">)</span>
<span class="n">VI_slow</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">vmap</span><span class="p">(</span><span class="n">snn</span><span class="o">.</span><span class="n">neuron_model</span><span class="o">.</span><span class="n">IV_slow</span><span class="p">)(</span><span class="n">v_range</span><span class="p">)</span>
<span class="n">VI_inst</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">vmap</span><span class="p">(</span><span class="n">neuron_model</span><span class="o">.</span><span class="n">IV_inst</span><span class="p">)(</span><span class="n">v_range</span><span class="p">)</span>
<span class="n">VI_fast</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">vmap</span><span class="p">(</span><span class="n">neuron_model</span><span class="o">.</span><span class="n">IV_fast</span><span class="p">)(</span><span class="n">v_range</span><span class="p">)</span>
<span class="n">VI_slow</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">vmap</span><span class="p">(</span><span class="n">neuron_model</span><span class="o">.</span><span class="n">IV_slow</span><span class="p">)(</span><span class="n">v_range</span><span class="p">)</span>
<span class="k">with</span> <span class="n">mpl</span><span class="o">.</span><span class="n">style</span><span class="o">.</span><span class="n">context</span><span class="p">(</span><span class="s2">"boilerplot.ieeetran"</span><span class="p">):</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">6.9</span><span class="p">,</span> <span class="mf">2.3</span><span class="p">),</span> <span class="n">dpi</span><span class="o">=</span><span class="mf">200.0</span><span class="p">,</span> <span class="n">sharey</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
@@ -1686,9 +1716,9 @@ snn = FFEvNN(
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
<div class="clipboard-copy-txt" id="cell-3">v_range = jnp.arange(-3.1, 3, 0.1)
VI_inst = jax.vmap(snn.neuron_model.IV_inst)(v_range)
VI_fast = jax.vmap(snn.neuron_model.IV_fast)(v_range)
VI_slow = jax.vmap(snn.neuron_model.IV_slow)(v_range)
VI_inst = jax.vmap(neuron_model.IV_inst)(v_range)
VI_fast = jax.vmap(neuron_model.IV_fast)(v_range)
VI_slow = jax.vmap(neuron_model.IV_slow)(v_range)
with mpl.style.context("boilerplot.ieeetran"):
fig, ax = plt.subplots(1, 3, figsize=(6.9, 2.3), dpi=200.0, sharey=True)
@@ -1707,7 +1737,7 @@ with mpl.style.context("boilerplot.ieeetran"):
<div class="jp-OutputArea-child">
<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
<div class="jp-RenderedImage jp-OutputArea-output" tabindex="0">
<img alt="No description has been provided for this image" class="" 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</div>
</div>
</div>
@@ -1719,7 +1749,7 @@ with mpl.style.context("boilerplot.ieeetran"):
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In [4]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="jp-InputPrompt jp-InputArea-prompt">In [25]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class="zeroclipboard-container">
<clipboard-copy ,="" aria-label="Copy to Clipboard" for="cell-4">
@@ -1732,27 +1762,23 @@ with mpl.style.context("boilerplot.ieeetran"):
</div>
</clipboard-copy>
</div>
<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">in_spikes</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span><span class="p">([[</span><span class="mf">0.00</span><span class="p">]])</span>
<span class="n">comp_times</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">max_time</span><span class="p">,</span> <span class="mi">500</span><span class="p">)</span>
<span class="n">state</span> <span class="o">=</span> <span class="n">snn</span><span class="o">.</span><span class="n">state_at_t</span><span class="p">(</span><span class="n">in_spikes</span><span class="p">,</span> <span class="n">comp_times</span><span class="p">)</span>
<span class="n">spikes</span> <span class="o">=</span> <span class="n">snn</span><span class="o">.</span><span class="n">spikes_until_t</span><span class="p">(</span><span class="n">in_spikes</span><span class="p">,</span> <span class="n">max_time</span><span class="p">)</span>
<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">comp_times</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">max_time</span><span class="p">,</span> <span class="mi">500</span><span class="p">)</span>
<span class="n">_</span><span class="p">,</span> <span class="n">state</span> <span class="o">=</span> <span class="n">state_at_t</span><span class="p">(</span><span class="n">comp_times</span><span class="p">)</span>
</pre></div>
<div class="clipboard-copy-txt" id="cell-4">in_spikes = jnp.asarray([[0.00]])
comp_times = jnp.linspace(0.0, max_time, 500)
state = snn.state_at_t(in_spikes, comp_times)
spikes = snn.spikes_until_t(in_spikes, max_time)</div>
<div class="clipboard-copy-txt" id="cell-4">comp_times = jnp.linspace(0.0, max_time, 500)
_, state = state_at_t(comp_times)</div>
</div>
</div>
</div>
</div>
</div>
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell">
<div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=b73fb06d">
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@@ -1765,16 +1791,152 @@ spikes = snn.spikes_until_t(in_spikes, max_time)</div>
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<div class="highlight-ipynb hl-python"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">compute_nullclines</span><span class="p">(</span><span class="n">neuron_model</span><span class="p">,</span> <span class="n">u_range</span><span class="p">,</span> <span class="n">v_range</span><span class="p">,</span> <span class="n">resolution</span><span class="o">=</span><span class="mi">200</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""</span>
<span class="sd"> Compute nullclines</span>
<span class="sd"> du/dt = 0 (u-nullcline)</span>
<span class="sd"> dv/dt = 0 (v-nullcline)</span>
<span class="sd"> """</span>
<span class="n">u_vals</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">u_range</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">u_range</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">resolution</span><span class="p">)</span>
<span class="n">v_vals</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">v_range</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">v_range</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">resolution</span><span class="p">)</span>
<span class="n">U</span><span class="p">,</span> <span class="n">V</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">u_vals</span><span class="p">,</span> <span class="n">v_vals</span><span class="p">)</span>
<span class="n">UV</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span>
<span class="p">[</span><span class="n">U</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="n">V</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">resolution</span> <span class="o">*</span> <span class="n">resolution</span><span class="p">,))],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span>
<span class="p">)</span>
<span class="n">dS</span> <span class="o">=</span> <span class="n">neuron_model</span><span class="o">.</span><span class="n">dynamics</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">UV</span><span class="p">,</span> <span class="p">{})</span>
<span class="n">dU</span> <span class="o">=</span> <span class="n">dS</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">U</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">dV</span> <span class="o">=</span> <span class="n">dS</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">V</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="k">return</span> <span class="n">U</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">dU</span><span class="p">,</span> <span class="n">dV</span>
<span class="k">def</span><span class="w"> </span><span class="nf">plot_vf</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">neuron_model</span><span class="p">,</span> <span class="n">u_range</span><span class="p">,</span> <span class="n">v_range</span><span class="p">):</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="n">u_sparse</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">u_range</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">u_range</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="mi">30</span><span class="p">)</span>
<span class="n">v_sparse</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">v_range</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">v_range</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="mi">30</span><span class="p">)</span>
<span class="n">Us</span><span class="p">,</span> <span class="n">Vs</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">u_sparse</span><span class="p">,</span> <span class="n">v_sparse</span><span class="p">)</span>
<span class="n">U</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">dU</span><span class="p">,</span> <span class="n">dV</span> <span class="o">=</span> <span class="n">compute_nullclines</span><span class="p">(</span><span class="n">neuron_model</span><span class="p">,</span> <span class="n">u_range</span><span class="p">,</span> <span class="n">v_range</span><span class="p">,</span> <span class="mi">200</span><span class="p">)</span>
<span class="n">UVs</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">stack</span><span class="p">([</span><span class="n">Us</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="n">Vs</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="n">jnp</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">30</span> <span class="o">*</span> <span class="mi">30</span><span class="p">,))],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">dS</span> <span class="o">=</span> <span class="n">neuron_model</span><span class="o">.</span><span class="n">dynamics</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">UVs</span><span class="p">,</span> <span class="p">{})</span>
<span class="n">dUs</span> <span class="o">=</span> <span class="n">dS</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">Us</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">dVs</span> <span class="o">=</span> <span class="n">dS</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">Vs</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="c1"># Normalize for visualization</span>
<span class="n">magnitude</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">dUs</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">dVs</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
<span class="n">magnitude</span><span class="p">[</span><span class="n">magnitude</span> <span class="o">==</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">dUs_norm</span> <span class="o">=</span> <span class="n">dUs</span> <span class="o">/</span> <span class="n">magnitude</span>
<span class="n">dVs_norm</span> <span class="o">=</span> <span class="n">dVs</span> <span class="o">/</span> <span class="n">magnitude</span>
<span class="c1"># Nullclines</span>
<span class="n">ax</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">U</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">dU</span><span class="p">,</span> <span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">colors</span><span class="o">=</span><span class="s2">"blue"</span><span class="p">,</span> <span class="n">linewidths</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">linestyles</span><span class="o">=</span><span class="s2">"-"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">U</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">dV</span><span class="p">,</span> <span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">colors</span><span class="o">=</span><span class="s2">"red"</span><span class="p">,</span> <span class="n">linewidths</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">linestyles</span><span class="o">=</span><span class="s2">"-"</span><span class="p">)</span>
<span class="c1"># Vector field</span>
<span class="n">ax</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="n">Us</span><span class="p">,</span> <span class="n">Vs</span><span class="p">,</span> <span class="n">dUs_norm</span><span class="p">,</span> <span class="n">dVs_norm</span><span class="p">,</span> <span class="n">magnitude</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s2">"viridis"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"v"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">"w"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">([</span><span class="s2">"u-nullcline (du/dt=0)"</span><span class="p">,</span> <span class="s2">"v-nullcline (dv/dt=0)"</span><span class="p">],</span> <span class="n">loc</span><span class="o">=</span><span class="s2">"upper right"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="n">u_range</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="n">v_range</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">axhline</span><span class="p">(</span><span class="n">y</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"gray"</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s2">"--"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">axvline</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"gray"</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s2">"--"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
</pre></div>
<div class="clipboard-copy-txt" id="cell-5">def compute_nullclines(neuron_model, u_range, v_range, resolution=200):
"""
Compute nullclines
du/dt = 0 (u-nullcline)
dv/dt = 0 (v-nullcline)
"""
u_vals = jnp.linspace(u_range[0], u_range[1], resolution)
v_vals = jnp.linspace(v_range[0], v_range[1], resolution)
U, V = jnp.meshgrid(u_vals, v_vals)
UV = jnp.stack(
[U.reshape(-1), V.reshape(-1), jnp.zeros((resolution * resolution,))], axis=1
)
dS = neuron_model.dynamics(0, UV, {})
dU = dS[:, 0].reshape(U.shape)
dV = dS[:, 1].reshape(V.shape)
return U, V, dU, dV
def plot_vf(ax, neuron_model, u_range, v_range):
import numpy as np
u_sparse = jnp.linspace(u_range[0], u_range[1], 30)
v_sparse = jnp.linspace(v_range[0], v_range[1], 30)
Us, Vs = jnp.meshgrid(u_sparse, v_sparse)
U, V, dU, dV = compute_nullclines(neuron_model, u_range, v_range, 200)
UVs = jnp.stack([Us.reshape(-1), Vs.reshape(-1), jnp.ones((30 * 30,))], axis=1)
dS = neuron_model.dynamics(0, UVs, {})
dUs = dS[:, 0].reshape(Us.shape)
dVs = dS[:, 1].reshape(Vs.shape)
# Normalize for visualization
magnitude = np.sqrt(dUs**2 + dVs**2)
magnitude[magnitude == 0] = 1
dUs_norm = dUs / magnitude
dVs_norm = dVs / magnitude
# Nullclines
ax.contour(U, V, dU, levels=[0], colors="blue", linewidths=1, linestyles="-")
ax.contour(U, V, dV, levels=[0], colors="red", linewidths=1, linestyles="-")
# Vector field
ax.quiver(Us, Vs, dUs_norm, dVs_norm, magnitude, cmap="viridis", alpha=0.6)
ax.set_xlabel("v")
ax.set_ylabel("w")
ax.legend(["u-nullcline (du/dt=0)", "v-nullcline (dv/dt=0)"], loc="upper right")
ax.set_xlim(u_range)
ax.set_ylim(v_range)
ax.axhline(y=0, color="gray", linestyle="--", alpha=0.3)
ax.axvline(x=0, color="gray", linestyle="--", alpha=0.3)</div>
</div>
</div>
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<div class="highlight-ipynb hl-python"><pre><span></span><span class="k">with</span> <span class="n">mpl</span><span class="o">.</span><span class="n">style</span><span class="o">.</span><span class="n">context</span><span class="p">(</span><span class="s2">"boilerplot.ieeetran"</span><span class="p">):</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">6.9</span><span class="p">,</span> <span class="mf">2.6</span><span class="p">),</span> <span class="n">dpi</span><span class="o">=</span><span class="mi">200</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">comp_times</span><span class="p">,</span> <span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">])</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">comp_times</span><span class="p">,</span> <span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"--"</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">comp_times</span><span class="p">,</span> <span class="n">state</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">comp_times</span><span class="p">,</span> <span class="n">state</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"--"</span><span class="p">)</span>
<span class="c1"># ax[0].plot(comp_times, state[0, :, 2], "-.")</span>
<span class="p">[</span><span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">axvline</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"g"</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s2">"--"</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">jnp</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">spikes</span><span class="p">)]</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"Time (ms)"</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">legend</span><span class="p">([</span><span class="s2">"v"</span><span class="p">,</span> <span class="s2">"vslow"</span><span class="p">,</span> <span class="s2">"syn"</span><span class="p">,</span> <span class="s2">"Spike"</span><span class="p">])</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">legend</span><span class="p">([</span><span class="s2">"v"</span><span class="p">,</span> <span class="s2">"vslow"</span><span class="p">,</span> <span class="s2">"syn"</span><span class="p">])</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:,</span> <span class="mi">1</span><span class="p">])</span>
<span class="n">plot_vf</span><span class="p">(</span><span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">neuron_model</span><span class="p">,</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">state</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">state</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"."</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"start"</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"."</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"end"</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"v"</span><span class="p">)</span>
@@ -1782,16 +1944,17 @@ spikes = snn.spikes_until_t(in_spikes, max_time)</div>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
<div class="clipboard-copy-txt" id="cell-5">with mpl.style.context("boilerplot.ieeetran"):
<div class="clipboard-copy-txt" id="cell-6">with mpl.style.context("boilerplot.ieeetran"):
fig, ax = plt.subplots(1, 2, figsize=(6.9, 2.6), dpi=200)
ax[0].plot(comp_times, state[0, :, 0])
ax[0].plot(comp_times, state[0, :, 1], "--")
ax[0].plot(comp_times, state[:, 0, 0])
ax[0].plot(comp_times, state[:, 0, 1], "--")
# ax[0].plot(comp_times, state[0, :, 2], "-.")
[ax[0].axvline(s, alpha=0.2, color="g", linestyle="--") for s in jnp.unique(spikes)]
ax[0].set_xlabel("Time (ms)")
ax[0].legend(["v", "vslow", "syn", "Spike"])
ax[0].legend(["v", "vslow", "syn"])
ax[1].plot(state[0, :, 0], state[0, :, 1])
plot_vf(ax[1], neuron_model, [-2, 2], [-2, 2])
ax[1].plot(state[:, 0, 0], state[:, 0, 1])
ax[1].plot(state[0, 0, 0], state[0, 0, 1], ".", label="start")
ax[1].plot(state[0, -1, 0], state[0, -1, 1], ".", label="end")
ax[1].set_xlabel("v")
@@ -1809,7 +1972,7 @@ spikes = snn.spikes_until_t(in_spikes, max_time)</div>
<div class="jp-OutputArea-child">
<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
<div class="jp-RenderedImage jp-OutputArea-output" tabindex="0">
<img alt="No description has been provided for this image" class="" 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<img alt="No description has been provided for this image" class="" 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@@ -1824,7 +1987,7 @@ spikes = snn.spikes_until_t(in_spikes, max_time)</div>
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neuron_models/index.html
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<td>Exponential Integrate-and-Fire neuron model</td>
<td>...</td>
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<tr>
<td><a href="lif/">LIF</a></td>
<td>Leaky Integrate-and-Fire neuron model</td>
<td>...</td>
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neuron_models/lif/index.html
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<h1 id="lif">LIF</h1>
<h2 id="circuit-design">Circuit Design</h2>
<p>W/L = 4/3</p>
<h2 id="circuit-simulation">Circuit Simulation</h2>
<p><img alt="lif, output plot" src="/docs-site/docs/img/lif_plot.png" /> Fig.1 The dynamics of leaky integrate and fire neuron. The grey signal is the input spikes, the yellow signal is the membrane potential and the dark blue is the output spikes from the neuron.</p>
<h2 id="referennces">Referennces</h2>
<ol>
<li>Sourikopoulos I, Hedayat S, Loyez C, Danneville F, Hoel V, Mercier E and Cappy A (2017) A 4-fJ/Spike Artificial Neuron in 65 nm CMOS Technology. Front. Neurosci. 11:123. doi: 10.3389/fnins.2017.00123</li>
</ol>
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neuron_models/wererabbit/wererabbit/index.html
+64 -143
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@@ -1564,7 +1564,7 @@ span.linenos.special { color: #000000; background-color: #ffffc0; padding-left:
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In [1]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="jp-InputPrompt jp-InputArea-prompt">In [10]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class="zeroclipboard-container">
<clipboard-copy ,="" aria-label="Copy to Clipboard" for="cell-1">
@@ -1583,7 +1583,6 @@ span.linenos.special { color: #000000; background-color: #ffffc0; padding-left:
<span class="kn">import</span><span class="w"> </span><span class="nn">jax.random</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jrand</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">mpl</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">eventpropjax.evnn</span><span class="w"> </span><span class="kn">import</span> <span class="n">FFEvNN</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">felice.neuron_models</span><span class="w"> </span><span class="kn">import</span> <span class="n">WereRabbit</span>
@@ -1595,7 +1594,6 @@ import jax.numpy as jnp
import jax.random as jrand
import matplotlib as mpl
import matplotlib.pyplot as plt
from eventpropjax.evnn import FFEvNN
from felice.neuron_models import WereRabbit
@@ -1611,7 +1609,7 @@ jax.config.update("jax_enable_x64", True)</div>
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In [2]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="jp-InputPrompt jp-InputArea-prompt">In [11]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class="zeroclipboard-container">
<clipboard-copy ,="" aria-label="Copy to Clipboard" for="cell-2">
@@ -1625,44 +1623,46 @@ jax.config.update("jax_enable_x64", True)</div>
</clipboard-copy>
</div>
<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">key</span> <span class="o">=</span> <span class="n">jrand</span><span class="o">.</span><span class="n">key</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">max_time</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">max_time</span> <span class="o">=</span> <span class="mi">40</span>
<span class="n">init_weights</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span><span class="p">([[</span><span class="mf">0.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.1</span><span class="p">]])</span>
<span class="n">snn</span> <span class="o">=</span> <span class="n">FFEvNN</span><span class="p">(</span>
<span class="n">layers</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
<span class="n">in_size</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">neuron_model</span><span class="o">=</span><span class="n">WereRabbit</span><span class="p">,</span>
<span class="n">solver</span><span class="o">=</span><span class="n">dfx</span><span class="o">.</span><span class="n">Tsit5</span><span class="p">(),</span>
<span class="c1"># stepsize_controller=PIDController(</span>
<span class="c1"># rtol=1e-6, atol=1e-3, pcoeff=0.1, icoeff=0.3, dcoeff=0.0</span>
<span class="c1"># ),</span>
<span class="n">max_solver_time</span><span class="o">=</span><span class="n">max_time</span><span class="p">,</span>
<span class="n">key</span><span class="o">=</span><span class="n">key</span><span class="p">,</span>
<span class="n">max_event_steps</span><span class="o">=</span><span class="mi">10000</span><span class="p">,</span>
<span class="n">solver_stepsize</span><span class="o">=</span><span class="mf">0.001</span><span class="p">,</span>
<span class="n">init_weights</span><span class="o">=</span><span class="n">init_weights</span><span class="p">,</span>
<span class="n">dtype</span><span class="o">=</span><span class="n">jnp</span><span class="o">.</span><span class="n">float64</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">WereRabbit</span><span class="p">(</span><span class="n">dtype</span><span class="o">=</span><span class="n">jnp</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">state_at_t</span><span class="p">(</span><span class="n">comp_times</span><span class="p">):</span>
<span class="n">sol</span> <span class="o">=</span> <span class="n">dfx</span><span class="o">.</span><span class="n">diffeqsolve</span><span class="p">(</span>
<span class="n">terms</span><span class="o">=</span><span class="n">dfx</span><span class="o">.</span><span class="n">ODETerm</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">dynamics</span><span class="p">),</span>
<span class="n">solver</span><span class="o">=</span><span class="n">dfx</span><span class="o">.</span><span class="n">Tsit5</span><span class="p">(),</span>
<span class="n">t0</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span>
<span class="n">t1</span><span class="o">=</span><span class="n">max_time</span><span class="p">,</span>
<span class="n">dt0</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span>
<span class="n">y0</span><span class="o">=</span><span class="n">model</span><span class="o">.</span><span class="n">init_state</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="o">+</span> <span class="n">jrand</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">minval</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">maxval</span><span class="o">=</span><span class="mf">0.5</span><span class="p">),</span>
<span class="n">saveat</span><span class="o">=</span><span class="n">dfx</span><span class="o">.</span><span class="n">SaveAt</span><span class="p">(</span><span class="n">ts</span><span class="o">=</span><span class="n">comp_times</span><span class="p">),</span>
<span class="n">max_steps</span><span class="o">=</span><span class="mi">100000</span><span class="p">,</span>
<span class="p">)</span>
<span class="k">return</span> <span class="n">sol</span><span class="o">.</span><span class="n">ts</span><span class="p">,</span> <span class="n">sol</span><span class="o">.</span><span class="n">ys</span>
</pre></div>
<div class="clipboard-copy-txt" id="cell-2">key = jrand.key(0)
max_time = 100
max_time = 40
init_weights = jnp.asarray([[0.0], [0.2], [-0.1]])
snn = FFEvNN(
layers=[1],
in_size=2,
neuron_model=WereRabbit,
solver=dfx.Tsit5(),
# stepsize_controller=PIDController(
# rtol=1e-6, atol=1e-3, pcoeff=0.1, icoeff=0.3, dcoeff=0.0
# ),
max_solver_time=max_time,
key=key,
max_event_steps=10000,
solver_stepsize=0.001,
init_weights=init_weights,
dtype=jnp.float64,
)</div>
model = WereRabbit(dtype=jnp.float64)
def state_at_t(comp_times):
sol = dfx.diffeqsolve(
terms=dfx.ODETerm(model.dynamics),
solver=dfx.Tsit5(),
t0=0.0,
t1=max_time,
dt0=1e-3,
y0=model.init_state(1)
+ jrand.uniform(key, shape=(1, 2), minval=0.1, maxval=0.5),
saveat=dfx.SaveAt(ts=comp_times),
max_steps=100000,
)
return sol.ts, sol.ys</div>
</div>
</div>
</div>
@@ -1674,7 +1674,7 @@ snn = FFEvNN(
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In [3]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="jp-InputPrompt jp-InputArea-prompt">In [12]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class="zeroclipboard-container">
<clipboard-copy ,="" aria-label="Copy to Clipboard" for="cell-3">
@@ -1687,15 +1687,11 @@ snn = FFEvNN(
</div>
</clipboard-copy>
</div>
<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">in_spikes</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span><span class="p">([[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">30</span><span class="p">],</span> <span class="p">[</span><span class="mi">20</span><span class="p">,</span> <span class="mi">21</span><span class="p">]])</span>
<span class="n">comp_times</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">max_time</span><span class="p">,</span> <span class="mi">2000</span><span class="p">)</span>
<span class="n">state</span> <span class="o">=</span> <span class="n">snn</span><span class="o">.</span><span class="n">state_at_t</span><span class="p">(</span><span class="n">in_spikes</span><span class="p">,</span> <span class="n">comp_times</span><span class="p">)</span>
<span class="n">spikes</span> <span class="o">=</span> <span class="n">snn</span><span class="o">.</span><span class="n">spikes_until_t</span><span class="p">(</span><span class="n">in_spikes</span><span class="p">,</span> <span class="n">max_time</span><span class="p">)</span>
<div class="highlight-ipynb hl-python"><pre><span></span><span class="n">comp_times</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">max_time</span><span class="p">,</span> <span class="mi">2000</span><span class="p">)</span>
<span class="n">_</span><span class="p">,</span> <span class="n">state</span> <span class="o">=</span> <span class="n">state_at_t</span><span class="p">(</span><span class="n">comp_times</span><span class="p">)</span>
</pre></div>
<div class="clipboard-copy-txt" id="cell-3">in_spikes = jnp.asarray([[10, 30], [20, 21]])
comp_times = jnp.linspace(0.0, max_time, 2000)
state = snn.state_at_t(in_spikes, comp_times)
spikes = snn.spikes_until_t(in_spikes, max_time)</div>
<div class="clipboard-copy-txt" id="cell-3">comp_times = jnp.linspace(0.0, max_time, 2000)
_, state = state_at_t(comp_times)</div>
</div>
</div>
</div>
@@ -1707,7 +1703,7 @@ spikes = snn.spikes_until_t(in_spikes, max_time)</div>
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
<div class="jp-InputArea jp-Cell-inputArea">
<div class="jp-InputPrompt jp-InputArea-prompt">In [4]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="jp-InputPrompt jp-InputArea-prompt">In [13]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
<div class="zeroclipboard-container">
<clipboard-copy ,="" aria-label="Copy to Clipboard" for="cell-4">
@@ -1733,7 +1729,7 @@ spikes = snn.spikes_until_t(in_spikes, max_time)</div>
<span class="n">UV</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span>
<span class="p">[</span><span class="n">U</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="n">V</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="n">jnp</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">resolution</span> <span class="o">*</span> <span class="n">resolution</span><span class="p">,))],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span>
<span class="p">)</span>
<span class="n">dS</span> <span class="o">=</span> <span class="n">snn</span><span class="o">.</span><span class="n">neuron_model</span><span class="o">.</span><span class="n">vector_field</span><span class="p">(</span><span class="n">UV</span><span class="p">)</span>
<span class="n">dS</span> <span class="o">=</span> <span class="n">snn</span><span class="o">.</span><span class="n">vector_field</span><span class="p">(</span><span class="n">UV</span><span class="p">)</span>
<span class="n">dU</span> <span class="o">=</span> <span class="n">dS</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">U</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">dV</span> <span class="o">=</span> <span class="n">dS</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">V</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
@@ -1751,7 +1747,7 @@ spikes = snn.spikes_until_t(in_spikes, max_time)</div>
<span class="n">U</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">dU</span><span class="p">,</span> <span class="n">dV</span> <span class="o">=</span> <span class="n">compute_nullclines</span><span class="p">(</span><span class="n">snn</span><span class="p">,</span> <span class="n">u_range</span><span class="p">,</span> <span class="n">v_range</span><span class="p">,</span> <span class="mi">200</span><span class="p">)</span>
<span class="n">UVs</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">stack</span><span class="p">([</span><span class="n">Us</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="n">Vs</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="n">jnp</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">20</span> <span class="o">*</span> <span class="mi">20</span><span class="p">,))],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">dS</span> <span class="o">=</span> <span class="n">snn</span><span class="o">.</span><span class="n">neuron_model</span><span class="o">.</span><span class="n">vector_field</span><span class="p">(</span><span class="n">UVs</span><span class="p">)</span>
<span class="n">dS</span> <span class="o">=</span> <span class="n">snn</span><span class="o">.</span><span class="n">vector_field</span><span class="p">(</span><span class="n">UVs</span><span class="p">)</span>
<span class="n">dUs</span> <span class="o">=</span> <span class="n">dS</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">Us</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">dVs</span> <span class="o">=</span> <span class="n">dS</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">Vs</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
@@ -1790,7 +1786,7 @@ spikes = snn.spikes_until_t(in_spikes, max_time)</div>
UV = jnp.stack(
[U.reshape(-1), V.reshape(-1), jnp.ones((resolution * resolution,))], axis=1
)
dS = snn.neuron_model.vector_field(UV)
dS = snn.vector_field(UV)
dU = dS[:, 0].reshape(U.shape)
dV = dS[:, 1].reshape(V.shape)
@@ -1808,7 +1804,7 @@ def plot_vf(ax, snn, u_range, v_range):
U, V, dU, dV = compute_nullclines(snn, u_range, v_range, 200)
UVs = jnp.stack([Us.reshape(-1), Vs.reshape(-1), jnp.ones((20 * 20,))], axis=1)
dS = snn.neuron_model.vector_field(UVs)
dS = snn.vector_field(UVs)
dUs = dS[:, 0].reshape(Us.shape)
dVs = dS[:, 1].reshape(Vs.shape)
@@ -1844,7 +1840,7 @@ def plot_vf(ax, snn, u_range, v_range):
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
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@@ -1859,29 +1855,27 @@ def plot_vf(ax, snn, u_range, v_range):
</div>
<div class="highlight-ipynb hl-python"><pre><span></span><span class="k">with</span> <span class="n">mpl</span><span class="o">.</span><span class="n">style</span><span class="o">.</span><span class="n">context</span><span class="p">(</span><span class="s2">"boilerplot.ieeetran"</span><span class="p">):</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">6.9</span><span class="p">,</span> <span class="mf">2.6</span><span class="p">),</span> <span class="n">dpi</span><span class="o">=</span><span class="mi">200</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">comp_times</span><span class="p">,</span> <span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"x1"</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">comp_times</span><span class="p">,</span> <span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"x2"</span><span class="p">)</span>
<span class="p">[</span><span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">axvline</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"g"</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s2">"--"</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">jnp</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">spikes</span><span class="p">)]</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">legend</span><span class="p">([</span><span class="s2">"x1"</span><span class="p">,</span> <span class="s2">"x2"</span><span class="p">,</span> <span class="s2">"Spike"</span><span class="p">])</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">comp_times</span><span class="p">,</span> <span class="n">state</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"x1"</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">comp_times</span><span class="p">,</span> <span class="n">state</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"x2"</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">legend</span><span class="p">([</span><span class="s2">"x1"</span><span class="p">,</span> <span class="s2">"x2"</span><span class="p">])</span>
<span class="n">plot_vf</span><span class="p">(</span><span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">snn</span><span class="p">,</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">])</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:,</span> <span class="mi">1</span><span class="p">])</span>
<span class="n">plot_vf</span><span class="p">(</span><span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">model</span><span class="p">,</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">])</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">state</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">state</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"."</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"start"</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">state</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"."</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"end"</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">state</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">state</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"."</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"end"</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
<div class="clipboard-copy-txt" id="cell-5">with mpl.style.context("boilerplot.ieeetran"):
fig, ax = plt.subplots(1, 2, figsize=(6.9, 2.6), dpi=200)
ax[0].plot(comp_times, state[0, :, 0], label="x1")
ax[0].plot(comp_times, state[0, :, 1], label="x2")
[ax[0].axvline(s, alpha=0.2, color="g", linestyle="--") for s in jnp.unique(spikes)]
ax[0].legend(["x1", "x2", "Spike"])
ax[0].plot(comp_times, state[:, 0, 0], label="x1")
ax[0].plot(comp_times, state[:, 0, 1], label="x2")
ax[0].legend(["x1", "x2"])
plot_vf(ax[1], snn, [-0.2, 0.5], [-0.2, 0.5])
ax[1].plot(state[0, :, 0], state[0, :, 1])
plot_vf(ax[1], model, [-0.2, 0.5], [-0.2, 0.5])
ax[1].plot(state[:, 0, 0], state[:, 0, 1])
ax[1].plot(state[0, 0, 0], state[0, 0, 1], ".", label="start")
ax[1].plot(state[0, -1, 0], state[0, -1, 1], ".", label="end")
ax[1].plot(state[-1, 0, 0], state[-1, 0, 1], ".", label="end")
ax[1].legend()
plt.show()</div>
</div>
@@ -1895,80 +1889,7 @@ def plot_vf(ax, snn, u_range, v_range):
<div class="jp-OutputArea-child">
<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
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<div class="highlight-ipynb hl-python"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">equinox</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">eqx</span>
<span class="k">def</span><span class="w"> </span><span class="nf">loss_fn</span><span class="p">(</span><span class="n">model</span><span class="p">,</span> <span class="n">spike_times</span><span class="p">,</span> <span class="n">comp_times</span><span class="p">):</span>
<span class="n">out_states</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">state_at_t</span><span class="p">(</span><span class="n">spike_times</span><span class="p">,</span> <span class="n">comp_times</span><span class="p">)</span>
<span class="n">logits</span> <span class="o">=</span> <span class="n">out_states</span><span class="p">[:,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">]</span>
<span class="k">return</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">logits</span><span class="p">)</span>
<span class="n">in_spikes</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span><span class="p">([[</span><span class="mf">0.01</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.157</span><span class="p">]])</span>
<span class="n">comp_times</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">max_time</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="n">loss</span><span class="p">,</span> <span class="n">gradients</span> <span class="o">=</span> <span class="n">eqx</span><span class="o">.</span><span class="n">filter_value_and_grad</span><span class="p">(</span><span class="n">loss_fn</span><span class="p">)(</span><span class="n">snn</span><span class="p">,</span> <span class="n">in_spikes</span><span class="p">,</span> <span class="n">comp_times</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Loss "</span><span class="p">,</span> <span class="n">loss</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Gradients "</span><span class="p">,</span> <span class="n">gradients</span><span class="o">.</span><span class="n">neuron_model</span><span class="o">.</span><span class="n">weight_u</span><span class="p">)</span>
</pre></div>
<div class="clipboard-copy-txt" id="cell-6">import equinox as eqx
def loss_fn(model, spike_times, comp_times):
out_states = model.state_at_t(spike_times, comp_times)
logits = out_states[:, :, 0]
return jnp.sum(logits)
in_spikes = jnp.asarray([[0.01], [0.157]])
comp_times = jnp.linspace(0.0, max_time, 10)
loss, gradients = eqx.filter_value_and_grad(loss_fn)(snn, in_spikes, comp_times)
print("Loss ", loss)
print("Gradients ", gradients.neuron_model.weight_u)</div>
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<pre>Loss 2.78585239490824
Gradients [[ 0. ]
[-1.81404788]
[-1.42144198]]
</pre>
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