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@@ -997,7 +997,7 @@
<section class="print-page" id="index" heading-number="1"><h1 id="index-felice">Felice</h1>
<p>This project provides a <a href="https://github.com/google/jax">JAX</a> implementation of the different neuron models in felice</p>
<h2 id="index-overview">Overview</h2>
<p>The framework is built on top of <a href="#.">EventPropJax</a> and leverages JAX's automatic differentiation for efficient simulation and training of SNNs using event-based exact gradients.</p>
<p>The framework is built on top of diffrax and leverages JAX's automatic differentiation for efficient simulation and training of analogue models.</p>
<h3 id="index-key-features">Key Features</h3>
<ul>
<li><strong>Delay learning</strong></li>
@@ -1016,37 +1016,6 @@
<p>For GPU acceleration with CUDA 13:</p>
<div class="language-bash highlight"><pre><span></span><code><span id="__span-1-1"><a id="__codelineno-1-1" name="__codelineno-1-1" href="#index-__codelineno-1-1"></a>uv<span class="w"> </span>sync<span class="w"> </span>--extra<span class="w"> </span>cuda
</span></code></pre></div>
<h2 id="index-quick-start">Quick Start</h2>
<p>Here's a simple example using the WereRabbit neuron model:</p>
<div class="language-py highlight"><pre><span></span><code><span id="__span-2-1"><a id="__codelineno-2-1" name="__codelineno-2-1" href="#index-__codelineno-2-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">diffrax</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">dfx</span>
</span><span id="__span-2-2"><a id="__codelineno-2-2" name="__codelineno-2-2" href="#index-__codelineno-2-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
</span><span id="__span-2-3"><a id="__codelineno-2-3" name="__codelineno-2-3" href="#index-__codelineno-2-3"></a><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><span id="__span-2-4"><a id="__codelineno-2-4" name="__codelineno-2-4" href="#index-__codelineno-2-4"></a><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><span id="__span-2-5"><a id="__codelineno-2-5" name="__codelineno-2-5" href="#index-__codelineno-2-5"></a><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>
</span><span id="__span-2-6"><a id="__codelineno-2-6" name="__codelineno-2-6" href="#index-__codelineno-2-6"></a>
</span><span id="__span-2-7"><a id="__codelineno-2-7" name="__codelineno-2-7" href="#index-__codelineno-2-7"></a><span class="c1"># Initialize random key and parameters</span>
</span><span id="__span-2-8"><a id="__codelineno-2-8" name="__codelineno-2-8" href="#index-__codelineno-2-8"></a><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><span id="__span-2-9"><a id="__codelineno-2-9" name="__codelineno-2-9" href="#index-__codelineno-2-9"></a><span class="n">max_time</span> <span class="o">=</span> <span class="mf">300e-3</span>
</span><span id="__span-2-10"><a id="__codelineno-2-10" name="__codelineno-2-10" href="#index-__codelineno-2-10"></a>
</span><span id="__span-2-11"><a id="__codelineno-2-11" name="__codelineno-2-11" href="#index-__codelineno-2-11"></a><span class="c1"># Create a feedforward event-driven neural network</span>
</span><span id="__span-2-12"><a id="__codelineno-2-12" name="__codelineno-2-12" href="#index-__codelineno-2-12"></a><span class="n">snn</span> <span class="o">=</span> <span class="n">FFEvNN</span><span class="p">(</span>
</span><span id="__span-2-13"><a id="__codelineno-2-13" name="__codelineno-2-13" href="#index-__codelineno-2-13"></a> <span class="n">layers</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
</span><span id="__span-2-14"><a id="__codelineno-2-14" name="__codelineno-2-14" href="#index-__codelineno-2-14"></a> <span class="n">in_size</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
</span><span id="__span-2-15"><a id="__codelineno-2-15" name="__codelineno-2-15" href="#index-__codelineno-2-15"></a> <span class="n">neuron_model</span><span class="o">=</span><span class="n">WereRabbit</span><span class="p">,</span>
</span><span id="__span-2-16"><a id="__codelineno-2-16" name="__codelineno-2-16" href="#index-__codelineno-2-16"></a> <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><span id="__span-2-17"><a id="__codelineno-2-17" name="__codelineno-2-17" href="#index-__codelineno-2-17"></a> <span class="n">max_solver_time</span><span class="o">=</span><span class="n">max_time</span><span class="p">,</span>
</span><span id="__span-2-18"><a id="__codelineno-2-18" name="__codelineno-2-18" href="#index-__codelineno-2-18"></a> <span class="n">key</span><span class="o">=</span><span class="n">key</span><span class="p">,</span>
</span><span id="__span-2-19"><a id="__codelineno-2-19" name="__codelineno-2-19" href="#index-__codelineno-2-19"></a> <span class="n">max_event_steps</span><span class="o">=</span><span class="mi">1000000</span><span class="p">,</span>
</span><span id="__span-2-20"><a id="__codelineno-2-20" name="__codelineno-2-20" href="#index-__codelineno-2-20"></a> <span class="n">solver_stepsize</span><span class="o">=</span><span class="mf">1e-6</span><span class="p">,</span>
</span><span id="__span-2-21"><a id="__codelineno-2-21" name="__codelineno-2-21" href="#index-__codelineno-2-21"></a> <span class="n">rtol</span><span class="o">=</span><span class="mf">10.0</span><span class="p">,</span>
</span><span id="__span-2-22"><a id="__codelineno-2-22" name="__codelineno-2-22" href="#index-__codelineno-2-22"></a> <span class="n">atol</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span>
</span><span id="__span-2-23"><a id="__codelineno-2-23" name="__codelineno-2-23" href="#index-__codelineno-2-23"></a> <span class="n">Ibias</span><span class="o">=</span><span class="mf">30e-12</span><span class="p">,</span>
</span><span id="__span-2-24"><a id="__codelineno-2-24" name="__codelineno-2-24" href="#index-__codelineno-2-24"></a><span class="p">)</span>
</span><span id="__span-2-25"><a id="__codelineno-2-25" name="__codelineno-2-25" href="#index-__codelineno-2-25"></a>
</span><span id="__span-2-26"><a id="__codelineno-2-26" name="__codelineno-2-26" href="#index-__codelineno-2-26"></a><span class="c1"># Simulate with input spikes</span>
</span><span id="__span-2-27"><a id="__codelineno-2-27" name="__codelineno-2-27" href="#index-__codelineno-2-27"></a><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">0.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.157</span><span class="p">]])</span>
</span><span id="__span-2-28"><a id="__codelineno-2-28" name="__codelineno-2-28" href="#index-__codelineno-2-28"></a><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>
</span></code></pre></div>
<p>See the <a href="#scripts-examples-neuron_models">examples</a> directory for more detailed usage examples.</p></section>
<section class='print-page md-section' id='section-2' heading-number='2'>
<h1>Neuron Models<a class='headerlink' href='#section-2' title='Permanent link'></a>
@@ -1078,6 +1047,11 @@
<td>Exponential Integrate-and-Fire neuron model</td>
<td>...</td>
</tr>
<tr>
<td><a href="#neuron_models-lif">LIF</a></td>
<td>Leaky Integrate-and-Fire neuron model</td>
<td>...</td>
</tr>
</tbody>
</table></section>
<section class='print-page md-section' id='section-2-2' heading-number='2.2'>
@@ -1941,7 +1915,7 @@ 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">
@@ -1960,7 +1934,6 @@ 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>
@@ -1972,7 +1945,6 @@ 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
@@ -1988,7 +1960,7 @@ 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">
@@ -2002,44 +1974,46 @@ 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>
@@ -2051,7 +2025,7 @@ 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">
@@ -2064,15 +2038,11 @@ 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>
@@ -2084,7 +2054,7 @@ spikes = snn.spikes_until_t(in_spikes, max_time)</div>
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
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@@ -2110,7 +2080,7 @@ 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>
@@ -2128,7 +2098,7 @@ 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>
@@ -2167,7 +2137,7 @@ 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)
@@ -2185,7 +2155,7 @@ 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)
@@ -2221,7 +2191,7 @@ def plot_vf(ax, snn, u_range, v_range):
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
</div>
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@@ -2236,29 +2206,27 @@ 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>
@@ -2272,80 +2240,7 @@ 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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src="data:image/png;base64,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@@ -2360,7 +2255,7 @@ Gradients [[ 0. ]
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@@ -2372,7 +2267,7 @@ Gradients [[ 0. ]
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<div class="highlight-ipynb hl-python"><pre><span></span>
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@@ -3133,7 +3028,7 @@ span.linenos.special { color: #000000; background-color: #ffffc0; padding-left:
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@@ -3152,9 +3047,8 @@ 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
@@ -3162,9 +3056,8 @@ 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>
@@ -3176,7 +3069,7 @@ from felice.neuron_models import FHN</div>
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@@ -3192,32 +3085,64 @@ 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>
@@ -3229,7 +3154,7 @@ snn = FFEvNN(
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@@ -3243,9 +3168,9 @@ snn = FFEvNN(
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<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>
@@ -3255,9 +3180,9 @@ 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)
@@ -3276,7 +3201,7 @@ 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">
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truncated
<img alt="No description has been provided for this image" class="" 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@@ -3288,7 +3213,7 @@ 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">
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@@ -3301,27 +3226,23 @@ 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>
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<div class="jp-InputPrompt jp-InputArea-prompt">In [5]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="jp-InputPrompt jp-InputArea-prompt">In [26]:</div><div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
<div class="CodeMirror cm-s-jupyter">
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@@ -3334,16 +3255,152 @@ spikes = snn.spikes_until_t(in_spikes, max_time)</div>
</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>
@@ -3351,16 +3408,17 @@ 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")
@@ -3378,7 +3436,7 @@ 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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@@ -3393,7 +3451,7 @@ spikes = snn.spikes_until_t(in_spikes, max_time)</div>
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@@ -3405,7 +3463,34 @@ spikes = snn.spikes_until_t(in_spikes, max_time)</div>
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<div class="highlight-ipynb hl-python"><pre><span></span>
</pre></div>
<div class="clipboard-copy-txt" id="cell-8"></div>
</div>
</div>
</div>