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<h1>mlx.optimizers.AdaDelta<a class="headerlink" href="#mlx-optimizers-adadelta" title="Permalink to this heading">#</a></h1>
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<dl class="py class">
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<dt class="sig sig-object py" id="mlx.optimizers.AdaDelta">
|
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<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mlx.optimizers.</span></span><span class="sig-name descname"><span class="pre">AdaDelta</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">learning_rate</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">rho</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.9</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-06</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.AdaDelta" title="Permalink to this definition">#</a></dt>
|
||||
<dd><p>The AdaDelta optimizer with a learning rate [1].</p>
|
||||
<p>Our AdaDelta implementation follows the original paper. In detail,</p>
|
||||
<p>[1]: Zeiler, M.D., 2012. ADADELTA: an adaptive learning rate method. arXiv preprint arXiv:1212.5701.</p>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[\begin{split}v_{t+1} &= \rho v_t + (1 - \rho) g_t^2 \\
|
||||
\Delta w_{t+1} &= \frac{\sqrt{u_t + \epsilon}}{\sqrt{v_{t+1} + \epsilon}} g_t \\
|
||||
u_{t+1} &= \rho u_t + (1 - \rho) \Delta w_{t+1}^2 \\
|
||||
w_{t+1} &= w_t - \lambda \Delta w_{t+1}\end{split}\]</div>
|
||||
<dl class="field-list simple">
|
||||
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
|
||||
<dd class="field-odd"><ul class="simple">
|
||||
<li><p><strong>learning_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a>) – The learning rate <span class="math notranslate nohighlight">\(\lambda\)</span>.</p></li>
|
||||
<li><p><strong>rho</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><em>optional</em>) – The coefficient <span class="math notranslate nohighlight">\(\rho\)</span> used for computing a
|
||||
running average of squared gradients. Default: <code class="docutils literal notranslate"><span class="pre">0.9</span></code></p></li>
|
||||
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><em>optional</em>) – The term <span class="math notranslate nohighlight">\(\epsilon\)</span> added to the denominator to improve
|
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numerical stability. Default: <cite>1e-8</cite></p></li>
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</ul>
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</dd>
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</dl>
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<p class="rubric">Methods</p>
|
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<table class="autosummary longtable table autosummary">
|
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<tbody>
|
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<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(learning_rate[, rho, eps])</p></td>
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<td><p></p></td>
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</tr>
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<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply_single</span></code>(gradient, parameter, state)</p></td>
|
||||
<td><p>Performs the AdaDelta parameter update and stores <span class="math notranslate nohighlight">\(v\)</span> and <span class="math notranslate nohighlight">\(u\)</span> in the optimizer state.</p></td>
|
||||
</tr>
|
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<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">init_single</span></code>(parameter, state)</p></td>
|
||||
<td><p>Initialize optimizer state</p></td>
|
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</dd></dl>
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<h1>mlx.optimizers.Adagrad</h1>
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<section id="mlx-optimizers-adagrad">
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<h1>mlx.optimizers.Adagrad<a class="headerlink" href="#mlx-optimizers-adagrad" title="Permalink to this heading">#</a></h1>
|
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<dl class="py class">
|
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<dt class="sig sig-object py" id="mlx.optimizers.Adagrad">
|
||||
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mlx.optimizers.</span></span><span class="sig-name descname"><span class="pre">Adagrad</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">learning_rate</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-08</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.Adagrad" title="Permalink to this definition">#</a></dt>
|
||||
<dd><p>The Adagrad optimizer [1].</p>
|
||||
<p>Our Adagrad implementation follows the original paper. In detail,</p>
|
||||
<p>[1]: Duchi, J., Hazan, E. and Singer, Y., 2011. Adaptive subgradient methods
|
||||
for online learning and stochastic optimization. JMLR 2011.</p>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[\begin{split}v_{t+1} &= v_t + g_t^2 \\
|
||||
w_{t+1} &= w_t - \lambda \frac{g_t}{\sqrt{v_{t+1}} + \epsilon}\end{split}\]</div>
|
||||
<dl class="field-list simple">
|
||||
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
|
||||
<dd class="field-odd"><ul class="simple">
|
||||
<li><p><strong>learning_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a>) – The learning rate <span class="math notranslate nohighlight">\(\lambda\)</span>.</p></li>
|
||||
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><em>optional</em>) – The term <span class="math notranslate nohighlight">\(\epsilon\)</span> added to the
|
||||
denominator to improve numerical stability. Default: <code class="docutils literal notranslate"><span class="pre">1e-8</span></code></p></li>
|
||||
</ul>
|
||||
</dd>
|
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</dl>
|
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<p class="rubric">Methods</p>
|
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<table class="autosummary longtable table autosummary">
|
||||
<tbody>
|
||||
<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(learning_rate[, eps])</p></td>
|
||||
<td><p></p></td>
|
||||
</tr>
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<h1>mlx.optimizers.Adam<a class="headerlink" href="#mlx-optimizers-adam" title="Permalink to this heading">#</a></h1>
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<dl class="py class">
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<dt class="sig sig-object py" id="mlx.optimizers.Adam">
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||||
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mlx.optimizers.</span></span><span class="sig-name descname"><span class="pre">Adam</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">learning_rate</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">betas</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.List" title="(in Python v3.12)"><span class="pre">List</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">[0.9,</span> <span class="pre">0.999]</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-08</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.Adam" title="Permalink to this definition">#</a></dt>
|
||||
<dd><p>The Adam optimizer [1].</p>
|
||||
<p>Our Adam implementation follows the original paper and omits the bias
|
||||
correction in the first and second moment estimates. In detail,</p>
|
||||
<p>[1]: Kingma, D.P. and Ba, J., 2015. Adam: A method for stochastic
|
||||
optimization. ICLR 2015.</p>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[\begin{split}m_{t+1} &= \beta_1 m_t + (1 - \beta_1) g_t \\
|
||||
v_{t+1} &= \beta_2 v_t + (1 - \beta_2) g_t^2 \\
|
||||
w_{t+1} &= w_t - \lambda \frac{m_{t+1}}{\sqrt{v_{t+1} + \epsilon}}\end{split}\]</div>
|
||||
<dl class="field-list simple">
|
||||
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
|
||||
<dd class="field-odd"><ul class="simple">
|
||||
<li><p><strong>learning_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a>) – The learning rate <span class="math notranslate nohighlight">\(\lambda\)</span>.</p></li>
|
||||
<li><p><strong>betas</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>]</em><em>, </em><em>optional</em>) – The coefficients
|
||||
<span class="math notranslate nohighlight">\((\beta_1, \beta_2)\)</span> used for computing running averages of the
|
||||
gradient and its square. Default: <code class="docutils literal notranslate"><span class="pre">(0.9,</span> <span class="pre">0.999)</span></code></p></li>
|
||||
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><em>optional</em>) – The term <span class="math notranslate nohighlight">\(\epsilon\)</span> added to the
|
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denominator to improve numerical stability. Default: <code class="docutils literal notranslate"><span class="pre">1e-8</span></code></p></li>
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</dd>
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</dl>
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<p class="rubric">Methods</p>
|
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<table class="autosummary longtable table autosummary">
|
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<tbody>
|
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<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(learning_rate[, betas, eps])</p></td>
|
||||
<td><p></p></td>
|
||||
</tr>
|
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<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply_single</span></code>(gradient, parameter, state)</p></td>
|
||||
<td><p>Performs the Adam parameter update and stores <span class="math notranslate nohighlight">\(v\)</span> and <span class="math notranslate nohighlight">\(m\)</span> in the optimizer state.</p></td>
|
||||
</tr>
|
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<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">init_single</span></code>(parameter, state)</p></td>
|
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<td><p>Initialize optimizer state</p></td>
|
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<section id="mlx-optimizers-adamw">
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<h1>mlx.optimizers.AdamW<a class="headerlink" href="#mlx-optimizers-adamw" title="Permalink to this heading">#</a></h1>
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<dl class="py class">
|
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<dt class="sig sig-object py" id="mlx.optimizers.AdamW">
|
||||
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mlx.optimizers.</span></span><span class="sig-name descname"><span class="pre">AdamW</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">learning_rate</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">betas</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.List" title="(in Python v3.12)"><span class="pre">List</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">[0.9,</span> <span class="pre">0.999]</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-08</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weight_decay</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.01</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.AdamW" title="Permalink to this definition">#</a></dt>
|
||||
<dd><p>The AdamW optimizer [1].</p>
|
||||
<p>Following the above convention, in contrast with [1], we do not use bias
|
||||
correction in the first and second moments for AdamW. We update the weights
|
||||
with a weight_decay (<span class="math notranslate nohighlight">\(\lambda\)</span>) value:</p>
|
||||
<p>[1]: Loshchilov, I. and Hutter, F., 2019. Decoupled weight decay
|
||||
regularization. ICLR 2019.</p>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[\begin{split}m_{t+1} &= \beta_1 m_t + (1 - \beta_1) g_t \\
|
||||
v_{t+1} &= \beta_2 v_t + (1 - \beta_2) g_t^2 \\
|
||||
w_{t+1} &= w_t - \alpha (\frac{m_{t+1}}{\sqrt{v_{t+1} + \epsilon}} + \lambda w_t)\end{split}\]</div>
|
||||
<dl class="field-list simple">
|
||||
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
|
||||
<dd class="field-odd"><ul class="simple">
|
||||
<li><p><strong>learning_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a>) – The learning rate <span class="math notranslate nohighlight">\(\alpha\)</span>.</p></li>
|
||||
<li><p><strong>betas</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>]</em><em>, </em><em>optional</em>) – The coefficients
|
||||
<span class="math notranslate nohighlight">\((\beta_1, \beta_2)\)</span> used for computing running averages of the
|
||||
gradient and its square. Default: <code class="docutils literal notranslate"><span class="pre">(0.9,</span> <span class="pre">0.999)</span></code></p></li>
|
||||
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><em>optional</em>) – The term <span class="math notranslate nohighlight">\(\epsilon\)</span> added to the
|
||||
denominator to improve numerical stability. Default: <code class="docutils literal notranslate"><span class="pre">1e-8</span></code></p></li>
|
||||
<li><p><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><em>optional</em>) – The weight decay <span class="math notranslate nohighlight">\(\lambda\)</span>.
|
||||
Default: <code class="docutils literal notranslate"><span class="pre">0</span></code>.</p></li>
|
||||
</ul>
|
||||
</dd>
|
||||
</dl>
|
||||
<p class="rubric">Methods</p>
|
||||
<table class="autosummary longtable table autosummary">
|
||||
<tbody>
|
||||
<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(learning_rate[, betas, eps, ...])</p></td>
|
||||
<td><p></p></td>
|
||||
</tr>
|
||||
<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply_single</span></code>(gradient, parameter, state)</p></td>
|
||||
<td><p>Performs the AdamW parameter update by modifying the parameters passed into Adam.</p></td>
|
||||
</tr>
|
||||
</tbody>
|
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</table>
|
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</dd></dl>
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<h1>mlx.optimizers.Adamax</h1>
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<section id="mlx-optimizers-adamax">
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<h1>mlx.optimizers.Adamax<a class="headerlink" href="#mlx-optimizers-adamax" title="Permalink to this heading">#</a></h1>
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<dl class="py class">
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<dt class="sig sig-object py" id="mlx.optimizers.Adamax">
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<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mlx.optimizers.</span></span><span class="sig-name descname"><span class="pre">Adamax</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">learning_rate</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">betas</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.List" title="(in Python v3.12)"><span class="pre">List</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">[0.9,</span> <span class="pre">0.999]</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-08</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.Adamax" title="Permalink to this definition">#</a></dt>
|
||||
<dd><p>The Adamax optimizer, a variant of Adam based on the infinity norm [1].</p>
|
||||
<p>Our Adam implementation follows the original paper and omits the bias
|
||||
correction in the first and second moment estimates. In detail,</p>
|
||||
<p>[1]: Kingma, D.P. and Ba, J., 2015. Adam: A method for stochastic
|
||||
optimization. ICLR 2015.</p>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[\begin{split}m_{t+1} &= \beta_1 m_t + (1 - \beta_1) g_t \\
|
||||
v_{t+1} &= \max(\beta_2 v_t, |g_t|) \\
|
||||
w_{t+1} &= w_t - \lambda \frac{m_{t+1}}{v_{t+1} + \epsilon}\end{split}\]</div>
|
||||
<dl class="field-list simple">
|
||||
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
|
||||
<dd class="field-odd"><ul class="simple">
|
||||
<li><p><strong>learning_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a>) – The learning rate <span class="math notranslate nohighlight">\(\lambda\)</span>.</p></li>
|
||||
<li><p><strong>betas</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>]</em><em>, </em><em>optional</em>) – The coefficients
|
||||
<span class="math notranslate nohighlight">\((\beta_1, \beta_2)\)</span> used for computing running averages of the
|
||||
gradient and its square. Default: <code class="docutils literal notranslate"><span class="pre">(0.9,</span> <span class="pre">0.999)</span></code></p></li>
|
||||
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><em>optional</em>) – The term <span class="math notranslate nohighlight">\(\epsilon\)</span> added to the
|
||||
denominator to improve numerical stability. Default: <code class="docutils literal notranslate"><span class="pre">1e-8</span></code></p></li>
|
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</ul>
|
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</dd>
|
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</dl>
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<p class="rubric">Methods</p>
|
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<table class="autosummary longtable table autosummary">
|
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<tbody>
|
||||
<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(learning_rate[, betas, eps])</p></td>
|
||||
<td><p></p></td>
|
||||
</tr>
|
||||
<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply_single</span></code>(gradient, parameter, state)</p></td>
|
||||
<td><p>Performs the Adamax parameter update and stores <span class="math notranslate nohighlight">\(v\)</span> and <span class="math notranslate nohighlight">\(m\)</span> in the optimizer state.</p></td>
|
||||
</tr>
|
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<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">init_single</span></code>(parameter, state)</p></td>
|
||||
<td><p>Initialize optimizer state</p></td>
|
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</tr>
|
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</tbody>
|
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</table>
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</dd></dl>
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<h1>mlx.optimizers.Lion</h1>
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<section id="mlx-optimizers-lion">
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<h1>mlx.optimizers.Lion<a class="headerlink" href="#mlx-optimizers-lion" title="Permalink to this heading">#</a></h1>
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<dl class="py class">
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<dt class="sig sig-object py" id="mlx.optimizers.Lion">
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<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mlx.optimizers.</span></span><span class="sig-name descname"><span class="pre">Lion</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">learning_rate</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">betas</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.List" title="(in Python v3.12)"><span class="pre">List</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">[0.9,</span> <span class="pre">0.99]</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weight_decay</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.0</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.Lion" title="Permalink to this definition">#</a></dt>
|
||||
<dd><p>The Lion optimizer [1].</p>
|
||||
<p>Since updates are computed through the sign operation, they tend to
|
||||
have larger norm than for other optimizers such as SGD and Adam.
|
||||
We recommend a learning rate that is 3-10x smaller than AdamW and a
|
||||
weight decay 3-10x larger than AdamW to maintain the strength
|
||||
(lr * wd). Our Lion implementation follows the original paper. In
|
||||
detail,</p>
|
||||
<p>[1]: Chen, X. Symbolic Discovery of Optimization Algorithms. arXiv
|
||||
preprint arXiv:2302.06675.</p>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[\begin{split}c_{t + 1} &= \beta_1 m_t + (1 - \beta_1) g_t \\
|
||||
m_{t + 1} &= \beta_2 m_t + (1 - \beta_2) g_t \\
|
||||
w_{t + 1} &= w_t - \eta (\text{sign}(c_t) + \lambda w_t)\end{split}\]</div>
|
||||
<dl class="field-list simple">
|
||||
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
|
||||
<dd class="field-odd"><ul class="simple">
|
||||
<li><p><strong>learning_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a>) – The learning rate <span class="math notranslate nohighlight">\(\eta\)</span>.</p></li>
|
||||
<li><p><strong>betas</strong> (<em>Tuple</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>]</em><em>, </em><em>optional</em>) – The coefficients
|
||||
<span class="math notranslate nohighlight">\((\beta_1, \beta_2)\)</span> used for computing the gradient
|
||||
momentum and update direction. Default: <code class="docutils literal notranslate"><span class="pre">(0.9,</span> <span class="pre">0.99)</span></code></p></li>
|
||||
<li><p><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><em>optional</em>) – The weight decay <span class="math notranslate nohighlight">\(\lambda\)</span>. Default: <code class="docutils literal notranslate"><span class="pre">0.0</span></code></p></li>
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</ul>
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</dd>
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</dl>
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<p class="rubric">Methods</p>
|
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<table class="autosummary longtable table autosummary">
|
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<tbody>
|
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<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(learning_rate[, betas, weight_decay])</p></td>
|
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<td><p></p></td>
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</tr>
|
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<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply_single</span></code>(gradient, parameter, state)</p></td>
|
||||
<td><p>Performs the Lion parameter update and stores <span class="math notranslate nohighlight">\(m\)</span> in the optimizer state.</p></td>
|
||||
</tr>
|
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<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">init_single</span></code>(parameter, state)</p></td>
|
||||
<td><p>Initialize optimizer state</p></td>
|
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</tr>
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</tbody>
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</dd></dl>
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<h1>mlx.optimizers.Optimizer.apply_gradients<a class="headerlink" href="#mlx-optimizers-optimizer-apply-gradients" title="Permalink to this heading">#</a></h1>
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<dl class="py method">
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<dt class="sig sig-object py" id="mlx.optimizers.Optimizer.apply_gradients">
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<span class="sig-prename descclassname"><span class="pre">Optimizer.</span></span><span class="sig-name descname"><span class="pre">apply_gradients</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">gradients</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.12)"><span class="pre">dict</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">parameters</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.12)"><span class="pre">dict</span></a></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.Optimizer.apply_gradients" title="Permalink to this definition">#</a></dt>
|
||||
<dd><p>Apply the gradients to the parameters and return the updated parameters.</p>
|
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<p>Can be used to update a model via
|
||||
<code class="docutils literal notranslate"><span class="pre">model.update(opt.apply_gradients(grads,</span> <span class="pre">model))</span></code> which is precisely
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how <a class="reference internal" href="mlx.optimizers.Optimizer.update.html#mlx.optimizers.Optimizer.update" title="mlx.optimizers.Optimizer.update"><code class="xref py py-meth docutils literal notranslate"><span class="pre">Optimizer.update()</span></code></a> is implemented.</p>
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<h1>mlx.optimizers.Optimizer.init<a class="headerlink" href="#mlx-optimizers-optimizer-init" title="Permalink to this heading">#</a></h1>
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<dl class="py method">
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<dt class="sig sig-object py" id="mlx.optimizers.Optimizer.init">
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<span class="sig-prename descclassname"><span class="pre">Optimizer.</span></span><span class="sig-name descname"><span class="pre">init</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">parameters</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.12)"><span class="pre">dict</span></a></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.Optimizer.init" title="Permalink to this definition">#</a></dt>
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<dd><p>Initialize the optimizer’s state</p>
|
||||
<p>This function can be used to initialize optimizers which have state
|
||||
(like momentum in <a class="reference internal" href="mlx.optimizers.SGD.html#mlx.optimizers.SGD" title="mlx.optimizers.SGD"><code class="xref py py-class docutils literal notranslate"><span class="pre">SGD</span></code></a>). Using this method is optional as the
|
||||
optimizer will initialize itself if the state is not yet set. However,
|
||||
there are some cases where explicit initialization is useful in order
|
||||
to have access to the <a class="reference internal" href="mlx.optimizers.Optimizer.state.html#mlx.optimizers.Optimizer.state" title="mlx.optimizers.Optimizer.state"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Optimizer.state</span></code></a> before the first call to
|
||||
<a class="reference internal" href="mlx.optimizers.Optimizer.update.html#mlx.optimizers.Optimizer.update" title="mlx.optimizers.Optimizer.update"><code class="xref py py-meth docutils literal notranslate"><span class="pre">Optimizer.update()</span></code></a>.</p>
|
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<dl class="field-list simple">
|
||||
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
|
||||
<dd class="field-odd"><p><strong>model</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.12)"><em>dict</em></a>) – A Python tree of parameters.</p>
|
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<p class="rubric">Example</p>
|
||||
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">optimizer</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">learning_rate</span><span class="o">=</span><span class="mf">1e-1</span><span class="p">,</span> <span class="n">momentum</span><span class="o">=</span><span class="mf">0.9</span><span class="p">)</span>
|
||||
<span class="gp">>>> </span><span class="n">model</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
|
||||
<span class="gp">>>> </span><span class="n">optimizer</span><span class="o">.</span><span class="n">init</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">trainable_parameters</span><span class="p">())</span>
|
||||
<span class="gp">>>> </span><span class="n">optimizer</span><span class="o">.</span><span class="n">state</span><span class="o">.</span><span class="n">keys</span><span class="p">()</span>
|
||||
<span class="go">dict_keys(['step', 'learning_rate', 'weight', 'bias'])</span>
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<h1>mlx.optimizers.Optimizer.state<a class="headerlink" href="#mlx-optimizers-optimizer-state" title="Permalink to this heading">#</a></h1>
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<dl class="py property">
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<dt class="sig sig-object py" id="mlx.optimizers.Optimizer.state">
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<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">Optimizer.</span></span><span class="sig-name descname"><span class="pre">state</span></span><a class="headerlink" href="#mlx.optimizers.Optimizer.state" title="Permalink to this definition">#</a></dt>
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<dd><p>The optimizer’s state dictionary.</p>
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<h1>mlx.optimizers.Optimizer.update<a class="headerlink" href="#mlx-optimizers-optimizer-update" title="Permalink to this heading">#</a></h1>
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<dt class="sig sig-object py" id="mlx.optimizers.Optimizer.update">
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<span class="sig-prename descclassname"><span class="pre">Optimizer.</span></span><span class="sig-name descname"><span class="pre">update</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">model</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="../../nn/module.html#mlx.nn.Module" title="mlx.nn.Module"><span class="pre">Module</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">gradients</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.12)"><span class="pre">dict</span></a></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.Optimizer.update" title="Permalink to this definition">#</a></dt>
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<li><p><strong>model</strong> (<a class="reference internal" href="../../nn/module.html#mlx.nn.Module" title="mlx.nn.Module"><em>Module</em></a>) – An mlx module to be updated.</p></li>
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<li><p><strong>gradients</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.12)"><em>dict</em></a>) – A Python tree of gradients, most likely computed
|
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<h1>mlx.optimizers.RMSprop</h1>
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<section id="mlx-optimizers-rmsprop">
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<h1>mlx.optimizers.RMSprop<a class="headerlink" href="#mlx-optimizers-rmsprop" title="Permalink to this heading">#</a></h1>
|
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<dl class="py class">
|
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<dt class="sig sig-object py" id="mlx.optimizers.RMSprop">
|
||||
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mlx.optimizers.</span></span><span class="sig-name descname"><span class="pre">RMSprop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">learning_rate</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">alpha</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.99</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">1e-08</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.RMSprop" title="Permalink to this definition">#</a></dt>
|
||||
<dd><p>The RMSprop optimizer [1].</p>
|
||||
<p>[1]: Tieleman, T. and Hinton, G. 2012. Lecture 6.5-rmsprop, coursera: Neural networks for machine learning</p>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[\begin{split}v_{t+1} &= \alpha v_t + (1 - \alpha) g_t^2 \\
|
||||
w_{t+1} &= w_t - \lambda \frac{g_t}{\sqrt{v_{t+1}} + \epsilon}\end{split}\]</div>
|
||||
<dl class="field-list simple">
|
||||
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
|
||||
<dd class="field-odd"><ul class="simple">
|
||||
<li><p><strong>learning_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a>) – The learning rate <span class="math notranslate nohighlight">\(\lambda\)</span>.</p></li>
|
||||
<li><p><strong>alpha</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><em>optional</em>) – The smoothing constant <span class="math notranslate nohighlight">\(\alpha\)</span>.
|
||||
Default: <code class="docutils literal notranslate"><span class="pre">0.99</span></code></p></li>
|
||||
<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><em>optional</em>) – The term <span class="math notranslate nohighlight">\(\epsilon\)</span> added to the denominator
|
||||
to improve numerical stability. Default: <code class="docutils literal notranslate"><span class="pre">1e-8</span></code></p></li>
|
||||
</ul>
|
||||
</dd>
|
||||
</dl>
|
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<p class="rubric">Methods</p>
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<section id="mlx-optimizers-sgd">
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<h1>mlx.optimizers.SGD<a class="headerlink" href="#mlx-optimizers-sgd" title="Permalink to this heading">#</a></h1>
|
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<dl class="py class">
|
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<dt class="sig sig-object py" id="mlx.optimizers.SGD">
|
||||
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mlx.optimizers.</span></span><span class="sig-name descname"><span class="pre">SGD</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">learning_rate</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.12)"><span class="pre">Union</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Callable" title="(in Python v3.12)"><span class="pre">Callable</span></a><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="../../_autosummary/mlx.core.array.html#mlx.core.array" title="mlx.core.array"><span class="pre">array</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference internal" href="../../_autosummary/mlx.core.array.html#mlx.core.array" title="mlx.core.array"><span class="pre">array</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">momentum</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weight_decay</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dampening</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nesterov</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.12)"><span class="pre">bool</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.SGD" title="Permalink to this definition">#</a></dt>
|
||||
<dd><p>The stochastic gradient descent optimizer.</p>
|
||||
<p>Updates a parameter <span class="math notranslate nohighlight">\(w\)</span> with a gradient <span class="math notranslate nohighlight">\(g\)</span> as follows</p>
|
||||
<div class="math notranslate nohighlight">
|
||||
\[\begin{split}v_{t+1} &= \mu v_t + (1 - \tau) g_t \\
|
||||
w_{t+1} &= w_t - \lambda v_{t+1}\end{split}\]</div>
|
||||
<dl class="field-list simple">
|
||||
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
|
||||
<dd class="field-odd"><ul class="simple">
|
||||
<li><p><strong>learning_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em> or </em><em>callable</em>) – The learning rate <span class="math notranslate nohighlight">\(\lambda\)</span>.</p></li>
|
||||
<li><p><strong>momentum</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><em>optional</em>) – The momentum strength <span class="math notranslate nohighlight">\(\mu\)</span>. Default: <code class="docutils literal notranslate"><span class="pre">0</span></code></p></li>
|
||||
<li><p><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><em>optional</em>) – The weight decay (L2 penalty). Default: <code class="docutils literal notranslate"><span class="pre">0</span></code></p></li>
|
||||
<li><p><strong>dampening</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a><em>, </em><em>optional</em>) – Dampening for momentum <span class="math notranslate nohighlight">\(\tau\)</span>. Default: <code class="docutils literal notranslate"><span class="pre">0</span></code></p></li>
|
||||
<li><p><strong>nesterov</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.12)"><em>bool</em></a><em>, </em><em>optional</em>) – Enables Nesterov momentum. Default: <code class="docutils literal notranslate"><span class="pre">False</span></code></p></li>
|
||||
</ul>
|
||||
</dd>
|
||||
</dl>
|
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<p class="rubric">Methods</p>
|
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<table class="autosummary longtable table autosummary">
|
||||
<tbody>
|
||||
<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">__init__</span></code>(learning_rate[, momentum, ...])</p></td>
|
||||
<td><p></p></td>
|
||||
</tr>
|
||||
<tr class="row-even"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply_single</span></code>(gradient, parameter, state)</p></td>
|
||||
<td><p>Performs the SGD parameter update and stores <span class="math notranslate nohighlight">\(v\)</span> in the optimizer state.</p></td>
|
||||
</tr>
|
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<tr class="row-odd"><td><p><code class="xref py py-obj docutils literal notranslate"><span class="pre">init_single</span></code>(parameter, state)</p></td>
|
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<td><p>Initialize optimizer state</p></td>
|
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|
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<h1>mlx.optimizers.cosine_decay<a class="headerlink" href="#mlx-optimizers-cosine-decay" title="Permalink to this heading">#</a></h1>
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<dl class="py function">
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<dt class="sig sig-object py" id="mlx.optimizers.cosine_decay">
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<span class="sig-prename descclassname"><span class="pre">mlx.optimizers.</span></span><span class="sig-name descname"><span class="pre">cosine_decay</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">init</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">decay_steps</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.12)"><span class="pre">int</span></a></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.cosine_decay" title="Permalink to this definition">#</a></dt>
|
||||
<dd><p>Make a cosine decay scheduler.</p>
|
||||
<dl class="field-list simple">
|
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<dt class="field-odd">Parameters<span class="colon">:</span></dt>
|
||||
<dd class="field-odd"><ul class="simple">
|
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<li><p><strong>init</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a>) – Initial value.</p></li>
|
||||
<li><p><strong>decay_steps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.12)"><em>int</em></a>) – Number of steps to decay over. The decayed
|
||||
value is constant for steps beyond <code class="docutils literal notranslate"><span class="pre">decay_steps</span></code>.</p></li>
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<p class="rubric">Example</p>
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<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">lr_schedule</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">cosine_decay</span><span class="p">(</span><span class="mf">1e-1</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
|
||||
<span class="gp">>>> </span><span class="n">optimizer</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">learning_rate</span><span class="o">=</span><span class="n">lr_schedule</span><span class="p">)</span>
|
||||
<span class="gp">>>> </span><span class="n">optimizer</span><span class="o">.</span><span class="n">learning_rate</span>
|
||||
<span class="go">array(0.1, dtype=float32)</span>
|
||||
<span class="go">>>></span>
|
||||
<span class="gp">>>> </span><span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span><span class="p">):</span> <span class="n">optimizer</span><span class="o">.</span><span class="n">update</span><span class="p">({},</span> <span class="p">{})</span>
|
||||
<span class="gp">...</span>
|
||||
<span class="gp">>>> </span><span class="n">optimizer</span><span class="o">.</span><span class="n">learning_rate</span>
|
||||
<span class="go">array(0.0999961, dtype=float32)</span>
|
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</pre></div>
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<section id="mlx-optimizers-exponential-decay">
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<h1>mlx.optimizers.exponential_decay<a class="headerlink" href="#mlx-optimizers-exponential-decay" title="Permalink to this heading">#</a></h1>
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<dl class="py function">
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<dt class="sig sig-object py" id="mlx.optimizers.exponential_decay">
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<span class="sig-prename descclassname"><span class="pre">mlx.optimizers.</span></span><span class="sig-name descname"><span class="pre">exponential_decay</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">init</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">decay_rate</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.exponential_decay" title="Permalink to this definition">#</a></dt>
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<dd><p>Make an exponential decay scheduler.</p>
|
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<dl class="field-list simple">
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<dt class="field-odd">Parameters<span class="colon">:</span></dt>
|
||||
<dd class="field-odd"><ul class="simple">
|
||||
<li><p><strong>init</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a>) – Initial value.</p></li>
|
||||
<li><p><strong>decay_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a>) – Multiplicative factor to decay by.</p></li>
|
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</ul>
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</dd>
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</dl>
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<p class="rubric">Example</p>
|
||||
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">lr_schedule</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">exponential_decay</span><span class="p">(</span><span class="mf">1e-1</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">)</span>
|
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<span class="gp">>>> </span><span class="n">optimizer</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">learning_rate</span><span class="o">=</span><span class="n">lr_schedule</span><span class="p">)</span>
|
||||
<span class="gp">>>> </span><span class="n">optimizer</span><span class="o">.</span><span class="n">learning_rate</span>
|
||||
<span class="go">array(0.1, dtype=float32)</span>
|
||||
<span class="go">>>></span>
|
||||
<span class="gp">>>> </span><span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span><span class="p">):</span> <span class="n">optimizer</span><span class="o">.</span><span class="n">update</span><span class="p">({},</span> <span class="p">{})</span>
|
||||
<span class="gp">...</span>
|
||||
<span class="gp">>>> </span><span class="n">optimizer</span><span class="o">.</span><span class="n">learning_rate</span>
|
||||
<span class="go">array(0.06561, dtype=float32)</span>
|
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</pre></div>
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<h1>mlx.optimizers.step_decay</h1>
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<h1>mlx.optimizers.step_decay<a class="headerlink" href="#mlx-optimizers-step-decay" title="Permalink to this heading">#</a></h1>
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<dl class="py function">
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<dt class="sig sig-object py" id="mlx.optimizers.step_decay">
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<span class="sig-prename descclassname"><span class="pre">mlx.optimizers.</span></span><span class="sig-name descname"><span class="pre">step_decay</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">init</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">decay_rate</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><span class="pre">float</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">step_size</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.12)"><span class="pre">int</span></a></span></em><span class="sig-paren">)</span><a class="headerlink" href="#mlx.optimizers.step_decay" title="Permalink to this definition">#</a></dt>
|
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<dd><p>Make a step decay scheduler.</p>
|
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<dl class="field-list simple">
|
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<dt class="field-odd">Parameters<span class="colon">:</span></dt>
|
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<dd class="field-odd"><ul class="simple">
|
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<li><p><strong>init</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a>) – Initial value.</p></li>
|
||||
<li><p><strong>decay_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><em>float</em></a>) – Multiplicative factor to decay by.</p></li>
|
||||
<li><p><strong>step_size</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.12)"><em>int</em></a>) – Decay every <code class="docutils literal notranslate"><span class="pre">step_size</span></code> steps.</p></li>
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</dd>
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</dl>
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<p class="rubric">Example</p>
|
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<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">lr_schedule</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">step_decay</span><span class="p">(</span><span class="mf">1e-1</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
|
||||
<span class="gp">>>> </span><span class="n">optimizer</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">learning_rate</span><span class="o">=</span><span class="n">lr_schedule</span><span class="p">)</span>
|
||||
<span class="gp">>>> </span><span class="n">optimizer</span><span class="o">.</span><span class="n">learning_rate</span>
|
||||
<span class="go">array(0.1, dtype=float32)</span>
|
||||
<span class="go">>>></span>
|
||||
<span class="gp">>>> </span><span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">21</span><span class="p">):</span> <span class="n">optimizer</span><span class="o">.</span><span class="n">update</span><span class="p">({},</span> <span class="p">{})</span>
|
||||
<span class="gp">...</span>
|
||||
<span class="gp">>>> </span><span class="n">optimizer</span><span class="o">.</span><span class="n">learning_rate</span>
|
||||
<span class="go">array(0.081, dtype=float32)</span>
|
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</pre></div>
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