docs/build/doctrees/python/_autosummary/mlx.optimizers.AdaDelta.doctree

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desc_sig_name<6D><65><EFBFBD>)<29><>}<7D>(h<05>
learning_rate<74>h]<5D>h<16>
learning_rate<74><65><EFBFBD><EFBFBD><EFBFBD>}<7D>(hh<>hhhNhNubah}<7D>(h!]<5D>h#]<5D><>n<>ah%]<5D>h']<5D>h)]<5D>uh+h<>hh<>ubh<00>desc_sig_punctuation<6F><6E><EFBFBD>)<29><>}<7D>(h<05>:<3A>h]<5D>h<16>:<3A><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hh<>hhhNhNubah}<7D>(h!]<5D>h#]<5D><>p<>ah%]<5D>h']<5D>h)]<5D>uh+h<>hh<>ubhT)<29><>}<7D>(h<05> <20>h]<5D>h<16> <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hh<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h`ah%]<5D>h']<5D>h)]<5D>uh+hShh<>ubh<62>)<29><>}<7D>(h<05>
floatfloat<EFBFBD>h]<5D>h<00>pending_xref<65><66><EFBFBD>)<29><>}<7D>(hhh]<5D>(h<00>pending_xref_condition<6F><6E><EFBFBD>)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hh<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F><6E>resolved<65>uh+h<>hh<>ubh<62>)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hh<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F><6E>*<2A>uh+h<>hh<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	refdomain<69><6E>py<70><79>reftype<70><65>class<73><73>	reftarget<65><74>float<61><74>refspecific<69><63><EFBFBD>	py:module<6C><65>mlx.optimizers<72><73>py:class<73>Nuh+h<>hh<>ubah}<7D>(h!]<5D>h#]<5D>h<EFBFBD>ah%]<5D>h']<5D>h)]<5D>uh+h<>hh<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>hjhkuh+h<>hh<>ubh<62>)<29><>}<7D>(h<05>rho: floatfloat = 0.9<EFBFBD>h]<5D>(h<>)<29><>}<7D>(h<05>rho<68>h]<5D>h<16>rho<68><6F><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubah}<7D>(h!]<5D>h#]<5D>h<EFBFBD>ah%]<5D>h']<5D>h)]<5D>uh+h<>hjubh<62>)<29><>}<7D>(h<05>:<3A>h]<5D>h<16>:<3A><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj&hhhNhNubah}<7D>(h!]<5D>h#]<5D>h<EFBFBD>ah%]<5D>h']<5D>h)]<5D>uh+h<>hjubhT)<29><>}<7D>(h<05> <20>h]<5D>h<16> <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj4hhhNhNubah}<7D>(h!]<5D>h#]<5D>h`ah%]<5D>h']<5D>h)]<5D>uh+hShjubh<62>)<29><>}<7D>(h<05>
floatfloat<EFBFBD>h]<5D>h<EFBFBD>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjIhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hjFubh<62>)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjXhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hjFubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	refdomain<69>h<EFBFBD><68>reftype<70>j<00>	reftarget<65><74>float<61><74>refspecific<69><63><EFBFBD>	py:module<6C>j<00>py:class<73>Nuh+h<>hjBubah}<7D>(h!]<5D>h#]<5D>h<EFBFBD>ah%]<5D>h']<5D>h)]<5D>uh+h<>hjubhT)<29><>}<7D>(h<05> <20>h]<5D>h<16> <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjzhhhNhNubah}<7D>(h!]<5D>h#]<5D>h`ah%]<5D>h']<5D>h)]<5D>uh+hShjubh<00>desc_sig_operator<6F><72><EFBFBD>)<29><>}<7D>(h<05>=<3D>h]<5D>h<16>=<3D><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D><>o<>ah%]<5D>h']<5D>h)]<5D>uh+j<>hjubhT)<29><>}<7D>(h<05> <20>h]<5D>h<16> <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h`ah%]<5D>h']<5D>h)]<5D>uh+hShjubh	<09>inline<6E><65><EFBFBD>)<29><>}<7D>(h<05>0.9<EFBFBD>h]<5D>h<16>0.9<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D><>
default_value<75>ah%]<5D>h']<5D>h)]<5D><>support_smartquotes<65><73>uh+j<>hjubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>hjhkuh+h<>hh<>ubh<62>)<29><>}<7D>(h<05>eps: floatfloat = 1e-06<30>h]<5D>(h<>)<29><>}<7D>(h<05>eps<70>h]<5D>h<16>eps<70><73><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h<EFBFBD>ah%]<5D>h']<5D>h)]<5D>uh+h<>hj<>ubh<62>)<29><>}<7D>(h<05>:<3A>h]<5D>h<16>:<3A><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h<EFBFBD>ah%]<5D>h']<5D>h)]<5D>uh+h<>hj<>ubhT)<29><>}<7D>(h<05> <20>h]<5D>h<16> <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h`ah%]<5D>h']<5D>h)]<5D>uh+hShj<>ubh<62>)<29><>}<7D>(h<05>
floatfloat<EFBFBD>h]<5D>h<EFBFBD>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hj<>ubh<62>)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	refdomain<69>h<EFBFBD><68>reftype<70>j<00>	reftarget<65><74>float<61><74>refspecific<69><63><EFBFBD>	py:module<6C>j<00>py:class<73>Nuh+h<>hj<>ubah}<7D>(h!]<5D>h#]<5D>h<EFBFBD>ah%]<5D>h']<5D>h)]<5D>uh+h<>hj<>ubhT)<29><>}<7D>(h<05> <20>h]<5D>h<16> <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj%hhhNhNubah}<7D>(h!]<5D>h#]<5D>h`ah%]<5D>h']<5D>h)]<5D>uh+hShj<>ubj<62>)<29><>}<7D>(h<05>=<3D>h]<5D>h<16>=<3D><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj3hhhNhNubah}<7D>(h!]<5D>h#]<5D>j<EFBFBD>ah%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubhT)<29><>}<7D>(h<05> <20>h]<5D>h<16> <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjAhhhNhNubah}<7D>(h!]<5D>h#]<5D>h`ah%]<5D>h']<5D>h)]<5D>uh+hShj<>ubj<62>)<29><>}<7D>(h<05>1e-06<30>h]<5D>h<16>1e-06<30><36><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjOhhhNhNubah}<7D>(h!]<5D>h#]<5D>j<EFBFBD>ah%]<5D>h']<5D>h)]<5D><>support_smartquotes<65><73>uh+j<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>hjhkuh+h<>hh<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>hjhkuh+h<>hhEhhhhlhNubeh}<7D>(h!]<5D>h<ah#]<5D>(<28>sig<69><67>
sig-object<63>eh%]<5D>h']<5D>h)]<5D><>module<6C><65>mlx.optimizers<72>jh<06>fullname<6D>h<EFBFBD>uh+hChhlhKhh@hhubh<00>desc_content<6E><74><EFBFBD>)<29><>}<7D>(hhh]<5D>(h	<09>	paragraph<70><68><EFBFBD>)<29><>}<7D>(h<05>?Implementation of the AdaDelta optimizer with learning rate[1].<2E>h]<5D>h<16>?Implementation of the AdaDelta optimizer with learning rate[1].<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj|hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jzh<1D>Y/Users/awnihannun/repos/mlx/python/mlx/optimizers.py:docstring of mlx.optimizers.AdaDelta<74>hKhjwhhubj{)<29><>}<7D>(h<05>BOur AdaDelta implementation follows the original paper. In detail,<2C>h]<5D>h<16>BOur AdaDelta implementation follows the original paper. In detail,<2C><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jzhj<>hKhjwhhubj{)<29><>}<7D>(h<05>d[1]: Zeiler, M.D., 2012. ADADELTA: an adaptive learning rate method. arXiv preprint arXiv:1212.5701.<2E>h]<5D>h<16>d[1]: Zeiler, M.D., 2012. ADADELTA: an adaptive learning rate method. arXiv preprint arXiv:1212.5701.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jzhj<>hKhjwhhubh	<09>
math_block<EFBFBD><EFBFBD><EFBFBD>)<29><>}<7D>(h<05><>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}<7D>h]<5D>h<16><>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}<7D><><EFBFBD><EFBFBD><EFBFBD>}<7D>hj<>sbah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>docname<6D><65>+python/_autosummary/mlx.optimizers.AdaDelta<74><61>number<65>N<EFBFBD>label<65>N<EFBFBD>nowrap<61><70>hjhkuh+j<>hj<>hKhjwhhubh	<09>
field_list<EFBFBD><EFBFBD><EFBFBD>)<29><>}<7D>(hhh]<5D>h	<09>field<6C><64><EFBFBD>)<29><>}<7D>(hhh]<5D>(h	<09>
field_name<EFBFBD><EFBFBD><EFBFBD>)<29><>}<7D>(h<05>
Parameters<EFBFBD>h]<5D>h<16>
Parameters<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>hhlhKubh	<09>
field_body<EFBFBD><EFBFBD><EFBFBD>)<29><>}<7D>(hhh]<5D>h	<09>bullet_list<73><74><EFBFBD>)<29><>}<7D>(hhh]<5D>(h	<09>	list_item<65><6D><EFBFBD>)<29><>}<7D>(hhh]<5D>j{)<29><>}<7D>(h<05>8learning_rate (floatfloat) -- The learning rate \lambda.<2E>h]<5D>(h<00>literal_strong<6E><67><EFBFBD>)<29><>}<7D>(h<05>
learning_rate<74>h]<5D>h<16>
learning_rate<74><65><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubh<16> (<28><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>float<61>h]<5D>h<00>literal_emphasis<69><73><EFBFBD>)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhjubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hj<>ubh<62>)<29><>}<7D>(h<05>float<61>h]<5D>j)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhjubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	refdomain<69><6E>py<70><79>refexplicit<69><74><EFBFBD>reftype<70>j<00>	reftarget<65>j!<00>refspecific<69><63><EFBFBD>	py:module<6C>js<00>py:class<73>h<EFBFBD>uh+h<>hj<>ubh<16>)<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubh<16> – <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubh<16>The learning rate <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubh	<09>math<74><68><EFBFBD>)<29><>}<7D>(h<05>:math:`\lambda`<60>h]<5D>h<16>\lambda<64><61><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjPhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jNhj<>hhhNhNubh<16>.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jzhj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubj<62>)<29><>}<7D>(hhh]<5D>j{)<29><>}<7D>(h<05><>rho (floatfloat, optionaloptional) -- The coefficient \rho used for computing a
running average of squared gradients. Default: 0.9<EFBFBD>h]<5D>(j<>)<29><>}<7D>(h<05>rho<68>h]<5D>h<16>rho<68><6F><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjuhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hjqubh<16> (<28><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjqhhhNhNubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>float<61>h]<5D>j)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hj<>ubh<62>)<29><>}<7D>(h<05>float<61>h]<5D>j)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	refdomain<69>j;<00>refexplicit<69><74><EFBFBD>reftype<70>j<00>	reftarget<65>j<EFBFBD>j?<00>j@jsjAh<>uh+h<>hjqubj)<29><>}<7D>(h<05>, <20>h]<5D>h<16>, <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhjqubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>optional<61>h]<5D>j)<29><>}<7D>(h<05>optional<61>h]<5D>h<16>optional<61><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hj<>ubh<62>)<29><>}<7D>(h<05>optional<61>h]<5D>j)<29><>}<7D>(h<05>optional<61>h]<5D>h<16>optional<61><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	refdomain<69>j;<00>refexplicit<69><74><EFBFBD>reftype<70>j<00>	reftarget<65>j<EFBFBD>j?<00>j@jsjAh<>uh+h<>hjqubh<16>)<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjqhhhNhNubh<16> – <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjqhhhNhNubh<16>The coefficient <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjqhhhNhNubjO)<29><>}<7D>(h<05>:math:`\rho`<60>h]<5D>h<16>\rho<68><6F><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jNhjqhhhNhNubh<16>E used for computing a
running average of squared gradients. Default: <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjqhhhNhNubh	<09>literal<61><6C><EFBFBD>)<29><>}<7D>(h<05>``0.9``<60>h]<5D>h<16>0.9<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj3hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j1hjqhhhNhNubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jzhjnubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubj<62>)<29><>}<7D>(hhh]<5D>j{)<29><>}<7D>(h<05>~eps (floatfloat, optionaloptional) -- The term \epsilon added to the denominator to improve
numerical stability. Default: 1e-8<>h]<5D>(j<>)<29><>}<7D>(h<05>eps<70>h]<5D>h<16>eps<70><73><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjThhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hjPubh<16> (<28><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjPhhhNhNubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>float<61>h]<5D>j)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjmhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhjiubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hjfubh<62>)<29><>}<7D>(h<05>float<61>h]<5D>j)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hjfubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	refdomain<69>j;<00>refexplicit<69><74><EFBFBD>reftype<70>j<00>	reftarget<65>j<EFBFBD>j?<00>j@jsjAh<>uh+h<>hjPubj)<29><>}<7D>(h<05>, <20>h]<5D>h<16>, <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhjPubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>optional<61>h]<5D>j)<29><>}<7D>(h<05>optional<61>h]<5D>h<16>optional<61><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hj<>ubh<62>)<29><>}<7D>(h<05>optional<61>h]<5D>j)<29><>}<7D>(h<05>optional<61>h]<5D>h<16>optional<61><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	condition<6F>h<EFBFBD>uh+h<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>	refdomain<69>j;<00>refexplicit<69><74><EFBFBD>reftype<70>j<00>	reftarget<65>j<EFBFBD>j?<00>j@jsjAh<>uh+h<>hjPubh<16>)<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjPhhhNhNubh<16> – <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjPhhhNhNubh<16>	The term <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjPhhhNhNubjO)<29><>}<7D>(h<05>:math:`\epsilon`<60>h]<5D>h<16>\epsilon<6F><6E><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jNhjPhhhNhNubh<16>C added to the denominator to improve
numerical stability. Default: <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjPhhhNhNubh	<09>title_reference<63><65><EFBFBD>)<29><>}<7D>(h<05>`1e-8`<60>h]<5D>h<16>1e-8<><38><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhjPhhhNhNubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jzhjMubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hjwhhhNhNubh	<09>rubric<69><63><EFBFBD>)<29><>}<7D>(h<05>Methods<64>h]<5D>h<16>Methods<64><73><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjFhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jDhjwhhhh,hKubh<00>tabular_col_spec<65><63><EFBFBD>)<29><>}<7D>(hhh]<5D>h}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>spec<65><63>\X{1}{2}\X{1}{2}<7D>uh+jThjwhhh<1D>e/Users/awnihannun/repos/mlx/docs/src/python/_autosummary/mlx.optimizers.AdaDelta.rst:16:<autosummary><3E>hNub<75>sphinx.ext.autosummary<72><79>autosummary_table<6C><65><EFBFBD>)<29><>}<7D>(h<05><>


__init__(learning_rate[, rho, eps])


apply_single(gradient, parameter, state)

Performs the AdaDelta parameter update and stores v and u in the optimizer state.<2E>h]<5D>h	<09>table<6C><65><EFBFBD>)<29><>}<7D>(hhh]<5D>h	<09>tgroup<75><70><EFBFBD>)<29><>}<7D>(hhh]<5D>(h	<09>colspec<65><63><EFBFBD>)<29><>}<7D>(hhh]<5D>h}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>colwidth<74>K
uh+jshjpubjt)<29><>}<7D>(hhh]<5D>h}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>colwidth<74>KZuh+jshjpubh	<09>tbody<64><79><EFBFBD>)<29><>}<7D>(hhh]<5D>(h	<09>row<6F><77><EFBFBD>)<29><>}<7D>(hhh]<5D>(h	<09>entry<72><79><EFBFBD>)<29><>}<7D>(hhh]<5D>j{)<29><>}<7D>(h<05>Y:py:obj:`__init__ <mlx.optimizers.AdaDelta.__init__>`\ \(learning\_rate\[\, rho\, eps\]\)<29>h]<5D>(h<>)<29><>}<7D>(h<05>5:py:obj:`__init__ <mlx.optimizers.AdaDelta.__init__>`<60>h]<5D>j2)<29><>}<7D>(hj<>h]<5D>h<16>__init__<5F><5F><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>(<28>xref<65><66>py<70><79>py-obj<62>eh%]<5D>h']<5D>h)]<5D>uh+j1hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>refdoc<6F>j<EFBFBD><00>	refdomain<69>j<EFBFBD><00>reftype<70><65>obj<62><6A>refexplicit<69><74><EFBFBD>refwarn<72><6E>j@jsjAh<><68>	reftarget<65><74> mlx.optimizers.AdaDelta.__init__<5F>uh+h<>h<1D>e/Users/awnihannun/repos/mlx/docs/src/python/_autosummary/mlx.optimizers.AdaDelta.rst:16:<autosummary><3E>hKhj<>ubh<16>(learning_rate[, rho, eps])<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jzhj<>hKhj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubj<62>)<29><>}<7D>(hhh]<5D>j{)<29><>}<7D>(hhh]<5D>h}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jzhj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubj<62>)<29><>}<7D>(hhh]<5D>(j<>)<29><>}<7D>(hhh]<5D>j{)<29><>}<7D>(h<05>_:py:obj:`apply_single <mlx.optimizers.AdaDelta.apply_single>`\ \(gradient\, parameter\, state\)<29>h]<5D>(h<>)<29><>}<7D>(h<05>=:py:obj:`apply_single <mlx.optimizers.AdaDelta.apply_single>`<60>h]<5D>j2)<29><>}<7D>(hj<>h]<5D>h<16>apply_single<6C><65><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>(j<><00>py<70><79>py-obj<62>eh%]<5D>h']<5D>h)]<5D>uh+j1hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>refdoc<6F>j<EFBFBD><00>	refdomain<69>j<EFBFBD><00>reftype<70><65>obj<62><6A>refexplicit<69><74><EFBFBD>refwarn<72><6E>j@jsjAh<>j<EFBFBD><00>$mlx.optimizers.AdaDelta.apply_single<6C>uh+h<>h<1D>e/Users/awnihannun/repos/mlx/docs/src/python/_autosummary/mlx.optimizers.AdaDelta.rst:16:<autosummary><3E>hKhj<>ubh<16>(gradient, parameter, state)<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jzhjhKhj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubj<62>)<29><>}<7D>(hhh]<5D>j{)<29><>}<7D>(h<05>aPerforms the AdaDelta parameter update and stores :math:`v` and :math:`u` in the optimizer state.<2E>h]<5D>(h<16>2Performs the AdaDelta parameter update and stores <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj%hhhNhNubjO)<29><>}<7D>(h<05>	:math:`v`<60>h]<5D>h<16>v<><76><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj-hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jNhj%ubh<16> and <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj%hhhNhNubjO)<29><>}<7D>(h<05>	:math:`u`<60>h]<5D>h<16>u<><75><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj?hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jNhj%ubh<16> in the optimizer state.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj%hhhNhNubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jzhjahKhj"ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hjpubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>cols<6C>Kuh+jnhjkubah}<7D>(h!]<5D>h#]<5D><>autosummary longtable<6C>ah%]<5D>h']<5D>h)]<5D>uh+jihjeubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>hjhkuh+jchjwhhhjahNubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+juhh@hhhhlhNubeh}<7D>(h!]<5D>h#]<5D>(j;<00>class<73>eh%]<5D>h']<5D>h)]<5D><>domain<69>j;<00>objtype<70>j<EFBFBD><00>desctype<70>j<EFBFBD><00>noindex<65><78>uh+h>hhhhhNhNubeh}<7D>(h!]<5D><>mlx-optimizers-adadelta<74>ah#]<5D>h%]<5D><>mlx.optimizers.adadelta<74>ah']<5D>h)]<5D>uh+h
hhhhhh,hKubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>source<63>h,uh+h<01>current_source<63>N<EFBFBD>current_line<6E>N<EFBFBD>settings<67><73>docutils.frontend<6E><64>Values<65><73><EFBFBD>)<29><>}<7D>(hN<>	generator<6F>N<EFBFBD>	datestamp<6D>N<EFBFBD>source_link<6E>N<EFBFBD>
source_url<EFBFBD>N<EFBFBD>
toc_backlinks<6B>j<EFBFBD><00>footnote_backlinks<6B>K<01>
sectnum_xform<72>K<01>strip_comments<74>N<EFBFBD>strip_elements_with_classes<65>N<EFBFBD>
strip_classes<65>N<EFBFBD>report_level<65>K<02>
halt_level<EFBFBD>K<05>exit_status_level<65>K<05>debug<75>N<EFBFBD>warning_stream<61>N<EFBFBD>	traceback<63><6B><EFBFBD>input_encoding<6E><67>	utf-8-sig<69><67>input_encoding_error_handler<65><72>strict<63><74>output_encoding<6E><67>utf-8<><38>output_encoding_error_handler<65>j<EFBFBD><00>error_encoding<6E><67>utf-8<><38>error_encoding_error_handler<65><72>backslashreplace<63><65>
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