+ &jah Rt^RIHt^RIt^RIHt^RIHtHtHtH t H t H t H t H t HtHtHtHtHtHtHtHtRR.t!RR]4tRR ] R ] R ] R ] R ] R 2 ,]nR RltRRlt] !]R7RRRll4tR#)z'Implementation for the NAdam algorithm.)castN)Tensor)_capturable_doc_default_to_fused_or_foreach_differentiable_doc_disable_dynamo_if_unsupported _foreach_doc!_get_capturable_supported_devices_get_scalar_dtype _get_value _maximize_doc _params_doc_stack_if_compiling _to_scalar_use_grad_for_differentiable _view_as_real OptimizerParamsTNAdamnadamc |aa]tRt^ toR RRRRRRRR/V3RlV3RlllltV3R ltR t]RR l4tR t Vt V;t #)rFforeachNmaximize capturabledifferentiablec<V^8dQhRS[RS[S[,RS[S[S[3,RS[RS[RS[RS[RS[R ,R S[R S[R S[R R / #)paramslrbetaseps weight_decaymomentum_decaydecoupled_weight_decayrNrrrreturn)rfloatrtuplebool)format __classdict__s"i/Users/jameslopez/projects/CWCArchive/cwc-podcast/.venv/lib/python3.14/site-packages/torch/optim/nadam.py __annotate__NAdam.__annotate__!s)+)+)+ FN)+UE\" )+  )+  )+)+!%)+)+)+)+)+ )+c<\V\4'd!VP4^8wd \R4hRV8:g\RV 24hRV8:g\RV 24hRV^,u;8:dR8gM\RV^, 24hRV^,u;8:dR8gM\RV^, 24hRV8:g\RV 24hRV8:g\R V 24hR VR VR VR VRVRVRV RVRV RV / p \S V`W4R#)zTensor lr must be 1-elementzInvalid learning rate: zInvalid epsilon value: ?z#Invalid beta parameter at index 0: z#Invalid beta parameter at index 1: zInvalid weight_decay value: zInvalid momentum_decay value: rrr r!r"r#rrrrN) isinstancernumel ValueErrorsuper__init__)selfrrrr r!r"r#rrrrdefaults __class__s&&&&&&&&$$$$ r*r6NAdam.__init__!s. b& ! !bhhjAo:; ;by6rd;< <cz6se<= =eAh$$B58*MN NeAh$$B58*MN Nl";L>JK Kn$=n=MNO O " U 3 L n $&<  w * n   *r-c<\SV`V4VPEFpVPRR4VPRR4VPRR4VPRR4VPRR4VR,EFOpVPP V.4p\ V4^8wgK2\P!VR,4'gp\VR,4pVR,'d,\P!V\4VPR 7M\P!V\4R 7VR&\P!VR ,4'dKVR ,pVR,'d,\P!V\4VPR 7M\P!V\4R 7VR &EKR EK R#) rFrNrrr#rstepdtypedevicer> mu_product) r5 __setstate__ param_groups setdefaultstategetlentorch is_tensorr%tensorr r?)r7rEgrouppp_statestep_val mu_prod_valr9s&& r*rBNAdam.__setstate__Lsr U#&&E   Z /   Y -   \5 1   -u 5   5u =8__**..B/w<1$ ??76?;;#(#9 %\22"LL (0A0CAHH"'h>O>Q!R  !??7<+@AA&-l&; %\22"LL +3D3Fqxx"'kARAT!U  -% 'r-cNRpVR,EFp V PfKV\P!V 4,pVPV 4V PP'd \ R4hVPV P4VP V ,p \V 4^8XEd VR,'d,\P!R \4V PR7M\P!R\4R7V R&VR,'d,\P!R \4V PR7M\P!R\4R7V R &\P!V \PR 7V R &\P!V \PR 7V R &VPV R ,4VPV R ,4VPV R ,4VPV R,4EK V#)Frz'NAdam does not support sparse gradientsrr=r0r@r<r1rA) memory_formatexp_avg exp_avg_sq)gradrH is_complexappend is_sparse RuntimeErrorrErGzerosr r?rJones zeros_likepreserve_format) r7rKparams_with_gradgradsexp_avgs exp_avg_sqs mu_products state_steps has_complexrLrEs &&&&&&&& r* _init_groupNAdam._init_groupjs xAvv!u//22  ''*66###&'PQQ QVV$ 1 u:? !.. B.?.A!((S"\\#5F5HI&M!.. 2->-@R"\\#5F5HI,' (-'7'7)>)>(E)$+0*:*:)>)>+E,'i 01""5#67""5#67""5=1I!Jr-c *VP4RpVe.\P!4;_uu_4V!4pRRR4VPFp.p.p.p.p.p.p \ \ \ \ 3,VR,4wrVPVVVVVVV 4p \VVVVVV V V VR,VR,VR,VR,VR,VR,VR ,VR ,VR ,V R 7K V# +'giL;i) zPerform a single optimization step. Args: closure (Callable, optional): A closure that reevaluates the model and returns the loss. Nrrr!r"r rr#rrr) beta1beta2rr!r"r rr#rrrre) '_accelerator_graph_capture_health_checkrH enable_gradrCrr&r%rfr) r7closurelossrKr_r`rarbrcrdrirjres && r*r< NAdam.steps' 446  ""$$y%&&E-/ "$E%'H(*K(*K(*KeUl 3U7^DLE** K  ;">2$%56%Lz*',-E'Fi( .$%56'% ''P W%$s D D rU)gMb`?)g?g+?g:0yE>gMbp?FN) __name__ __module__ __qualname____firstlineno__r6rBrfrr<__static_attributes____classdictcell__ __classcell__)r9r)s@@r*rr s\)+ $)+)+!)+ %)+)+V<0d"6"66r-a Implements NAdam algorithm. .. math:: \begin{aligned} &\rule{110mm}{0.4pt} \\ &\textbf{input} : \gamma_t \text{ (lr)}, \: \beta_1,\beta_2 \text{ (betas)}, \: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)} \\ &\hspace{13mm} \: \lambda \text{ (weight decay)}, \:\psi \text{ (momentum decay)} \\ &\hspace{13mm} \: \textit{decoupled\_weight\_decay}, \:\textit{maximize} \\ &\textbf{initialize} : m_0 \leftarrow 0 \text{ ( first moment)}, v_0 \leftarrow 0 \text{ ( second moment)} \\[-1.ex] &\rule{110mm}{0.4pt} \\ &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\ &\hspace{5mm}\textbf{if} \: \textit{maximize}: \\ &\hspace{10mm}g_t \leftarrow -\nabla_{\theta} f_t (\theta_{t-1}) \\ &\hspace{5mm}\textbf{else} \\ &\hspace{10mm}g_t \leftarrow \nabla_{\theta} f_t (\theta_{t-1}) \\ &\hspace{5mm} \theta_t \leftarrow \theta_{t-1} \\ &\hspace{5mm} \textbf{if} \: \lambda \neq 0 \\ &\hspace{10mm}\textbf{if} \: \textit{decoupled\_weight\_decay} \\ &\hspace{15mm} \theta_t \leftarrow \theta_{t-1} - \gamma \lambda \theta_{t-1} \\ &\hspace{10mm}\textbf{else} \\ &\hspace{15mm} g_t \leftarrow g_t + \lambda \theta_{t-1} \\ &\hspace{5mm} \mu_t \leftarrow \beta_1 \big(1 - \frac{1}{2} 0.96^{t \psi} \big) \\ &\hspace{5mm} \mu_{t+1} \leftarrow \beta_1 \big(1 - \frac{1}{2} 0.96^{(t+1)\psi}\big)\\ &\hspace{5mm}m_t \leftarrow \beta_1 m_{t-1} + (1 - \beta_1) g_t \\ &\hspace{5mm}v_t \leftarrow \beta_2 v_{t-1} + (1-\beta_2) g^2_t \\ &\hspace{5mm}\widehat{m_t} \leftarrow \mu_{t+1} m_t/(1-\prod_{i=1}^{t+1}\mu_i)\\[-1.ex] & \hspace{11mm} + (1-\mu_t) g_t /(1-\prod_{i=1}^{t} \mu_{i}) \\ &\hspace{5mm}\widehat{v_t} \leftarrow v_t/\big(1-\beta_2^t \big) \\ &\hspace{5mm}\theta_t \leftarrow \theta_t - \gamma \widehat{m_t}/ \big(\sqrt{\widehat{v_t}} + \epsilon \big) \\ &\rule{110mm}{0.4pt} \\[-1.ex] &\bf{return} \: \theta_t \\[-1.ex] &\rule{110mm}{0.4pt} \\[-1.ex] \end{aligned} For further details regarding the algorithm we refer to `Incorporating Nesterov Momentum into Adam`_. z Args: a lr (float, Tensor, optional): learning rate (default: 2e-3) betas (Tuple[float, float], optional): coefficients used for computing running averages of gradient and its square (default: (0.9, 0.999)) eps (float, optional): term added to the denominator to improve numerical stability (default: 1e-8) weight_decay (float, optional): weight decay (L2 penalty) (default: 0) momentum_decay (float, optional): momentum momentum_decay (default: 4e-3) decoupled_weight_decay (bool, optional): whether to decouple the weight decay as in AdamW to obtain NAdamW. If True, the algorithm does not accumulate weight decay in the momentum nor variance. (default: False) z z .. _Incorporating Nesterov Momentum into Adam: https://openreview.net/forum?id=OM0jvwB8jIp57ZJjtNEZ .. _Decoupled Weight Decay Regularization: https://arxiv.org/abs/1711.05101 c$lV^8dQhR\\,R\\,R\\,R\\,R\\,R\\,R\R\R \R \R \R \R \R\R\R\R\RR/#rrr`rarbrcrdrirjrr!r"r r#rrrrer$Nlistrr%r')r(s"r*r+r+saa La <a6laf a f a f a a a aaa a!aa !a"#a$%a& 'ar-c \PP4'g \V4p\ V4EFwppV 'g VV,M VV,)pVV,pVV,pVV,pVV,p\P !V4'dY\P !V4p\P !V4p\P !V4p\P !V4p\PP4'gV'd\4pVPPVPPu;8XdVPP8XdMMVPPV9g\RV R24hV^, pV'dTpM \V4p^VV,, pV ^8wd;V 'd VP^W,, 4MVPVV R7pVRRRVV ,,,, ,pVRRRV^,V ,,,, ,pVV,pVP!V^V, 4VPV4P#VV^V, R7VP%V4P'4pV'g V'dVPV 4pVV,pVV)RV, ,RV, , ,pVV)V,RV, , ,pVP)VV4VP)VV4EK*\V4V,pVP+V 4VP)VVV)RV, ,R\V4, , R7VP)VV\-\.V)V,RV, , 4R7EK R#)zVIf capturable=True, params, mu_products and state_steps must be on supported devices: .alphar1?Q?)valueN)rHjit is_scriptingr enumeraterW view_as_realcompiler is_compilingr r?typeAssertionErrorr mul_addlerp_addcmul_divsqrtaddcdiv_add_rr%)rr`rarbrcrdrirjrr!r"r r#rrrreiparamrVrSrTrAstep_tcapturable_supported_devicesr<bias_correction2mumu_nextdenommu_product_nexts&&&&&&$$$$$$$$$$$ r*_single_tensor_nadamrs&( 99 ! ! # # ^f%5'uQxeAhY1+ ^  ^ Q   E " "&&u-E%%d+D((1G++J7J~~**,,+L+N ( !!Z%6%6%;%;Qv}}?Q?QQLL%%)EE$--I,J!M !  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