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Nrr rr!r"rrr) r beta1beta2rr!r"rrrrR) _cuda_graph_capture_health_checkr: enable_gradr5rSr)r)closurelossr>rMrNrOrPrQrTrUr rr!r"rrrrRr-r-r.r/usR    z Adamax.step)rrrrNN)__name__ __module__ __qualname__rr<rrboolr(r4rSrr/ __classcell__r-r-r+r.rsB      $#aImplements Adamax algorithm (a variant of Adam based on infinity norm). .. math:: \begin{aligned} &\rule{110mm}{0.4pt} \\ &\textbf{input} : \gamma \text{ (lr)}, \beta_1, \beta_2 \text{ (betas)},\theta_0 \text{ (params)},f(\theta) \text{ (objective)}, \: \lambda \text{ (weight decay)}, \\ &\hspace{13mm} \epsilon \text{ (epsilon)} \\ &\textbf{initialize} : m_0 \leftarrow 0 \text{ ( first moment)}, u_0 \leftarrow 0 \text{ ( infinity norm)} \\[-1.ex] &\rule{110mm}{0.4pt} \\ &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\ &\hspace{5mm}g_t \leftarrow \nabla_{\theta} f_t (\theta_{t-1}) \\ &\hspace{5mm}if \: \lambda \neq 0 \\ &\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1} \\ &\hspace{5mm}m_t \leftarrow \beta_1 m_{t-1} + (1 - \beta_1) g_t \\ &\hspace{5mm}u_t \leftarrow \mathrm{max}(\beta_2 u_{t-1}, |g_{t}|+\epsilon) \\ &\hspace{5mm}\theta_t \leftarrow \theta_{t-1} - \frac{\gamma m_t}{(1-\beta^t_1) u_t} \\ &\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 `Adam: A Method for Stochastic Optimization`_. a  Args: params (iterable): iterable of parameters to optimize or dicts defining parameter groups lr (float, optional): learning rate (default: 2e-3) betas (Tuple[float, float], optional): coefficients used for computing running averages of gradient and its square 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) z zd .. _Adam\: A Method for Stochastic Optimization: https://arxiv.org/abs/1412.6980 rrNrOrPrQr rTrUrr!rrrrRc Cst|D]\}}||}| s|n| }||}||}||}tjs?| r?t}|jj|jjkr7|jj|vs?Jd|d|d7}| dkrN|j|| d}t|rgt |}t |}t |}t |}| |d|| stj | || ||dn!t| |d| |dgd}|tj|ddd| r||d}||||}|||qd|t|}||}|j||| d qdS) NIIf capturable=True, params and state_steps must be on supported devices: .rralpha)outF)keepdim)value) enumerater:_utils is_compilingr r2typeaddrF view_as_reallerp_maximummul_absadd_cat unsqueeze unsqueeze_copy_amaxdiv_addcdiv_r)rrNrOrPrQr rTrUrr!rrrrRiparamrErCrDstep_tcapturable_supported_devicesnorm_bufneg_bias_correctiondenombias_correctionclrr-r-r._single_tensor_adamaxsR       "  rc s| rJdt|dkrdStjs0| r0tddtfddt||Ds0Jddt|||||g}| D]\\}}}}}}| rPt ||||| rWt |}|dj rjtj |tjd d d d d nt |d | dkr| rtj ||| d ntj||| d }t||d t||| s| dkrt|}nt|t ||t||| rt|}t|d t|t||}t|||q>fdd|D}fdd|D}t||||q>dS)Nz#_foreach ops don't support autogradrF) supports_xlac3s0|]\}}|jj|jjko|jjvVqdSrZ)r2rj).0r?r/)r|r-r. Cs   z'_multi_tensor_adamax..r`rar$cpu)r2rbrcsg|] }dt|qS)rr)rr/)rTr-r. sz(_multi_tensor_adamax..csg|] }t|dqS)r)rbc)rr-r.rs)r9r:rhrir allzipr"_group_tensors_by_device_and_dtypevaluesr _foreach_negis_cpu _foreach_add_r= _foreach_add_foreach_lerp_ _foreach_mul_ _foreach_abs _foreach_abs__foreach_maximum_ _foreach_pow _foreach_sub_ _foreach_div_ _foreach_mul_foreach_addcdiv_)rrNrOrPrQr rTrUrr!rrrrRgrouped_tensorsgrouped_params grouped_gradsgrouped_exp_avgsgrouped_exp_infsgrouped_state_steps_bias_correctionsr step_sizer-)rTr|rr._multi_tensor_adamax(sz                    r)single_tensor_fnFr"c Cstjstdd|Dstd|durt||dd\}}|r*tjr*td|r4tjs4t}nt }||||||| | | | |||| |ddS) zrFunctional API that performs adamax algorithm computation. 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