File size: 29,242 Bytes
c61ccee
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
import torch
from torch import Tensor
from .optimizer import (Optimizer, _use_grad_for_differentiable, _get_value, _dispatch_sqrt,
                        _stack_if_compiling, _get_scalar_dtype, _capturable_doc, _differentiable_doc,
                        _foreach_doc, _fused_doc, _maximize_doc, _default_to_fused_or_foreach,
                        ParamsT, _view_as_real)
from typing import List, Optional, Tuple, Union
from torch.utils._foreach_utils import _get_fused_kernels_supported_devices

__all__ = ["AdamW", "adamw"]


class AdamW(Optimizer):
    def __init__(

        self,

        params: ParamsT,

        lr: Union[float, Tensor] = 1e-3,

        betas: Tuple[float, float] = (0.9, 0.999),

        eps: float = 1e-8,

        weight_decay: float = 1e-2,

        amsgrad: bool = False,

        *,

        maximize: bool = False,

        foreach: Optional[bool] = None,

        capturable: bool = False,

        differentiable: bool = False,

        fused: Optional[bool] = None,

    ):
        if not 0.0 <= lr:
            raise ValueError(f"Invalid learning rate: {lr}")
        if isinstance(lr, Tensor) and foreach and not capturable:
            raise ValueError("lr as a Tensor is not supported for capturable=False and foreach=True")
        if not 0.0 <= eps:
            raise ValueError(f"Invalid epsilon value: {eps}")
        if not 0.0 <= betas[0] < 1.0:
            raise ValueError(f"Invalid beta parameter at index 0: {betas[0]}")
        if not 0.0 <= betas[1] < 1.0:
            raise ValueError(f"Invalid beta parameter at index 1: {betas[1]}")
        if not 0.0 <= weight_decay:
            raise ValueError(f"Invalid weight_decay value: {weight_decay}")
        defaults = dict(
            lr=lr,
            betas=betas,
            eps=eps,
            weight_decay=weight_decay,
            amsgrad=amsgrad,
            foreach=foreach,
            maximize=maximize,
            capturable=capturable,
            differentiable=differentiable,
            fused=fused,
        )
        super().__init__(params, defaults)

        if fused:
            if differentiable:
                raise RuntimeError("`fused` does not support `differentiable`")
            self._step_supports_amp_scaling = True
            # TODO(crcrpar): [low prec params & their higher prec copy]
            # Suppor AMP with FP16/BF16 model params which would need
            # higher prec copy of params to do update math in higher prec to
            # alleviate the loss of information.
            fused_supported_devices = _get_fused_kernels_supported_devices()
            if not all(
                p.device.type in fused_supported_devices and
                torch.is_floating_point(p)
                for pg in self.param_groups for p in pg['params']
            ):
                raise RuntimeError("`fused=True` requires all the params to be floating point Tensors of "
                                   f"supported devices: {fused_supported_devices}.")
            if foreach:
                raise RuntimeError("`fused` and `foreach` cannot be `True` together.")

    def __setstate__(self, state):
        super().__setstate__(state)
        for group in self.param_groups:
            group.setdefault("amsgrad", False)
            group.setdefault("maximize", False)
            group.setdefault("foreach", None)
            group.setdefault("capturable", False)
            group.setdefault("differentiable", False)
            fused = group.setdefault("fused", None)
            for p in group["params"]:
                p_state = self.state.get(p, [])
                if len(p_state) != 0 and not torch.is_tensor(p_state['step']):
                    step_val = float(p_state["step"])
                    p_state["step"] = (torch.tensor(step_val, dtype=_get_scalar_dtype(is_fused=fused), device=p.device)
                                       if group['capturable'] or group['fused']
                                       else torch.tensor(step_val, dtype=_get_scalar_dtype()))

    def _init_group(

        self,

        group,

        params_with_grad,

        grads,

        amsgrad,

        exp_avgs,

        exp_avg_sqs,

        max_exp_avg_sqs,

        state_steps,

    ):
        has_complex = False
        for p in group["params"]:
            if p.grad is None:
                continue
            has_complex |= torch.is_complex(p)
            params_with_grad.append(p)
            if p.grad.is_sparse:
                raise RuntimeError("AdamW does not support sparse gradients")
            grads.append(p.grad)

            state = self.state[p]

            # State initialization
            if len(state) == 0:
                # note(crcrpar): Deliberately host `step` on CPU if both capturable and fused are off.
                # This is because kernel launches are costly on CUDA and XLA.
                state["step"] = (
                    torch.zeros((), dtype=_get_scalar_dtype(is_fused=group["fused"]), device=p.device)
                    if group["capturable"] or group["fused"]
                    else torch.tensor(0.0, dtype=_get_scalar_dtype())
                )
                # Exponential moving average of gradient values
                state["exp_avg"] = torch.zeros_like(
                    p, memory_format=torch.preserve_format
                )
                # Exponential moving average of squared gradient values
                state["exp_avg_sq"] = torch.zeros_like(
                    p, memory_format=torch.preserve_format
                )
                if amsgrad:
                    # Maintains max of all exp. moving avg. of sq. grad. values
                    state["max_exp_avg_sq"] = torch.zeros_like(
                        p, memory_format=torch.preserve_format
                    )

            exp_avgs.append(state["exp_avg"])
            exp_avg_sqs.append(state["exp_avg_sq"])

            if group['amsgrad']:
                max_exp_avg_sqs.append(state["max_exp_avg_sq"])
            if group['differentiable'] and state['step'].requires_grad:
                raise RuntimeError('`requires_grad` is not supported for `step` in differentiable mode')

            # Foreach without capturable does not support a tensor lr
            if group['foreach'] and isinstance(group['lr'], Tensor) and not group['capturable']:
                raise RuntimeError('lr as a Tensor is not supported for capturable=False and foreach=True')

            state_steps.append(state["step"])
        return has_complex

    @_use_grad_for_differentiable
    def step(self, closure=None):
        """Perform a single optimization step.



        Args:

            closure (Callable, optional): A closure that reevaluates the model

                and returns the loss.

        """
        self._cuda_graph_capture_health_check()

        loss = None
        if closure is not None:
            with torch.enable_grad():
                loss = closure()

        for group in self.param_groups:
            params_with_grad = []
            grads = []
            exp_avgs = []
            exp_avg_sqs = []
            max_exp_avg_sqs = []
            state_steps = []
            amsgrad = group["amsgrad"]
            beta1, beta2 = group["betas"]

            has_complex = self._init_group(
                group,
                params_with_grad,
                grads,
                amsgrad,
                exp_avgs,
                exp_avg_sqs,
                max_exp_avg_sqs,
                state_steps,
            )

            adamw(
                params_with_grad,
                grads,
                exp_avgs,
                exp_avg_sqs,
                max_exp_avg_sqs,
                state_steps,
                amsgrad=amsgrad,
                beta1=beta1,
                beta2=beta2,
                lr=group["lr"],
                weight_decay=group["weight_decay"],
                eps=group["eps"],
                maximize=group["maximize"],
                foreach=group["foreach"],
                capturable=group["capturable"],
                differentiable=group["differentiable"],
                fused=group["fused"],
                grad_scale=getattr(self, "grad_scale", None),
                found_inf=getattr(self, "found_inf", None),
                has_complex=has_complex,
            )

        return loss


AdamW.__doc__ = r"""Implements AdamW algorithm.



    .. 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)},

                \: \epsilon \text{ (epsilon)}                                                    \\

            &\hspace{13mm}      \lambda \text{(weight decay)},  \: \textit{amsgrad},

                \: \textit{maximize}                                                             \\

            &\textbf{initialize} : m_0 \leftarrow 0 \text{ (first moment)}, v_0 \leftarrow 0

                \text{ ( second moment)}, \: \widehat{v_0}^{max}\leftarrow 0              \\[-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} - \gamma \lambda \theta_{t-1}         \\

            &\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   m_t/\big(1-\beta_1^t \big)                   \\

            &\hspace{5mm}\widehat{v_t} \leftarrow   v_t/\big(1-\beta_2^t \big)                   \\

            &\hspace{5mm}\textbf{if} \: amsgrad                                                  \\

            &\hspace{10mm}\widehat{v_t}^{max} \leftarrow \mathrm{max}(\widehat{v_t}^{max},

                \widehat{v_t})                                                                   \\

            &\hspace{10mm}\theta_t \leftarrow \theta_t - \gamma \widehat{m_t}/

                \big(\sqrt{\widehat{v_t}^{max}} + \epsilon \big)                                 \\

            &\hspace{5mm}\textbf{else}                                                           \\

            &\hspace{10mm}\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 `Decoupled Weight Decay Regularization`_.

    """ + fr"""

    Args:

        params (iterable): iterable of parameters to optimize or dicts defining

            parameter groups

        lr (float, Tensor, optional): learning rate (default: 1e-3). A tensor LR

            is not yet supported for all our implementations. Please use a float

            LR if you are not also specifying fused=True or capturable=True.

        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 coefficient (default: 1e-2)

        amsgrad (bool, optional): whether to use the AMSGrad variant of this

            algorithm from the paper `On the Convergence of Adam and Beyond`_

            (default: False)

        {_maximize_doc}

        {_foreach_doc}

        {_capturable_doc}

        {_differentiable_doc}

        {_fused_doc}

    .. _Decoupled Weight Decay Regularization:

        https://arxiv.org/abs/1711.05101

    .. _On the Convergence of Adam and Beyond:

        https://openreview.net/forum?id=ryQu7f-RZ



    """


def adamw(

    params: List[Tensor],

    grads: List[Tensor],

    exp_avgs: List[Tensor],

    exp_avg_sqs: List[Tensor],

    max_exp_avg_sqs: List[Tensor],

    state_steps: List[Tensor],

    # kwonly args with defaults are not supported by functions compiled with torchscript issue #70627

    # setting this as kwarg for now as functional API is compiled by torch/distributed/optim

    foreach: Optional[bool] = None,

    capturable: bool = False,

    differentiable: bool = False,

    fused: Optional[bool] = None,

    grad_scale: Optional[Tensor] = None,

    found_inf: Optional[Tensor] = None,

    has_complex: bool = False,

    *,

    amsgrad: bool,

    beta1: float,

    beta2: float,

    lr: Union[float, Tensor],

    weight_decay: float,

    eps: float,

    maximize: bool,

):
    r"""Functional API that performs AdamW algorithm computation.



    See :class:`~torch.optim.AdamW` for details.

    """
    if not torch._utils.is_compiling() and not all(isinstance(t, torch.Tensor) for t in state_steps):
        raise RuntimeError(
            "API has changed, `state_steps` argument must contain a list of singleton tensors"
        )

    # Respect when the user inputs False/True for foreach or fused. We only want to change
    # the default when neither have been user-specified. Note that we default to foreach
    # and pass False to use_fused. This is not a mistake--we want to give the fused impl
    # bake-in time before making it the default, even if it is typically faster.
    if fused is None and foreach is None:
        _, foreach = _default_to_fused_or_foreach(params, differentiable, use_fused=False)
        # Do not flip on foreach for the unsupported case where lr is a Tensor and capturable=False.
        if foreach and isinstance(lr, Tensor) and not capturable:
            foreach = False
    if fused is None:
        fused = False
    if foreach is None:
        foreach = False

    if foreach and torch.jit.is_scripting():
        raise RuntimeError("torch.jit.script not supported with foreach optimizers")
    if fused and torch.jit.is_scripting():
        raise RuntimeError("torch.jit.script not supported with fused optimizers")

    if fused and not torch.jit.is_scripting():
        func = _fused_adamw
    elif foreach and not torch.jit.is_scripting():
        func = _multi_tensor_adamw
    else:
        func = _single_tensor_adamw

    func(
        params,
        grads,
        exp_avgs,
        exp_avg_sqs,
        max_exp_avg_sqs,
        state_steps,
        amsgrad=amsgrad,
        beta1=beta1,
        beta2=beta2,
        lr=lr,
        weight_decay=weight_decay,
        eps=eps,
        maximize=maximize,
        capturable=capturable,
        differentiable=differentiable,
        grad_scale=grad_scale,
        found_inf=found_inf,
        has_complex=has_complex,
    )


def _single_tensor_adamw(

    params: List[Tensor],

    grads: List[Tensor],

    exp_avgs: List[Tensor],

    exp_avg_sqs: List[Tensor],

    max_exp_avg_sqs: List[Tensor],

    state_steps: List[Tensor],

    grad_scale: Optional[Tensor],

    found_inf: Optional[Tensor],

    *,

    amsgrad: bool,

    beta1: float,

    beta2: float,

    lr: Union[Tensor, float],

    weight_decay: float,

    eps: float,

    maximize: bool,

    capturable: bool,

    differentiable: bool,

    has_complex: bool,

):

    assert grad_scale is None and found_inf is None

    if torch.jit.is_scripting():
        # this assert is due to JIT being dumb and not realizing that the ops below
        # have overloads to handle both float and Tensor lrs, so we just assert it's
        # a float since most people using JIT are using floats
        assert isinstance(lr, float)

    for i, param in enumerate(params):
        grad = grads[i] if not maximize else -grads[i]
        exp_avg = exp_avgs[i]
        exp_avg_sq = exp_avg_sqs[i]
        step_t = state_steps[i]

        # If compiling, the compiler will handle cudagraph checks, see note [torch.compile x capturable]
        if not torch._utils.is_compiling() and capturable:
            assert (
                (param.is_cuda and step_t.is_cuda) or (param.is_xla and step_t.is_xla)
            ), "If capturable=True, params and state_steps must be CUDA or XLA tensors."

        if torch.is_complex(param):
            grad = torch.view_as_real(grad)
            exp_avg = torch.view_as_real(exp_avg)
            exp_avg_sq = torch.view_as_real(exp_avg_sq)
            if amsgrad:
                max_exp_avg_sqs[i] = torch.view_as_real(max_exp_avg_sqs[i])
            param = torch.view_as_real(param)

        # update step
        step_t += 1

        # Perform stepweight decay
        param.mul_(1 - lr * weight_decay)

        # Decay the first and second moment running average coefficient
        exp_avg.lerp_(grad, 1 - beta1)
        exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)

        if capturable or differentiable:
            step = step_t

            bias_correction1 = 1 - beta1 ** step
            bias_correction2 = 1 - beta2 ** step

            step_size = lr / bias_correction1
            step_size_neg = step_size.neg()

            bias_correction2_sqrt = bias_correction2.sqrt()

            if amsgrad:
                # Maintains the maximum of all 2nd moment running avg. till now
                if differentiable:
                    max_exp_avg_sq = max_exp_avg_sqs[i].clone()
                else:
                    max_exp_avg_sq = max_exp_avg_sqs[i]

                max_exp_avg_sqs[i].copy_(torch.maximum(max_exp_avg_sq, exp_avg_sq))

                # Uses the max. for normalizing running avg. of gradient
                # Folds in (admittedly ugly) 1-elem step_size math here to avoid extra param-set-sized read+write
                # (can't fold it into addcdiv_ below because addcdiv_ requires value is a Number, not a Tensor)
                denom = (
                    max_exp_avg_sqs[i].sqrt() / (bias_correction2_sqrt * step_size_neg)
                ).add_(eps / step_size_neg)
            else:
                denom = (
                    exp_avg_sq.sqrt() / (bias_correction2_sqrt * step_size_neg)
                ).add_(eps / step_size_neg)

            param.addcdiv_(exp_avg, denom)
        else:
            step = _get_value(step_t)

            bias_correction1 = 1 - beta1 ** step
            bias_correction2 = 1 - beta2 ** step

            step_size = lr / bias_correction1

            bias_correction2_sqrt = _dispatch_sqrt(bias_correction2)

            if amsgrad:
                # Maintains the maximum of all 2nd moment running avg. till now
                torch.maximum(max_exp_avg_sqs[i], exp_avg_sq, out=max_exp_avg_sqs[i])

                # Use the max. for normalizing running avg. of gradient
                denom = (max_exp_avg_sqs[i].sqrt() / bias_correction2_sqrt).add_(eps)
            else:
                denom = (exp_avg_sq.sqrt() / bias_correction2_sqrt).add_(eps)

            param.addcdiv_(exp_avg, denom, value=-step_size)

        # Lastly, switch back to complex view
        if amsgrad and torch.is_complex(params[i]):
            max_exp_avg_sqs[i] = torch.view_as_complex(max_exp_avg_sqs[i])


def _multi_tensor_adamw(

    params: List[Tensor],

    grads: List[Tensor],

    exp_avgs: List[Tensor],

    exp_avg_sqs: List[Tensor],

    max_exp_avg_sqs: List[Tensor],

    state_steps: List[Tensor],

    grad_scale: Optional[Tensor],

    found_inf: Optional[Tensor],

    *,

    amsgrad: bool,

    beta1: float,

    beta2: float,

    lr: Union[Tensor, float],

    weight_decay: float,

    eps: float,

    maximize: bool,

    capturable: bool,

    differentiable: bool,

    has_complex: bool,

):
    if len(params) == 0:
        return

    if isinstance(lr, Tensor) and not capturable:
        raise RuntimeError("lr as a Tensor is not supported for capturable=False and foreach=True")

    # If compiling, the compiler will handle cudagraph checks, see note [torch.compile x capturable]
    if not torch._utils.is_compiling() and capturable:
        assert all(
            p.is_cuda and step.is_cuda for p, step in zip(params, state_steps)
        ), "If capturable=True, params and state_steps must be CUDA tensors."

    assert not differentiable, "_foreach ops don't support autograd"

    assert grad_scale is None and found_inf is None

    grouped_tensors = Optimizer._group_tensors_by_device_and_dtype([
        params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps])
    for ((
        device_params,
        device_grads,
        device_exp_avgs,
        device_exp_avg_sqs,
        device_max_exp_avg_sqs,
        device_state_steps,
    ), _) in grouped_tensors.values():
        if has_complex:
            if amsgrad:
                _view_as_real(device_params, device_grads, device_exp_avgs, device_exp_avg_sqs, device_max_exp_avg_sqs)
            else:
                _view_as_real(device_params, device_grads, device_exp_avgs, device_exp_avg_sqs)

        if maximize:
            device_grads = torch._foreach_neg(device_grads)

        # Update steps
        # If steps are on CPU, foreach will fall back to the slow path, which is a for-loop calling t.add(1) over
        # and over. 1 will then be wrapped into a Tensor over and over again, which is slower than if we just
        # wrapped it once now. The alpha is required to assure we go to the right overload.
        if device_state_steps[0].is_cpu:
            torch._foreach_add_(device_state_steps, torch.tensor(1.0, device='cpu'), alpha=1.0)
        else:
            torch._foreach_add_(device_state_steps, 1)

        # Perform stepweight decay
        if weight_decay != 0:
            torch._foreach_mul_(device_params, 1 - lr * weight_decay)

        # Decay the first and second moment running average coefficient
        torch._foreach_lerp_(device_exp_avgs, device_grads, 1 - beta1)

        torch._foreach_mul_(device_exp_avg_sqs, beta2)
        torch._foreach_addcmul_(device_exp_avg_sqs, device_grads, device_grads, 1 - beta2)

        # Delete the local intermediate since it won't be used anymore to save on peak memory
        del device_grads

        if capturable:
            bias_correction1 = torch._foreach_pow(beta1, device_state_steps)
            bias_correction2 = torch._foreach_pow(beta2, device_state_steps)
            # foreach_sub doesn't allow a scalar as the first arg
            torch._foreach_sub_(bias_correction1, 1)
            torch._foreach_sub_(bias_correction2, 1)
            # we do not negate bias_correction1 as it'll need to be negated later anyway
            torch._foreach_neg_(bias_correction2)

            # foreach_div doesn't allow a scalar as the first arg
            torch._foreach_div_(bias_correction1, lr)
            torch._foreach_reciprocal_(bias_correction1)

            torch._foreach_sqrt_(bias_correction2)

            # Re-assign for clarity as we maintain minimal intermediates: we'll have
            # step_size = - lr / (1 - beta1 ^ t) where t = num_steps
            # bias_correction2_sqrt = sqrt(1 - beta2 ^ t)
            step_size = bias_correction1
            bias_correction2_sqrt = bias_correction2

            if amsgrad:
                # Maintains the maximum of all 2nd moment running avg. till now
                torch._foreach_maximum_(device_max_exp_avg_sqs, device_exp_avg_sqs)

                # Use the max. for normalizing running avg. of gradient
                exp_avg_sq_sqrt = torch._foreach_sqrt(device_max_exp_avg_sqs)
            else:
                exp_avg_sq_sqrt = torch._foreach_sqrt(device_exp_avg_sqs)

            torch._foreach_div_(exp_avg_sq_sqrt, bias_correction2_sqrt)
            torch._foreach_add_(exp_avg_sq_sqrt, eps)
            torch._foreach_div_(exp_avg_sq_sqrt, step_size)

            # at this point, exp_avg_sq_sqrt = - (1 - beta^t) * [sqrt(exp_avg_sq / (1 - beta2^t)) + eps] / lr
            torch._foreach_addcdiv_(device_params, device_exp_avgs, exp_avg_sq_sqrt)
        else:
            bias_correction1 = [1 - beta1 ** _get_value(step) for step in device_state_steps]
            bias_correction2 = [1 - beta2 ** _get_value(step) for step in device_state_steps]

            step_size = _stack_if_compiling([(lr / bc) * -1 for bc in bias_correction1])

            bias_correction2_sqrt = [_dispatch_sqrt(bc) for bc in bias_correction2]

            if amsgrad:
                # Maintains the maximum of all 2nd moment running avg. till now
                torch._foreach_maximum_(device_max_exp_avg_sqs, device_exp_avg_sqs)

                # Use the max. for normalizing running avg. of gradient
                exp_avg_sq_sqrt = torch._foreach_sqrt(device_max_exp_avg_sqs)
            else:
                exp_avg_sq_sqrt = torch._foreach_sqrt(device_exp_avg_sqs)

            torch._foreach_div_(exp_avg_sq_sqrt, bias_correction2_sqrt)
            torch._foreach_add_(exp_avg_sq_sqrt, eps)
            torch._foreach_addcdiv_(device_params, device_exp_avgs, exp_avg_sq_sqrt, step_size)


def _fused_adamw(

    params: List[Tensor],

    grads: List[Tensor],

    exp_avgs: List[Tensor],

    exp_avg_sqs: List[Tensor],

    max_exp_avg_sqs: List[Tensor],

    state_steps: List[Tensor],

    grad_scale: Optional[Tensor],

    found_inf: Optional[Tensor],

    *,

    amsgrad: bool,

    beta1: float,

    beta2: float,

    lr: Union[float, Tensor],

    weight_decay: float,

    eps: float,

    maximize: bool,

    capturable: bool,  # Needed for consistency.

    differentiable: bool,

    has_complex: bool,

) -> None:
    if not params:
        return
    if differentiable:
        raise RuntimeError("Adam with fused=True does not support differentiable=True")

    grad_scale_dict = {grad_scale.device: grad_scale} if grad_scale is not None else None
    found_inf_dict = {found_inf.device: found_inf} if found_inf is not None else None

    # We only shuffle around the lr when it is a Tensor and on CUDA, otherwise, we prefer
    # treating it as a scalar.
    lr_dict = {lr.device: lr} if isinstance(lr, Tensor) and str(lr.device) != "cpu" else None

    grouped_tensors = Optimizer._group_tensors_by_device_and_dtype(
        [params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps])
    for (device, _), ((device_params,
                       device_grads,
                       device_exp_avgs,
                       device_exp_avg_sqs,
                       device_max_exp_avg_sqs,
                       device_state_steps,), _) in grouped_tensors.items():
        device_grad_scale, device_found_inf = None, None
        if grad_scale is not None:
            if device not in grad_scale_dict:
                grad_scale_dict[device] = grad_scale.to(device, non_blocking=True)
            device_grad_scale = grad_scale_dict[device]
        if found_inf is not None:
            if found_inf not in found_inf_dict:
                found_inf_dict[device] = found_inf.to(device, non_blocking=True)
            device_found_inf = found_inf_dict[device]
        if lr_dict is not None and device not in lr_dict:
            lr_dict[device] = lr.to(device=device, non_blocking=True)
            lr = lr_dict[device]
        torch._foreach_add_(device_state_steps, 1)
        torch._fused_adamw_(
            device_params,
            device_grads,
            device_exp_avgs,
            device_exp_avg_sqs,
            device_max_exp_avg_sqs,
            device_state_steps,
            amsgrad=amsgrad,
            lr=lr,
            beta1=beta1,
            beta2=beta2,
            weight_decay=weight_decay,
            eps=eps,
            maximize=maximize,
            grad_scale=device_grad_scale,
            found_inf=device_found_inf,
        )
        if device_found_inf is not None:
            torch._foreach_sub_(device_state_steps, [device_found_inf] * len(device_state_steps))