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157 lines
6.4 KiB
157 lines
6.4 KiB
""" AdaHessian Optimizer
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Lifted from https://github.com/davda54/ada-hessian/blob/master/ada_hessian.py
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Originally licensed MIT, Copyright 2020, David Samuel
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"""
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import torch
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class Adahessian(torch.optim.Optimizer):
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"""
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Implements the AdaHessian algorithm from "ADAHESSIAN: An Adaptive Second OrderOptimizer for Machine Learning"
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Arguments:
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params (iterable): iterable of parameters to optimize or dicts defining parameter groups
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lr (float, optional): learning rate (default: 0.1)
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betas ((float, float), optional): coefficients used for computing running averages of gradient and the
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squared hessian trace (default: (0.9, 0.999))
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eps (float, optional): term added to the denominator to improve numerical stability (default: 1e-8)
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weight_decay (float, optional): weight decay (L2 penalty) (default: 0.0)
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hessian_power (float, optional): exponent of the hessian trace (default: 1.0)
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update_each (int, optional): compute the hessian trace approximation only after *this* number of steps
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(to save time) (default: 1)
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n_samples (int, optional): how many times to sample `z` for the approximation of the hessian trace (default: 1)
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"""
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def __init__(self, params, lr=0.1, betas=(0.9, 0.999), eps=1e-8, weight_decay=0.0,
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hessian_power=1.0, update_each=1, n_samples=1, avg_conv_kernel=False):
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if not 0.0 <= lr:
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raise ValueError(f"Invalid learning rate: {lr}")
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if not 0.0 <= eps:
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raise ValueError(f"Invalid epsilon value: {eps}")
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if not 0.0 <= betas[0] < 1.0:
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raise ValueError(f"Invalid beta parameter at index 0: {betas[0]}")
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if not 0.0 <= betas[1] < 1.0:
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raise ValueError(f"Invalid beta parameter at index 1: {betas[1]}")
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if not 0.0 <= hessian_power <= 1.0:
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raise ValueError(f"Invalid Hessian power value: {hessian_power}")
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self.n_samples = n_samples
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self.update_each = update_each
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self.avg_conv_kernel = avg_conv_kernel
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# use a separate generator that deterministically generates the same `z`s across all GPUs in case of distributed training
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self.seed = 2147483647
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self.generator = torch.Generator().manual_seed(self.seed)
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defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay, hessian_power=hessian_power)
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super(Adahessian, self).__init__(params, defaults)
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for p in self.get_params():
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p.hess = 0.0
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self.state[p]["hessian step"] = 0
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@property
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def is_second_order(self):
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return True
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def get_params(self):
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"""
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Gets all parameters in all param_groups with gradients
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"""
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return (p for group in self.param_groups for p in group['params'] if p.requires_grad)
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def zero_hessian(self):
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"""
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Zeros out the accumalated hessian traces.
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"""
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for p in self.get_params():
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if not isinstance(p.hess, float) and self.state[p]["hessian step"] % self.update_each == 0:
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p.hess.zero_()
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@torch.no_grad()
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def set_hessian(self):
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"""
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Computes the Hutchinson approximation of the hessian trace and accumulates it for each trainable parameter.
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"""
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params = []
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for p in filter(lambda p: p.grad is not None, self.get_params()):
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if self.state[p]["hessian step"] % self.update_each == 0: # compute the trace only each `update_each` step
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params.append(p)
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self.state[p]["hessian step"] += 1
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if len(params) == 0:
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return
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if self.generator.device != params[0].device: # hackish way of casting the generator to the right device
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self.generator = torch.Generator(params[0].device).manual_seed(self.seed)
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grads = [p.grad for p in params]
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for i in range(self.n_samples):
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# Rademacher distribution {-1.0, 1.0}
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zs = [torch.randint(0, 2, p.size(), generator=self.generator, device=p.device) * 2.0 - 1.0 for p in params]
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h_zs = torch.autograd.grad(
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grads, params, grad_outputs=zs, only_inputs=True, retain_graph=i < self.n_samples - 1)
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for h_z, z, p in zip(h_zs, zs, params):
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p.hess += h_z * z / self.n_samples # approximate the expected values of z*(H@z)
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@torch.no_grad()
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def step(self, closure=None):
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"""
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Performs a single optimization step.
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Arguments:
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closure (callable, optional) -- a closure that reevaluates the model and returns the loss (default: None)
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"""
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loss = None
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if closure is not None:
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loss = closure()
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self.zero_hessian()
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self.set_hessian()
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for group in self.param_groups:
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for p in group['params']:
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if p.grad is None or p.hess is None:
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continue
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if self.avg_conv_kernel and p.dim() == 4:
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p.hess = torch.abs(p.hess).mean(dim=[2, 3], keepdim=True).expand_as(p.hess).clone()
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# Perform correct stepweight decay as in AdamW
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p.mul_(1 - group['lr'] * group['weight_decay'])
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state = self.state[p]
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# State initialization
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if len(state) == 1:
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state['step'] = 0
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# Exponential moving average of gradient values
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state['exp_avg'] = torch.zeros_like(p)
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# Exponential moving average of Hessian diagonal square values
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state['exp_hessian_diag_sq'] = torch.zeros_like(p)
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exp_avg, exp_hessian_diag_sq = state['exp_avg'], state['exp_hessian_diag_sq']
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beta1, beta2 = group['betas']
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state['step'] += 1
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# Decay the first and second moment running average coefficient
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exp_avg.mul_(beta1).add_(p.grad, alpha=1 - beta1)
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exp_hessian_diag_sq.mul_(beta2).addcmul_(p.hess, p.hess, value=1 - beta2)
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bias_correction1 = 1 - beta1 ** state['step']
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bias_correction2 = 1 - beta2 ** state['step']
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k = group['hessian_power']
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denom = (exp_hessian_diag_sq / bias_correction2).pow_(k / 2).add_(group['eps'])
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# make update
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step_size = group['lr'] / bias_correction1
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p.addcdiv_(exp_avg, denom, value=-step_size)
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return loss
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