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