Number Steps

// http://www.spoj.com/problems/NSTEPS/
#include <iostream>

using std::cin;
using std::cout;
using std::endl;

int main(int argc, char* argv[]) {
	int testnum;
	cin >> testnum;

	while (testnum-- > 0) {
		int x,y;
		cin >> x >> y;
		bool atLine1 = (x==y);
		bool atLine2 = ((x-y) == 2);
		if (atLine1 || atLine2) {
			int number;
			if (x%2==0) {
				if (y<x) {
					number = x*2 - 2;
				} else {
					number = x*2;
				}
			} else {
				if (x==y) {
					number = 1 + 4*(x/2);
				} else {
					number = 4*(x/2) -1;
				}
			}
			cout << number << endl;
		} 
		else {
			cout << "No Number" << endl;
		}
	}
}

### Warmup Steps in Machine Learning Context In the context of machine learning, particularly during the training phase involving optimization algorithms like Adam or SGD (Stochastic Gradient Descent), **warmup steps** refer to an initial period where the learning rate gradually increases from a small value to its full intended value over a predefined number of iterations or epochs. This technique helps stabilize the early stages of training by preventing large updates that could destabilize convergence when starting with high learning rates. The concept behind using warmup steps lies in addressing potential instability issues caused by initializing weights randomly before they have been sufficiently adjusted through backpropagation. By slowly ramping up the learning rate instead of applying it fully right away, models may achieve better performance metrics such as accuracy while reducing divergence risks associated with overly aggressive parameter changes too soon into their lifecycle [^1]. Here’s how one might implement this within PyTorch framework: ```python import torch.optim.lr_scheduler as lr_sched def get_linear_schedule_with_warmup(optimizer, num_warmup_steps, num_training_steps, last_epoch=-1): def lr_lambda(current_step: int): if current_step < num_warmup_steps: return float(current_step) / float(max(1, num_warmup_steps)) return max( 0.0, float(num_training_steps - current_step) / float(max(1, num_training_steps - num_warmup_steps)) ) return lr_sched.LambdaLR(optimizer, lr_lambda, last_epoch) # Example Usage optimizer = torch.optim.Adam(model.parameters(), lr=initial_lr) scheduler = get_linear_schedule_with_warmup(optimizer, num_warmup_steps=warmup_steps_count, num_training_steps=total_steps) for epoch in range(epochs): for batch in dataloader: optimizer.zero_grad() loss = model(batch) loss.backward() optimizer.step() scheduler.step() # Adjusts LR based on schedule defined above. ``` This implementation creates a linear increase followed by decay pattern suitable for many NLP tasks utilizing transformers architectures among others requiring fine-grained control over hyperparameters throughout different phases including warming-up stage described earlier [^2].
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