Beginner Explanation
Imagine you’re learning to ride a bike. At first, you might fall a lot, so your parents give you extra support. As you get better, they gradually reduce that support. Time-dependent loss weighting is like that; it helps a machine learning model learn better by giving it more help (or weight) when it’s struggling and less help as it gets better over time. This way, the model can learn more effectively and become stable in its predictions.Technical Explanation
Time-dependent loss weighting is a technique used in training machine learning models where the loss function is adjusted over time based on the training epoch or iteration. The idea is to prioritize certain samples or classes at different stages of training. For instance, we can define a loss function L(t) that decreases its contribution as time progresses. A common approach is to use a decay factor, such as: L'(t) = L(t) * exp(-λt), where λ is a decay rate. This means that the loss from earlier epochs is weighted more heavily than from later ones, promoting stability and convergence. Here’s a simple implementation in PyTorch: “`python import torch import torch.nn as nn class WeightedLoss(nn.Module): def __init__(self, decay_rate): super(WeightedLoss, self).__init__() self.decay_rate = decay_rate def forward(self, outputs, targets, epoch): loss = nn.CrossEntropyLoss()(outputs, targets) weighted_loss = loss * torch.exp(-self.decay_rate * epoch) return weighted_loss “`Academic Context
Time-dependent loss weighting is rooted in the concept of adaptive learning rates and dynamic sample weighting. It draws from foundational theories in optimization, particularly those that address the trade-off between exploration and exploitation in machine learning. Key papers include ‘Dynamic Sample Weighting for Deep Learning’ by Liu et al. (2019), which discusses how sample importance can evolve during training. The mathematical basis often involves the use of exponential decay functions to modulate loss contributions over time, aligning with principles from stochastic optimization and reinforcement learning that emphasize the importance of temporal dynamics in learning.Code Examples
Example 1:
import torch
import torch.nn as nn
class WeightedLoss(nn.Module):
def __init__(self, decay_rate):
super(WeightedLoss, self).__init__()
self.decay_rate = decay_rate
def forward(self, outputs, targets, epoch):
loss = nn.CrossEntropyLoss()(outputs, targets)
weighted_loss = loss * torch.exp(-self.decay_rate * epoch)
return weighted_lossExample 2:
def __init__(self, decay_rate):
super(WeightedLoss, self).__init__()
self.decay_rate = decay_rateExample 3:
def forward(self, outputs, targets, epoch):
loss = nn.CrossEntropyLoss()(outputs, targets)
weighted_loss = loss * torch.exp(-self.decay_rate * epoch)
return weighted_lossExample 4:
Time-dependent loss weighting is a technique used in training machine learning models where the loss function is adjusted over time based on the training epoch or iteration. The idea is to prioritize certain samples or classes at different stages of training. For instance, we can define a loss function L(t) that decreases its contribution as time progresses. A common approach is to use a decay factor, such as: L'(t) = L(t) * exp(-λt), where λ is a decay rate. This means that the loss from earlier epochs is weighted more heavily than from later ones, promoting stability and convergence. Here’s a simple implementation in PyTorch:
```python
import torch
import torch.nn as nnExample 5:
import torch
import torch.nn as nn
class WeightedLoss(nn.Module):
def __init__(self, decay_rate):Example 6:
import torch.nn as nn
class WeightedLoss(nn.Module):
def __init__(self, decay_rate):
super(WeightedLoss, self).__init__()Example 7:
class WeightedLoss(nn.Module):
def __init__(self, decay_rate):
super(WeightedLoss, self).__init__()
self.decay_rate = decay_rate
Example 8:
def __init__(self, decay_rate):
super(WeightedLoss, self).__init__()
self.decay_rate = decay_rate
def forward(self, outputs, targets, epoch):Example 9:
def forward(self, outputs, targets, epoch):
loss = nn.CrossEntropyLoss()(outputs, targets)
weighted_loss = loss * torch.exp(-self.decay_rate * epoch)
return weighted_loss
```View Source: https://arxiv.org/abs/2511.16599v1