AdamW - Revision history

Fall2024 Wiki Team8 at 23:02, 12 December 2024

2024-12-12T23:02:07Z

← Older revision		Revision as of 19:02, 12 December 2024
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	*For each time step <math>t</math>:		*For each time step <math>t</math>:
	**Compute Gradient:		**Compute Gradient:
	***Calculate the gradient of the objective function:		***Calculate the gradient of the objective function: <math>g_t = \nabla_{\theta_t} f(\theta_t)</math>
	<math>g_t = \nabla_{\theta_t} f(\theta_t)</math>
	**Update First Moment Estimate:		**Update First Moment Estimate:
	***Update the exponentially decaying average of past gradients:		***Update the exponentially decaying average of past gradients: <math>m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t</math>
	<math>m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t</math>
	**Update Second Moment Estimate:		**Update Second Moment Estimate:
	***Update the exponentially decaying average of squared gradients (element-wise square):		***Update the exponentially decaying average of squared gradients (element-wise square): <math>v_t = \beta_2 v_{t-1} + (1 - \beta_2) (g_t \odot g_t),</math>where <math>g_t \odot g_t</math> denotes element-wise multiplication of <math>g_t</math> with itself.
	<math>v_t = \beta_2 v_{t-1} + (1 - \beta_2) (g_t \odot g_t)</math>
	# where <math>g_t \odot g_t</math> denotes element-wise multiplication of <math>g_t</math> with itself.
	**Bias Correction:		**Bias Correction:
	***Compute bias-corrected first and second moment estimates:		***Compute bias-corrected first and second moment estimates: <math>\hat{m}_t = \frac{m_t}{1 - \beta_1^t},</math> <math>\hat{v}_t = \frac{v_t}{1 - \beta_2^t}</math>
	<math>\hat{m}_t = \frac{m_t}{1 - \beta_1^t},</math>
	<math>\hat{v}_t = \frac{v_t}{1 - \beta_2^t}</math>
	**Parameter Update with Weight Decay:		**Parameter Update with Weight Decay:
	***Update parameters <math>\theta_t</math> with weight decay applied separately from the gradient step:		***Update parameters <math>\theta_t</math> with weight decay applied separately from the gradient step: <math>\theta_{t+1} = \theta_t - \alpha \left( \frac{\hat{m}_t}{\sqrt{\hat{v}_t} + \epsilon} + \lambda \theta_t \right)</math>
	<math>\theta_{t+1} = \theta_t - \alpha \left( \frac{\hat{m}_t}{\sqrt{\hat{v}_t} + \epsilon} + \lambda \theta_t \right)</math>
	***This form highlights that weight decay <math>\lambda \theta_t</math> is applied as a separate additive term to the parameter update, reinforcing the decoupling concept.		***This form highlights that weight decay <math>\lambda \theta_t</math> is applied as a separate additive term to the parameter update, reinforcing the decoupling concept.

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	*Small constant: <math>\epsilon = 10^{-8}</math>		*Small constant: <math>\epsilon = 10^{-8}</math>
	*Objective function gradient: <math>g_t</math>		*Objective function gradient: <math>g_t</math>
	For this example, assume we have a simple quadratic function:		For this example, assume we have a simple quadratic function: <math>f(\theta) = \theta^2</math>
	<math>f(\theta) = \theta^2</math>		The gradient of this function is: <math>g_t = 2 \theta_t</math>
	The gradient of this function is:
	<math>g_t = 2 \theta_t</math>

	=== Step-by-Step Calculation ===		=== Step-by-Step Calculation ===
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	==== Iteration 1 ====		==== Iteration 1 ====
	*Step 1: Compute Gradient:		*Step 1: Compute Gradient: <math>g_1 = 2 \times \theta_0 = 2 \times 10 = 20</math>
			*Step 2: Update First Moment Estimate: <math>m_1 = \beta_1 m_0 + (1 - \beta_1) g_1 = 0.9 \times 0 + 0.1 \times 20 = 2</math>
	<math>g_1 = 2 \times \theta_0 = 2 \times 10 = 20</math>		*Step 3: Update Second Moment Estimate: <math>v_1 = \beta_2 v_0 + (1 - \beta_2) g_1^2 = 0.999 \times 0 + 0.001 \times 20^2 = 0 + 0.4 = 0.4</math>
	*Step 2: Update First Moment Estimate:		*Step 4: Bias Correction for First Moment: <math>\hat{m}_1 = \frac{m_1}{1 - \beta_1^1} = \frac{2}{1 - 0.9} = \frac{2}{0.1} = 20</math>
			*Step 5: Bias Correction for Second Moment: <math>\hat{v}_1 = \frac{v_1}{1 - \beta_2^1} = \frac{0.4}{1 - 0.999} = \frac{0.4}{0.001} = 400</math>
	<math>m_1 = \beta_1 m_0 + (1 - \beta_1) g_1 = 0.9 \times 0 + 0.1 \times 20 = 2</math>
	*Step 3: Update Second Moment Estimate:

	<math>v_1 = \beta_2 v_0 + (1 - \beta_2) g_1^2 = 0.999 \times 0 + 0.001 \times 20^2 = 0 + 0.4 = 0.4</math>
	*Step 4: Bias Correction for First Moment:

	<math>\hat{m}_1 = \frac{m_1}{1 - \beta_1^1} = \frac{2}{1 - 0.9} = \frac{2}{0.1} = 20</math>
	*Step 5: Bias Correction for Second Moment:

	<math>\hat{v}_1 = \frac{v_1}{1 - \beta_2^1} = \frac{0.4}{1 - 0.999} = \frac{0.4}{0.001} = 400</math>
	*Step 6: Parameter Update with Weight Decay:		*Step 6: Parameter Update with Weight Decay:
			**Gradient Update: <math>\theta_{1} = \theta_{0} - \alpha \times \frac{\hat{m}_1}{\sqrt{\hat{v}_1} + \epsilon} = 10 - 0.1 \times \frac{20}{\sqrt{400} + 10^{-8}}</math>
	**Gradient Update:		**Simplify the denominator: <math>\sqrt{\hat{v}_1} + \epsilon = \sqrt{400} + 10^{-8} = 20 + 10^{-8}</math>
			**Compute the update: <math>\theta_{1} = 10 - 0.1 \times \frac{20}{20 + 10^{-8}} = 10 - 0.1 \times 1 = 9.9</math>
	<math>\theta_{1} = \theta_{0} - \alpha \times \frac{\hat{m}_1}{\sqrt{\hat{v}_1} + \epsilon} = 10 - 0.1 \times \frac{20}{\sqrt{400} + 10^{-8}}</math>		**Weight Decay:<math>\theta_{1} = \theta_{1} - \alpha \times \lambda \times \theta_{0} = 9.9 - 0.1 \times 0.01 \times 10 = 9.9 - 0.01 = 9.89</math>
			**Updated Parameter:<math>\theta_{1} = 9.89</math>
	**Simplify the denominator:

	<math>\sqrt{\hat{v}_1} + \epsilon = \sqrt{400} + 10^{-8} = 20 + 10^{-8}</math>

	**Compute the update:

	<math>\theta_{1} = 10 - 0.1 \times \frac{20}{20 + 10^{-8}} = 10 - 0.1 \times 1 = 9.9</math>

	**Weight Decay:

	<math>\theta_{1} = \theta_{1} - \alpha \times \lambda \times \theta_{0} = 9.9 - 0.1 \times 0.01 \times 10 = 9.9 - 0.01 = 9.89</math>

	**Updated Parameter:

	<math>\theta_{1} = 9.89</math>

	==== Iteration 2 ====		==== Iteration 2 ====
	*Step 1: Compute Gradient:		*Step 1: Compute Gradient: <math>g_1 = 2 \times \theta_0 = 2 \times 10 = 20</math>
			*Step 2: Update First Moment Estimate: <math>m_1 = \beta_1 m_0 + (1 - \beta_1) g_1 = 0.9 \times 0 + 0.1 \times 20 = 2</math>
	<math>g_1 = 2 \times \theta_0 = 2 \times 10 = 20</math>		*Step 3: Update Second Moment Estimate: <math>v_1 = \beta_2 v_0 + (1 - \beta_2) g_1^2 = 0.999 \times 0 + 0.001 \times 20^2 = 0 + 0.4 = 0.4</math>
	*Step 2: Update First Moment Estimate:		*Step 4: Bias Correction for First Moment: <math>\hat{m}_1 = \frac{m_1}{1 - \beta_1^1} = \frac{2}{1 - 0.9} = \frac{2}{0.1} = 20</math>
			*Step 5: Bias Correction for Second Moment: <math>\hat{v}_1 = \frac{v_1}{1 - \beta_2^1} = \frac{0.4}{1 - 0.999} = \frac{0.4}{0.001} = 400</math>
	<math>m_1 = \beta_1 m_0 + (1 - \beta_1) g_1 = 0.9 \times 0 + 0.1 \times 20 = 2</math>
	*Step 3: Update Second Moment Estimate:

	<math>v_1 = \beta_2 v_0 + (1 - \beta_2) g_1^2 = 0.999 \times 0 + 0.001 \times 20^2 = 0 + 0.4 = 0.4</math>
	*Step 4: Bias Correction for First Moment:

	<math>\hat{m}_1 = \frac{m_1}{1 - \beta_1^1} = \frac{2}{1 - 0.9} = \frac{2}{0.1} = 20</math>
	*Step 5: Bias Correction for Second Moment:

	<math>\hat{v}_1 = \frac{v_1}{1 - \beta_2^1} = \frac{0.4}{1 - 0.999} = \frac{0.4}{0.001} = 400</math>
	*Step 6: Parameter Update with Weight Decay:		*Step 6: Parameter Update with Weight Decay:
			**Gradient Update:<math>\theta_{1} = \theta_{0} - \alpha \times \frac{\hat{m}_1}{\sqrt{\hat{v}_1} + \epsilon} = 10 - 0.1 \times \frac{20}{\sqrt{400} + 10^{-8}}</math>
	**Gradient Update:		**Simplify the denominator:<math>\sqrt{\hat{v}_1} + \epsilon = \sqrt{400} + 10^{-8} = 20 + 10^{-8}</math>
			**Compute the update:<math>\theta_{1} = 10 - 0.1 \times \frac{20}{20 + 10^{-8}} = 10 - 0.1 \times 1 = 9.9</math>
	<math>\theta_{1} = \theta_{0} - \alpha \times \frac{\hat{m}_1}{\sqrt{\hat{v}_1} + \epsilon} = 10 - 0.1 \times \frac{20}{\sqrt{400} + 10^{-8}}</math>		**Weight Decay: <math>\theta_{1} = \theta_{1} - \alpha \times \lambda \times \theta_{0} = 9.9 - 0.1 \times 0.01 \times 10 = 9.9 - 0.01 = 9.89</math>
			**Updated Parameter: <math>\theta_{1} = 9.89</math>
	**Simplify the denominator:

	<math>\sqrt{\hat{v}_1} + \epsilon = \sqrt{400} + 10^{-8} = 20 + 10^{-8}</math>

	**Compute the update:

	<math>\theta_{1} = 10 - 0.1 \times \frac{20}{20 + 10^{-8}} = 10 - 0.1 \times 1 = 9.9</math>

	**Weight Decay:

	<math>\theta_{1} = \theta_{1} - \alpha \times \lambda \times \theta_{0} = 9.9 - 0.1 \times 0.01 \times 10 = 9.9 - 0.01 = 9.89</math>

	**Updated Parameter:

	<math>\theta_{1} = 9.89</math>

	=== Explanations for Each Step ===		=== Explanations for Each Step ===

Fall2024 Wiki Team8: /* Explanations for Each Step */

2024-12-12T22:40:42Z

Explanations for Each Step

← Older revision		Revision as of 18:40, 12 December 2024
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	=== Explanations for Each Step ===		=== Explanations for Each Step ===
	Step 1: The gradient is calculated based on the current parameter value. For the function <math>f(\theta) = \theta^2</math>, the gradient <math>g_t = 2 \theta_t</math> represents the slope of the function at <math>\theta_t</math>.		*Step 1: The gradient is calculated based on the current parameter value. For the function <math>f(\theta) = \theta^2</math>, the gradient <math>g_t = 2 \theta_t</math> represents the slope of the function at <math>\theta_t</math>.

	Steps 2 and 3: The first and second moment estimates (<math>m_t</math> and <math>v_t</math>) are updated using exponentially decaying averages of past gradients and squared gradients, respectively. These updates help the optimizer adjust the learning rate dynamically for each parameter, improving efficiency.		*Steps 2 and 3: The first and second moment estimates (<math>m_t</math> and <math>v_t</math>) are updated using exponentially decaying averages of past gradients and squared gradients, respectively. These updates help the optimizer adjust the learning rate dynamically for each parameter, improving efficiency.

	Steps 4 and 5: Bias correction is applied to the moment estimates to address their initial bias toward zero. This correction is particularly important during the early stages of optimization, ensuring more accurate estimates.		*Steps 4 and 5: Bias correction is applied to the moment estimates to address their initial bias toward zero. This correction is particularly important during the early stages of optimization, ensuring more accurate estimates.

	Step 6: The parameter is updated in two key parts:		*Step 6: The parameter is updated in two key parts:
	*Gradient Update: The parameter is adjusted in the opposite direction of the gradient. This adjustment is scaled by the learning rate and adapted using the corrected moment estimates.		**Gradient Update: The parameter is adjusted in the opposite direction of the gradient. This adjustment is scaled by the learning rate and adapted using the corrected moment estimates.
	*Weight Decay: A regularization term is applied by reducing the parameter's value slightly. This encourages smaller parameter values, which helps to prevent overfitting.		**Weight Decay: A regularization term is applied by reducing the parameter's value slightly. This encourages smaller parameter values, which helps to prevent overfitting.

	By repeatedly performing these steps, the AdamW optimizer effectively moves the parameters closer to the function's minimum while controlling overfitting through the use of decoupled weight decay.		By repeatedly performing these steps, the AdamW optimizer effectively moves the parameters closer to the function's minimum while controlling overfitting through the use of decoupled weight decay.

Fall2024 Wiki Team8 at 22:39, 12 December 2024

2024-12-12T22:39:08Z

Fall2024 Wiki Team8 at 22:26, 12 December 2024

2024-12-12T22:26:01Z

← Older revision		Revision as of 18:26, 12 December 2024
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	== Introduction ==		== Introduction ==
	AdamW is an influential optimization algorithm in deep learning, developed as a modification to the [[Adam]] optimizer to decouple weight decay from gradient-based updates(Loshchilov & Hutter, 2017). This decoupling was introduced to address overfitting issues that often arise when using standard Adam, especially for large-scale neural network models.		AdamW is an influential optimization algorithm in deep learning, developed as a modification to the [[Adam]] optimizer to decouple weight decay from gradient-based updates<ref name="source1" />(Loshchilov & Hutter, 2017). This decoupling was introduced to address overfitting issues that often arise when using standard Adam, especially for large-scale neural network models.

	By applying weight decay separately from the adaptive updates of parameters, AdamW achieves more effective regularization while retaining Adam’s strengths, such as adaptive learning rates and computational efficiency. This characteristic enables AdamW to achieve superior convergence and generalization compared to its predecessor, making it particularly advantageous for complex tasks involving large transformer-based architectures like BERT and GPT (Devlin et al., 2019; Brown et al., 2020).		By applying weight decay separately from the adaptive updates of parameters, AdamW achieves more effective regularization while retaining Adam’s strengths, such as adaptive learning rates and computational efficiency. This characteristic enables AdamW to achieve superior convergence and generalization compared to its predecessor, making it particularly advantageous for complex tasks involving large transformer-based architectures like BERT and GPT (Devlin et al., 2019; Brown et al., 2020).
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	== Reference ==		== Reference ==

	# Brown, T. B., Mann, B., Ryder, N., Subbiah, M., et al. (2020). ''Language Models are Few-Shot Learners''. Advances in Neural Information Processing Systems (NeurIPS). https://arxiv.org/abs/2005.14165.		# Brown, T. B., Mann, B., Ryder, N., Subbiah, M., et al. (2020). ''Language Models are Few-Shot Learners''. Advances in Neural Information Processing Systems (NeurIPS). https://arxiv.org/abs/2005.14165. <ref name="source1">Source of the information.</ref>
	# Chen, X., Zhan, Y., Wu, W., Yang, Y., & Yang, Y. (2021). Improving Stock Movement Prediction with Adversarial Training and AdamW. ''IEEE Access'', 9, 25842–25850. https://doi.org/10.1109/ACCESS.2021.3057083.		# Chen, X., Zhan, Y., Wu, W., Yang, Y., & Yang, Y. (2021). Improving Stock Movement Prediction with Adversarial Training and AdamW. ''IEEE Access'', 9, 25842–25850. https://doi.org/10.1109/ACCESS.2021.3057083.
	# Devlin, J., Chang, M.-W., Lee, K., & Toutanova, K. (2019). ''BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding''. Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics (NAACL). https://arxiv.org/abs/1810.04805.		# Devlin, J., Chang, M.-W., Lee, K., & Toutanova, K. (2019). ''BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding''. Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics (NAACL). https://arxiv.org/abs/1810.04805.
	# Dosovitskiy, A., Beyer, L., Kolesnikov, A., et al. (2021). ''An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale''. International Conference on Learning Representations (ICLR). https://arxiv.org/abs/2010.11929.		# Dosovitskiy, A., Beyer, L., Kolesnikov, A., et al. (2021). ''An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale''. International Conference on Learning Representations (ICLR). https://arxiv.org/abs/2010.11929.
	# Loshchilov, I., & Hutter, F. (2017). ''Decoupled Weight Decay Regularization''. arXiv preprint arXiv:1711.05101. https://arxiv.org/abs/1711.05101.		# Loshchilov, I., & Hutter, F. (2017). ''Decoupled Weight Decay Regularization''. arXiv preprint arXiv:1711.05101. https://arxiv.org/abs/1711.05101.

Fall2024 Wiki Team8 at 22:17, 12 December 2024

2024-12-12T22:17:18Z

← Older revision		Revision as of 18:17, 12 December 2024
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	== Introduction ==		== Introduction ==
	AdamW is an influential optimization algorithm in deep learning, developed as a modification to the Adam optimizer to decouple weight decay from gradient-based ~~[https://arxiv.org/abs/2005.14165~~ updates] . This decoupling was introduced to address overfitting issues that often arise when using standard Adam, especially for large-scale neural network models.		AdamW is an influential optimization algorithm in deep learning, developed as a modification to the [[Adam]] optimizer to decouple weight decay from gradient-based updates(Loshchilov & Hutter, 2017). This decoupling was introduced to address overfitting issues that often arise when using standard Adam, especially for large-scale neural network models.

	By applying weight decay separately from the adaptive updates of parameters, AdamW achieves more effective regularization while retaining Adam’s strengths, such as adaptive learning rates and computational efficiency. This characteristic enables AdamW to achieve superior convergence and generalization compared to its predecessor, making it particularly advantageous for complex tasks involving large transformer-based architectures like BERT and GPT (Devlin et al., 2019; Brown et al., 2020).		By applying weight decay separately from the adaptive updates of parameters, AdamW achieves more effective regularization while retaining Adam’s strengths, such as adaptive learning rates and computational efficiency. This characteristic enables AdamW to achieve superior convergence and generalization compared to its predecessor, making it particularly advantageous for complex tasks involving large transformer-based architectures like BERT and GPT (Devlin et al., 2019; Brown et al., 2020).

Fall2024 Wiki Team8 at 21:54, 12 December 2024

2024-12-12T21:54:39Z

← Older revision		Revision as of 17:54, 12 December 2024
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	== Introduction ==		== Introduction ==
	AdamW is an influential optimization algorithm in deep learning, developed as a modification to the Adam optimizer to decouple weight decay from gradient-based updates ~~(Loshchilov & Hutter, 2017)~~. This decoupling was introduced to address overfitting issues that often arise when using standard Adam, especially for large-scale neural network models.		AdamW is an influential optimization algorithm in deep learning, developed as a modification to the Adam optimizer to decouple weight decay from gradient-based [https://arxiv.org/abs/2005.14165 updates] . This decoupling was introduced to address overfitting issues that often arise when using standard Adam, especially for large-scale neural network models.

	By applying weight decay separately from the adaptive updates of parameters, AdamW achieves more effective regularization while retaining Adam’s strengths, such as adaptive learning rates and computational efficiency. This characteristic enables AdamW to achieve superior convergence and generalization compared to its predecessor, making it particularly advantageous for complex tasks involving large transformer-based architectures like BERT and GPT (Devlin et al., 2019; Brown et al., 2020).		By applying weight decay separately from the adaptive updates of parameters, AdamW achieves more effective regularization while retaining Adam’s strengths, such as adaptive learning rates and computational efficiency. This characteristic enables AdamW to achieve superior convergence and generalization compared to its predecessor, making it particularly advantageous for complex tasks involving large transformer-based architectures like BERT and GPT (Devlin et al., 2019; Brown et al., 2020).

Fall2024 Wiki Team8: /* Reference */

2024-12-12T21:50:28Z

Reference

← Older revision		Revision as of 17:50, 12 December 2024
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	== Reference ==		== Reference ==

	* Brown, T. B., Mann, B., Ryder, N., Subbiah, M., et al. (2020). ''Language Models are Few-Shot Learners''. Advances in Neural Information Processing Systems (NeurIPS). https://arxiv.org/abs/2005.14165.		# Brown, T. B., Mann, B., Ryder, N., Subbiah, M., et al. (2020). ''Language Models are Few-Shot Learners''. Advances in Neural Information Processing Systems (NeurIPS). https://arxiv.org/abs/2005.14165.
	* Chen, X., Zhan, Y., Wu, W., Yang, Y., & Yang, Y. (2021). Improving Stock Movement Prediction with Adversarial Training and AdamW. ''IEEE Access'', 9, 25842–25850. https://doi.org/10.1109/ACCESS.2021.3057083.		# Chen, X., Zhan, Y., Wu, W., Yang, Y., & Yang, Y. (2021). Improving Stock Movement Prediction with Adversarial Training and AdamW. ''IEEE Access'', 9, 25842–25850. https://doi.org/10.1109/ACCESS.2021.3057083.
	* Devlin, J., Chang, M.-W., Lee, K., & Toutanova, K. (2019). ''BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding''. Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics (NAACL). https://arxiv.org/abs/1810.04805.		# Devlin, J., Chang, M.-W., Lee, K., & Toutanova, K. (2019). ''BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding''. Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics (NAACL). https://arxiv.org/abs/1810.04805.
	* Dosovitskiy, A., Beyer, L., Kolesnikov, A., et al. (2021). ''An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale''. International Conference on Learning Representations (ICLR). https://arxiv.org/abs/2010.11929.		# Dosovitskiy, A., Beyer, L., Kolesnikov, A., et al. (2021). ''An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale''. International Conference on Learning Representations (ICLR). https://arxiv.org/abs/2010.11929.
	* Loshchilov, I., & Hutter, F. (2017). ''Decoupled Weight Decay Regularization''. arXiv preprint arXiv:1711.05101. https://arxiv.org/abs/1711.05101.		# Loshchilov, I., & Hutter, F. (2017). ''Decoupled Weight Decay Regularization''. arXiv preprint arXiv:1711.05101. https://arxiv.org/abs/1711.05101.

Fall2024 Wiki Team8 at 21:43, 12 December 2024

2024-12-12T21:43:45Z

@@ Line 179: / Line 179: @@
 ==== Natural Language Processing (NLP) ====
 AdamW has been effectively employed in training large-scale transformer models like BERT and GPT. For BERT, improved downstream performance on NLP benchmarks has been reported compared to earlier optimizers (Devlin et al., 2019). Similarly, GPT-3’s training benefited from AdamW-like optimization for stable and efficient training (Brown et al., 2020).
 == Conclusion ==

Fall2024 Wiki Team8 at 21:42, 12 December 2024

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 AdamW is commonly used to optimize large-scale deep learning models in areas such as natural language processing (NLP), computer vision, reinforcement learning, and generative modeling (Devlin et al., 2019; Brown et al., 2020; Dosovitskiy et al., 2021).
-==== '''Natural Language Processing (NLP)''' ====
+==== Natural Language Processing (NLP) ====
 AdamW has been effectively employed in training large-scale transformer models like BERT and GPT. For BERT, improved downstream performance on NLP benchmarks has been reported compared to earlier optimizers (Devlin et al., 2019). Similarly, GPT-3’s training benefited from AdamW-like optimization for stable and efficient training (Brown et al., 2020).
 == Conclusion ==

Fall2024 Wiki Team8 at 21:41, 12 December 2024

2024-12-12T21:41:14Z

← Older revision		Revision as of 17:41, 12 December 2024
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	AdamW is commonly used to optimize large-scale deep learning models in areas such as natural language processing (NLP), computer vision, reinforcement learning, and generative modeling (Devlin et al., 2019; Brown et al., 2020; Dosovitskiy et al., 2021).		AdamW is commonly used to optimize large-scale deep learning models in areas such as natural language processing (NLP), computer vision, reinforcement learning, and generative modeling (Devlin et al., 2019; Brown et al., 2020; Dosovitskiy et al., 2021).

	==== '''Natural Language Processing (NLP):''' ====		==== '''Natural Language Processing (NLP)''' ====
	AdamW has been effectively employed in training large-scale transformer models like BERT and GPT. For BERT, improved downstream performance on NLP benchmarks has been reported compared to earlier optimizers (Devlin et al., 2019). Similarly, GPT-3’s training benefited from AdamW-like optimization for stable and efficient training (Brown et al., 2020).		AdamW has been effectively employed in training large-scale transformer models like BERT and GPT. For BERT, improved downstream performance on NLP benchmarks has been reported compared to earlier optimizers (Devlin et al., 2019). Similarly, GPT-3’s training benefited from AdamW-like optimization for stable and efficient training (Brown et al., 2020).

	==== '''Computer Vision:''' ====		==== '''Computer Vision''' ====
	Vision Transformers (ViT) utilize AdamW to achieve state-of-the-art results in image classification tasks. Training with AdamW improved top-1 accuracy on ImageNet compared to traditional optimizers, contributing to the success of ViT models (Dosovitskiy et al., 2021).		Vision Transformers (ViT) utilize AdamW to achieve state-of-the-art results in image classification tasks. Training with AdamW improved top-1 accuracy on ImageNet compared to traditional optimizers, contributing to the success of ViT models (Dosovitskiy et al., 2021).

	==== '''Reinforcement Learning:''' ====		==== '''Reinforcement Learning''' ====
	AdamW has been used in reinforcement learning scenarios where stable policy convergence is important. Empirical findings have demonstrated that AdamW leads to more predictable and stable training dynamics than standard Adam (Loshchilov & Hutter, 2017).		AdamW has been used in reinforcement learning scenarios where stable policy convergence is important. Empirical findings have demonstrated that AdamW leads to more predictable and stable training dynamics than standard Adam (Loshchilov & Hutter, 2017).

	==== '''Generative Models:''' ====		==== '''Generative Models''' ====
	Generative models, including variants of GANs and VAEs, benefit from AdamW’s improved regularization properties. Evaluations have indicated that AdamW can result in more stable training and improved generative quality (Loshchilov & Hutter, 2017).		Generative models, including variants of GANs and VAEs, benefit from AdamW’s improved regularization properties. Evaluations have indicated that AdamW can result in more stable training and improved generative quality (Loshchilov & Hutter, 2017).

	==== '''Time-Series Forecasting and Finance:''' ====		==== '''Time-Series Forecasting and Finance''' ====
	Financial applications, such as stock price prediction, have employed AdamW to enhance training stability and predictive performance of deep learning models. Empirical studies have reported lower validation errors and reduced overfitting when using AdamW compared to standard Adam (Chen et al., 2021).		Financial applications, such as stock price prediction, have employed AdamW to enhance training stability and predictive performance of deep learning models. Empirical studies have reported lower validation errors and reduced overfitting when using AdamW compared to standard Adam (Chen et al., 2021).

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	== Introduction ==		== Introduction ==
	AdamW is an influential optimization algorithm in deep learning, developed as a modification to the [[Adam]] optimizer to decouple weight decay from gradient-based updates<ref name="~~source1~~" />~~(Loshchilov & Hutter, 2017)~~. This decoupling was introduced to address overfitting issues that often arise when using standard Adam, especially for large-scale neural network models.		AdamW is an influential optimization algorithm in deep learning, developed as a modification to the [[Adam]] optimizer to decouple weight decay from gradient-based updates<ref name="source5" />. This decoupling was introduced to address overfitting issues that often arise when using standard Adam, especially for large-scale neural network models.

	By applying weight decay separately from the adaptive updates of parameters, AdamW achieves more effective regularization while retaining Adam’s strengths, such as adaptive learning rates and computational efficiency. This characteristic enables AdamW to achieve superior convergence and generalization compared to its predecessor, making it particularly advantageous for complex tasks involving large transformer-based architectures like BERT and GPT ~~(Devlin et al., 2019; Brown et al., 2020)~~.		By applying weight decay separately from the adaptive updates of parameters, AdamW achieves more effective regularization while retaining Adam’s strengths, such as adaptive learning rates and computational efficiency. This characteristic enables AdamW to achieve superior convergence and generalization compared to its predecessor, making it particularly advantageous for complex tasks involving large transformer-based architectures like BERT and GPT <ref name="source3" /><ref name="source1" />.

	As deep learning models grow in scale and complexity, AdamW has become a preferred optimizer due to its robust and stable convergence properties. Research has shown that AdamW can yield improved validation accuracy, faster convergence, and better generalization compared to both standard Adam and stochastic gradient descent (SGD) with momentum, especially in large-scale applications ~~(Loshchilov & Hutter, 2017; Devlin et al., 2019; Dosovitskiy et al., 2021)~~.		As deep learning models grow in scale and complexity, AdamW has become a preferred optimizer due to its robust and stable convergence properties. Research has shown that AdamW can yield improved validation accuracy, faster convergence, and better generalization compared to both standard Adam and stochastic gradient descent (SGD) with momentum, especially in large-scale applications<ref name="source5" /> <ref name="source3" /> <ref name="source4" />.

	== Algorithm Discussion ==		== Algorithm Discussion ==
	The standard Adam optimizer integrates weight decay by adding a term proportional to the parameters directly to the gradient, effectively acting as an L2 regularization term. This approach can interfere with Adam’s adaptive learning rates, leading to suboptimal convergence characteristics ~~(Loshchilov & Hutter, 2017)~~.		The standard Adam optimizer integrates weight decay by adding a term proportional to the parameters directly to the gradient, effectively acting as an L2 regularization term. This approach can interfere with Adam’s adaptive learning rates, leading to suboptimal convergence characteristics<ref name="source5" />.

	AdamW addresses this shortcoming by decoupling the weight decay step from the gradient-based parameter updates. Weight decay is applied after the parameter update is performed, preserving the integrity of the adaptive learning rate mechanism while maintaining effective regularization. This decoupling leads to more stable and predictable training dynamics, which is critical for large-scale models prone to overfitting ~~(Loshchilov & Hutter, 2017)~~.		AdamW addresses this shortcoming by decoupling the weight decay step from the gradient-based parameter updates. Weight decay is applied after the parameter update is performed, preserving the integrity of the adaptive learning rate mechanism while maintaining effective regularization. This decoupling leads to more stable and predictable training dynamics, which is critical for large-scale models prone to overfitting<ref name="source5" />.

	=== Algorithm Steps ===		=== Algorithm Steps ===
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	=== Areas of Application ===		=== Areas of Application ===
	AdamW is commonly used to optimize large-scale deep learning models in areas such as natural language processing (NLP), computer vision, reinforcement learning, and generative modeling ~~(Devlin et al., 2019; Brown et al., 2020; Dosovitskiy et al., 2021)~~.		AdamW is commonly used to optimize large-scale deep learning models in areas such as natural language processing (NLP), computer vision, reinforcement learning, and generative modeling<ref name="source3" /><ref name="source1" /><ref name="source4" />.

	==== Natural Language Processing (NLP) ====		==== Natural Language Processing (NLP) ====
	AdamW has been effectively employed in training large-scale transformer models like BERT and GPT. For BERT, improved downstream performance on NLP benchmarks has been reported compared to earlier optimizers ~~(Devlin et al., 2019)~~. Similarly, GPT-3’s training benefited from AdamW-like optimization for stable and efficient training ~~(Brown et al., 2020)~~.		AdamW has been effectively employed in training large-scale transformer models like BERT and GPT. For BERT, improved downstream performance on NLP benchmarks has been reported compared to earlier optimizers <ref name="source3" />. Similarly, GPT-3’s training benefited from AdamW-like optimization for stable and efficient training <ref name="source1" />.

	==== Computer Vision ====		==== Computer Vision ====
	Vision Transformers (ViT) utilize AdamW to achieve state-of-the-art results in image classification tasks. Training with AdamW improved top-1 accuracy on ImageNet compared to traditional optimizers, contributing to the success of ViT models ~~(Dosovitskiy et al., 2021)~~.		Vision Transformers (ViT) utilize AdamW to achieve state-of-the-art results in image classification tasks. Training with AdamW improved top-1 accuracy on ImageNet compared to traditional optimizers, contributing to the success of ViT models <ref name="source4" />.

	==== Reinforcement Learning ====		==== Reinforcement Learning ====
	AdamW has been used in reinforcement learning scenarios where stable policy convergence is important. Empirical findings have demonstrated that AdamW leads to more predictable and stable training dynamics than standard Adam ~~(Loshchilov & Hutter, 2017)~~.		AdamW has been used in reinforcement learning scenarios where stable policy convergence is important. Empirical findings have demonstrated that AdamW leads to more predictable and stable training dynamics than standard Adam<ref name="source5" />.

	==== Generative Models ====		==== Generative Models ====
	Generative models, including variants of GANs and VAEs, benefit from AdamW’s improved regularization properties. Evaluations have indicated that AdamW can result in more stable training and improved generative quality ~~(Loshchilov & Hutter, 2017)~~.		Generative models, including variants of GANs and VAEs, benefit from AdamW’s improved regularization properties. Evaluations have indicated that AdamW can result in more stable training and improved generative quality <ref name="source5" />.

	==== Time-Series Forecasting and Finance ====		==== Time-Series Forecasting and Finance ====
	Financial applications, such as stock price prediction, have employed AdamW to enhance training stability and predictive performance of deep learning models. Empirical studies have reported lower validation errors and reduced overfitting when using AdamW compared to standard Adam ~~(Chen et al., 2021)~~.		Financial applications, such as stock price prediction, have employed AdamW to enhance training stability and predictive performance of deep learning models. Empirical studies have reported lower validation errors and reduced overfitting when using AdamW compared to standard Adam<ref name="source2" />.

	=== Advantages over Other Approaches ===		=== Advantages over Other Approaches ===
	Quantitative studies have supported the superiority of AdamW over traditional Adam and other optimizers. The original AdamW paper demonstrated improved test accuracy and more stable validation losses ~~(Loshchilov & Hutter, 2017). Devlin et al~~. ~~(2019)~~ reported that AdamW contributed to BERT’s superior performance on the GLUE benchmark, and Dosovitskiy et al. ~~(2021)~~ showed that ViT models trained with AdamW achieved higher accuracy than models trained with classical optimizers like SGD with momentum.		Quantitative studies have supported the superiority of AdamW over traditional Adam and other optimizers. The original AdamW paper demonstrated improved test accuracy and more stable validation losses<ref name="source5" /><ref name="source3" />. reported that AdamW contributed to BERT’s superior performance on the GLUE benchmark, and Dosovitskiy et al<ref name="source4" />.showed that ViT models trained with AdamW achieved higher accuracy than models trained with classical optimizers like SGD with momentum.

	== Conclusion ==		== Conclusion ==
	AdamW is a highly effective optimization algorithm for training large-scale deep learning models. Its key innovation—decoupling weight decay from gradient-based parameter updates—preserves the adaptive learning rate mechanism, leading to improved generalization and stable convergence ~~(Loshchilov & Hutter, 2017)~~. These properties make AdamW well-suited for modern architectures, including transformer-based models in NLP and computer vision, as well as for applications in reinforcement learning, generative modeling, and time-series forecasting ~~(Devlin et al., 2019; Dosovitskiy et al., 2021; Chen et al., 2021)~~.		AdamW is a highly effective optimization algorithm for training large-scale deep learning models. Its key innovation—decoupling weight decay from gradient-based parameter updates—preserves the adaptive learning rate mechanism, leading to improved generalization and stable convergence <ref name="source5" />. These properties make AdamW well-suited for modern architectures, including transformer-based models in NLP and computer vision, as well as for applications in reinforcement learning, generative modeling, and time-series forecasting <ref name="source3" /> <ref name="source4" /> <ref name="source2" />.

	As deep learning continues to evolve, AdamW is likely to remain a critical tool. Future work may involve integrating AdamW with learning rate schedules, second-order optimization techniques, or further algorithmic refinements to improve efficiency and robustness under varied and challenging training conditions.		As deep learning continues to evolve, AdamW is likely to remain a critical tool. Future work may involve integrating AdamW with learning rate schedules, second-order optimization techniques, or further algorithmic refinements to improve efficiency and robustness under varied and challenging training conditions.
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	== Reference ==		== Reference ==

	# Brown, T. B., Mann, B., Ryder, N., Subbiah, M., et al. (2020). ''Language Models are Few-Shot Learners''. Advances in Neural Information Processing Systems (NeurIPS). https://arxiv.org/abs/2005.14165. <ref name="~~source1~~">~~Source of the information.</ref>~~		<ref name="source1">Brown, T. B., Mann, B., Ryder, N., Subbiah, M., et al. (2020). ''Language Models are Few-Shot Learners''. Advances in Neural Information Processing Systems (NeurIPS). https://arxiv.org/abs/2005.14165.</ref>
	# Chen, X., Zhan, Y., Wu, W., Yang, Y., & Yang, Y. (2021). Improving Stock Movement Prediction with Adversarial Training and AdamW. ''IEEE Access'', 9, 25842–25850. https://doi.org/10.1109/ACCESS.2021.3057083.		<ref name="source2">Chen, X., Zhan, Y., Wu, W., Yang, Y., & Yang, Y. (2021). Improving Stock Movement Prediction with Adversarial Training and AdamW. ''IEEE Access'', 9, 25842–25850. https://doi.org/10.1109/ACCESS.2021.3057083. </ref>
	# Devlin, J., Chang, M.-W., Lee, K., & Toutanova, K. (2019). ''BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding''. Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics (NAACL). https://arxiv.org/abs/1810.04805.		<ref name="source3">Devlin, J., Chang, M.-W., Lee, K., & Toutanova, K. (2019). ''BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding''. Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics (NAACL). https://arxiv.org/abs/1810.04805. </ref>
	# Dosovitskiy, A., Beyer, L., Kolesnikov, A., et al. (2021). ''An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale''. International Conference on Learning Representations (ICLR). https://arxiv.org/abs/2010.11929.		<ref name="source4">Dosovitskiy, A., Beyer, L., Kolesnikov, A., et al. (2021). ''An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale''. International Conference on Learning Representations (ICLR).https://arxiv.org/abs/2010.11929. </ref>
	# Loshchilov, I., & Hutter, F. (2017). ''Decoupled Weight Decay Regularization''. arXiv preprint arXiv:1711.05101. https://arxiv.org/abs/1711.05101.		<ref name="source5">Loshchilov, I., & Hutter, F. (2017). ''Decoupled Weight Decay Regularization''. arXiv preprint arXiv:1711.05101. https://arxiv.org/abs/1711.05101.</ref>