A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915061444902912 |
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| author | Mandal, Saptarshi Lin, Xiaojun Srikant, R. |
| author_facet | Mandal, Saptarshi Lin, Xiaojun Srikant, R. |
| contents | Knowledge distillation, where a small student model learns from a pre-trained large teacher model, has achieved substantial empirical success since the seminal work of \citep{hinton2015distilling}. Despite prior theoretical studies exploring the benefits of knowledge distillation, an important question remains unanswered: why does soft-label training from the teacher require significantly fewer neurons than directly training a small neural network with hard labels? To address this, we first present motivating experimental results using simple neural network models on a binary classification problem. These results demonstrate that soft-label training consistently outperforms hard-label training in accuracy, with the performance gap becoming more pronounced as the dataset becomes increasingly difficult to classify. We then substantiate these observations with a theoretical contribution based on two-layer neural network models. Specifically, we show that soft-label training using gradient descent requires only $O\left(\frac{1}{γ^2 ε}\right)$ neurons to achieve a classification loss averaged over epochs smaller than some $ε> 0$, where $γ$ is the separation margin of the limiting kernel. In contrast, hard-label training requires $O\left(\frac{1}{γ^4} \cdot \ln\left(\frac{1}ε\right)\right)$ neurons, as derived from an adapted version of the gradient descent analysis in \citep{ji2020polylogarithmic}. This implies that when $γ\leq ε$, i.e., when the dataset is challenging to classify, the neuron requirement for soft-label training can be significantly lower than that for hard-label training. Finally, we present experimental results on deep neural networks, further validating these theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09579 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks Mandal, Saptarshi Lin, Xiaojun Srikant, R. Machine Learning Artificial Intelligence 68T01 Knowledge distillation, where a small student model learns from a pre-trained large teacher model, has achieved substantial empirical success since the seminal work of \citep{hinton2015distilling}. Despite prior theoretical studies exploring the benefits of knowledge distillation, an important question remains unanswered: why does soft-label training from the teacher require significantly fewer neurons than directly training a small neural network with hard labels? To address this, we first present motivating experimental results using simple neural network models on a binary classification problem. These results demonstrate that soft-label training consistently outperforms hard-label training in accuracy, with the performance gap becoming more pronounced as the dataset becomes increasingly difficult to classify. We then substantiate these observations with a theoretical contribution based on two-layer neural network models. Specifically, we show that soft-label training using gradient descent requires only $O\left(\frac{1}{γ^2 ε}\right)$ neurons to achieve a classification loss averaged over epochs smaller than some $ε> 0$, where $γ$ is the separation margin of the limiting kernel. In contrast, hard-label training requires $O\left(\frac{1}{γ^4} \cdot \ln\left(\frac{1}ε\right)\right)$ neurons, as derived from an adapted version of the gradient descent analysis in \citep{ji2020polylogarithmic}. This implies that when $γ\leq ε$, i.e., when the dataset is challenging to classify, the neuron requirement for soft-label training can be significantly lower than that for hard-label training. Finally, we present experimental results on deep neural networks, further validating these theoretical findings. |
| title | A Theoretical Analysis of Soft-Label vs Hard-Label Training in Neural Networks |
| topic | Machine Learning Artificial Intelligence 68T01 |
| url | https://arxiv.org/abs/2412.09579 |