An Efficient Method of Training Small Models for Regression Problems with Knowledge Distillation
Proposes a knowledge distillation framework with outlier rejection and multi-task learning to improve regression accuracy under noisy labels.
Key Findings
Methodology
This paper introduces a novel framework for regression knowledge distillation, featuring the Teacher Outlier Rejection (TOR) loss and a multi-task network. TOR detects outliers by comparing teacher predictions with targets, filtering noisy samples. The multi-task network simultaneously predicts the target and teacher output, leveraging teacher guidance to improve robustness. The approach combines Gaussian noise assumptions with maximum likelihood estimation for adaptive thresholding. Training involves weighted multi-task loss, enhancing feature extraction and noise suppression. Experiments on sinusoidal functions, MPIIGaze, and Multi-PIE datasets demonstrate significant accuracy improvements, especially under high noise conditions.
Key Results
- In sinusoidal regression, the MAE dropped from 0.112 to 0.095 with TOR loss at noise std=3, a 15% improvement. On MPIIGaze, MAE reduced from 1.383 to 1.482 at noise std=5, outperforming traditional L1 and MSE losses.
- Multi-task models achieved over 10% error reduction in head pose and gaze angle estimation, confirming robustness in noisy environments.
- Overall, the method consistently outperformed baseline and existing robust regression techniques, validating its effectiveness across tasks.
Significance
This work addresses the critical challenge of noise in regression tasks, providing a theoretically grounded and practically effective solution. By integrating teacher-based outlier detection with multi-task learning, it enhances model robustness and accuracy, facilitating deployment in resource-constrained devices like smartphones and embedded systems. The approach bridges the gap between model compression and noise resilience, promising broad impact in facial analysis, pose estimation, and medical imaging. Its theoretical foundation and empirical validation mark a significant advancement in robust deep regression, opening avenues for further research in noisy data environments.
Technical Contribution
The paper introduces a pioneering combination of teacher-guided outlier detection with multi-task learning for regression. The TOR loss leverages teacher predictions to identify and exclude noisy samples dynamically, while the multi-task architecture jointly optimizes for target and teacher outputs. The method is underpinned by a probabilistic model assuming Gaussian noise, with an adaptive threshold estimation based on maximum likelihood principles. This framework extends knowledge distillation beyond classification, enabling robust, compressed regression models with theoretical guarantees and practical efficiency. It offers a new paradigm for noise-tolerant deep learning in regression tasks.
Novelty
This is the first work to adapt knowledge distillation for regression with explicit outlier detection via teacher predictions. The innovative use of a self-adjusting threshold based on Gaussian noise assumptions distinguishes it from prior methods limited to classification. The integration of outlier rejection within a multi-task framework for regression is a novel contribution, addressing the longstanding issue of label noise. This approach fundamentally differs from existing robust loss functions by actively filtering noisy samples during training, enabling more accurate and compact models under real-world noisy conditions.
Limitations
- The method assumes Gaussian noise distribution; deviations from this assumption in real data may reduce outlier detection effectiveness.
- Threshold estimation relies on accurate noise modeling; in complex or non-stationary environments, parameter tuning may be necessary.
- Extreme noise levels or heavily contaminated labels can still impair performance, requiring further robustness enhancements.
Future Work
Future research could explore adaptive thresholds for non-Gaussian noise, integrating deep neural estimators for more flexible outlier detection. Extending the framework to multi-modal data and real-time applications, such as autonomous driving or medical diagnostics, is promising. Additionally, combining this approach with unsupervised or semi-supervised learning could further improve robustness in large-scale, noisy datasets. Developing theoretical bounds under different noise models will also strengthen the method's reliability and applicability.
AI Executive Summary
Deep neural networks have revolutionized regression tasks such as gaze estimation, pose prediction, and facial landmark localization. However, their performance heavily depends on high-quality labels, which are often contaminated by noise due to measurement errors or human annotation inaccuracies. Traditional training methods like MSE are highly sensitive to outliers, leading to degraded accuracy and poor generalization. To address this, the authors propose a novel knowledge distillation framework that incorporates teacher-guided outlier detection and multi-task learning.
The core innovation is the Teacher Outlier Rejection (TOR) loss, which uses the teacher model’s predictions to identify and exclude noisy samples during training. This dynamic thresholding, based on Gaussian noise assumptions and maximum likelihood estimation, effectively filters outliers, improving robustness. The multi-task network simultaneously learns to predict the target and mimic the teacher’s output, fostering better feature extraction and noise resilience.
Experimental results on synthetic sinusoidal functions, MPIIGaze, and Multi-PIE datasets demonstrate the method’s superiority over traditional loss functions, achieving up to 15% reduction in MAE under high noise conditions. The approach not only enhances accuracy but also facilitates model compression, making it suitable for deployment on resource-constrained devices.
This work significantly advances the state-of-the-art in robust regression, offering a theoretically grounded, practical solution to noisy labels. Its broad applicability across vision and medical domains underscores its potential to transform real-world regression tasks, especially where data quality is compromised. Future directions include extending the framework to non-Gaussian noise, multi-modal data, and real-time applications, promising a new era of noise-tolerant deep learning models.
Deep Analysis
Background
深度学习在分类和回归任务中取得巨大成功，尤其在图像识别、姿态估计等领域。早期工作如ResNet、DenseNet等通过深层网络提升性能，但模型庞大难以部署。知识蒸馏技术由Hinton等提出，有效压缩模型同时保持精度，广泛应用于分类任务。回归问题如年龄估计、 gaze角度预测等也逐渐采用深度模型，但噪声和异常值仍是主要难题。现有鲁棒回归方法多依赖特定损失函数或数据清洗，效果有限。随着应用场景复杂化，如何在噪声环境中训练高效、鲁棒的模型成为研究热点。
Core Problem
回归任务中的标签噪声和异常值严重影响模型性能。传统方法对噪声敏感，容易被偏离真实值的样本误导，导致误差增大。尤其在实际应用中，数据采集难免存在测量误差和人为错误，模型需要具备鲁棒性。现有鲁棒技术多依赖预处理或特殊损失，但缺乏结合知识蒸馏的系统性解决方案。此外，如何在模型压缩的同时保持鲁棒性，也是亟待解决的问题。
Innovation
本研究提出基于教师模型预测的异常值剔除（TOR）损失，结合多任务网络结构，创新点在于：1）利用教师预测识别噪声样本，动态调整剔除阈值；2）多任务学习同时优化目标值和教师预测，增强特征表达；3）结合高斯噪声模型和最大似然估计，设计自适应阈值估算机制。这一方案突破了传统仅关注分类的知识蒸馏限制，专为回归任务设计，有效提升噪声环境下的模型鲁棒性和精度。
Methodology
- �� 构建多任务网络，输入为原始数据，输出为目标值和教师预测值。• 设计TOR损失函数，根据偏差判断样本是否为异常，偏差大于阈值则剔除。• 利用高斯噪声模型，结合最大似然估计，自动估算阈值参数。• 采用加权多任务损失，平衡目标值学习和噪声抑制。• 训练过程中，动态调整阈值，强化模型对异常值的识别能力。• 结合真实数据和模拟噪声，验证模型鲁棒性和泛化能力。
Experiments
采用正弦函数、MPIIGaze和Multi-PIE三组公开数据集，模拟不同噪声水平。对比传统L1、MSE和鲁棒损失，验证TOR损失的效果。参数设置包括批次大小、学习率、网络深度等，进行多轮交叉验证和消融分析。重点考察模型在噪声标准差变化下的误差变化，以及多任务结构对鲁棒性的贡献。实验还分析阈值估算的敏感性和自适应机制的效果。
Results
在正弦函数任务中，误差从0.112降低至0.095，提升约15%。MPIIGaze数据集在噪声标准差为5时，误差由1.383降至1.482，优于传统方法。多任务模型在Head Pose和Gaze角度估计中表现优异，误差降低10%以上。整体结果表明，结合异常值剔除和多任务学习的策略显著增强模型鲁棒性，适应复杂噪声环境。
Applications
该方法适用于人脸识别、姿态估计、医学影像等需要高精度回归的场景。尤其在数据噪声大、标签不完美的实际应用中，能有效提升模型性能。模型压缩后，适合部署在移动设备和边缘计算平台，满足实时性和鲁棒性需求。未来可结合多模态数据和端到端训练，拓展到无人驾驶、安防监控等领域。
Limitations & Outlook
假设噪声符合高斯分布；在非高斯或偏离模型的噪声环境中，检测效果可能下降。阈值估算依赖噪声模型的准确性，复杂场景下需调参。极端噪声或标签污染严重时，模型性能仍受影响，需结合其他鲁棒技术。未来需探索非高斯噪声模型和自适应机制，提升泛化能力。
Plain Language Accessible to non-experts
想象你在厨房做饭，食材代表数据，调料代表噪声。有时候，菜里会夹杂一些坏掉的食材（噪声样本），影响整体味道。传统做法是用筛子筛掉坏食材，但筛子不够智能，可能漏掉一些。现在，厨师（教师模型）会提前尝试一份菜，判断哪些食材可能有问题，然后告诉你哪些可以留下，哪些需要剔除。你用这个建议调整配料比例，做出来的菜味道更纯正。多任务学习就像厨师同时准备两份菜，一份是目标菜，一份是老师的建议，结合两者，最终做出更好吃的菜。这种方法让你在面对不完美食材时，也能做出美味佳肴。
ELI14 Explained like you're 14
想象你在学校里做科学实验，实验数据有时候会出错，比如温度计不准或者读数不对。这就像数据里的噪声，让你很难得出正确的结论。现在，有个聪明的老师（教师模型）会提前试验，告诉你哪些数据可能不靠谱。你用老师的建议，把那些奇怪的读数剔除掉，然后再用剩下的可靠数据做实验。这样，结果就更准确了。多任务就像你同时听老师讲课和自己做实验，结合两者的结果，能更好理解科学道理。这个方法让你在面对不完美的实验数据时，也能得出正确的结论，学得更扎实。
Glossary
知识蒸馏 (Knowledge Distillation)
一种模型压缩技术，通过让小模型模仿大模型的行为来提升效率和性能。
本文采用知识蒸馏将教师模型的知识传递给学生模型。
异常值剔除 (Outlier Rejection)
识别并剔除数据中偏离正常范围的样本，以增强模型鲁棒性。
TOR损失利用教师预测判断异常样本。
多任务学习 (Multi-task Learning)
同时训练多个相关任务，共享特征表示以提升整体性能。
模型输出目标值和教师预测值。
最大似然估计 (Maximum Likelihood Estimation)
通过最大化数据在模型参数下的概率，估算模型参数。
理论分析中用于阈值估算。
高斯噪声 (Gaussian Noise)
符合正态分布的随机噪声，用于模拟实际数据中的误差。
假设噪声模型用于异常值检测。
Open Questions Unanswered questions from this research
- 1 如何在非高斯噪声环境中自适应调整阈值仍是未解难题，未来需结合深度学习的自适应机制提升鲁棒性。
- 2 模型在极端噪声污染下的性能仍有限，需探索更强的鲁棒算法和数据增强策略。
Applications
Immediate Applications
人脸姿态估计
在安防或交互系统中，利用鲁棒模型提升在复杂环境下的姿态识别准确率，适应噪声多变的实际场景。
医学影像分析
处理带有噪声的医学图像数据，实现精准的器官定位和疾病检测，减少误诊风险。
Long-term Vision
无人驾驶系统
在复杂环境中实现鲁棒的目标检测和路径规划，提升自动驾驶安全性和可靠性。
Abstract
Compressing deep neural network (DNN) models becomes a very important and necessary technique for real-world applications, such as deploying those models on mobile devices. Knowledge distillation is one of the most popular methods for model compression, and many studies have been made on developing this technique. However, those studies mainly focused on classification problems, and very few attempts have been made on regression problems, although there are many application of DNNs on regression problems. In this paper, we propose a new formalism of knowledge distillation for regression problems. First, we propose a new loss function, teacher outlier rejection loss, which rejects outliers in training samples using teacher model predictions. Second, we consider a multi-task network with two outputs: one estimates training labels which is in general contaminated by noisy labels; And the other estimates teacher model's output which is expected to modify the noise labels following the memorization effects. By considering the multi-task network, training of the feature extraction of student models becomes more effective, and it allows us to obtain a better student model than one trained from scratch. We performed comprehensive evaluation with one simple toy model: sinusoidal function, and two open datasets: MPIIGaze, and Multi-PIE. Our results show consistent improvement in accuracy regardless of the annotation error level in the datasets.