Curvature-Learning-Framework 教程

Curvature-Learning-Framework 教程

Curvature-Learning-FrameworkCurvlearn, a Tensorflow based non-Euclidean deep learning framework.项目地址:https://gitcode.com/gh_mirrors/cu/Curvature-Learning-Framework

1. 项目介绍

Curvature-Learning-Framework 是一个由阿里巴巴妈妈技术团队研发的非欧几里得深度学习框架。它基于 TensorFlow 实现,设计目标是使得在非欧空间中训练深度学习模型变得方便易用。CurvLearn 提供了多种非欧流形、算子和黎曼优化器,支持大规模分布式训练,并已经在阿里的推荐系统等多个关键业务场景中落地,表现出优于欧几里得空间的效果。

2. 项目快速启动

安装依赖

确保你已经安装了 Python 和 TensorFlow。然后通过 pip 来安装 CurvLearn:

pip install tensorflow
git clone https://github.com/alibaba/Curvature-Learning-Framework.git
cd Curvature-Learning-Framework
pip install .

快速示例

以下是一个简单的示例,展示了如何在双曲空间中初始化并操作张量:

import tensorflow as tf
from curvlearn.manifolds import PoincareBall

manifold = PoincareBall()
x = tf.random.uniform(shape=(2, 3), minval=-0.99, maxval=0.99)
y = manifold.expmap(x, tf.zeros_like(x))  # 在双曲空间中进行指数映射

print("双曲张量:", y)

运行以上代码,你将在控制台看到双曲空间中的张量值。

3. 应用案例和最佳实践

在实际应用中,例如商品类别树的嵌入,CurvLearn 可以帮助更好地表示层次关系。以下是一份简化的步骤:

# 创建商品类别树的嵌入
category_tree = ...
embedding_model = CurvLearnModel(category_tree.size())  # 根据类别数量创建模型
embedding_model.compile(optimizer='curvadam')  # 使用曲率优化器
embedding_model.fit(category_tree.data, epochs=10)  # 训练模型

# 获取商品类别的双曲嵌入
category_embeddings = embedding_model.predict(category_tree.data)

请注意,这只是一个基础示例,实际应用可能涉及更复杂的模型结构和训练策略。

4. 典型生态项目

CurvLearn 融合到阿里巴巴内部的分布式训练引擎,如 Euler 和 x-deeplearning 中。此外,它还与 TensorFlow 生态兼容,开发者可以通过 CurvLearn 扩展 TensorFlow 的功能来探索非欧几里得空间的学习方法。尽管如此,目前尚未有公开的第三方库或工具直接与 CurvLearn 集成。


本教程提供了 CurvLearn 基础知识及快速入手指南。更多详细信息和高级用法可参考项目官方文档。如果你在使用过程中遇到问题或者想要贡献代码,欢迎访问 GitHub 仓库 查看更新和提交 issue。

Curvature-Learning-FrameworkCurvlearn, a Tensorflow based non-Euclidean deep learning framework.项目地址:https://gitcode.com/gh_mirrors/cu/Curvature-Learning-Framework

创作声明:本文部分内容由AI辅助生成(AIGC),仅供参考

### Hessian Matrix Pruning in Machine Learning Techniques and Implementation In the context of machine learning, particularly within optimization algorithms used during training neural networks or other models, the Hessian matrix plays a critical role. This square matrix contains all second-order partial derivatives of a function, which can provide valuable information about local curvature around points on an error surface. #### Understanding Hessian-Based Pruning Pruning based on the Hessian involves identifying less important parameters by analyzing their impact through this matrix's eigenvalues and eigenvectors. Parameters associated with smaller absolute values tend to have lesser influence over model performance; hence they are candidates for removal without significantly affecting accuracy[^1]. For instance, when considering weight matrices W in deep learning architectures: - Compute the full Hessian \( \mathbf{H} \). - Diagonalize it into its spectral decomposition form. ```python import numpy as np # Assuming we already computed the Hessian matrix 'hessian' evals, evecs = np.linalg.eigh(hessian) ``` - Analyze each parameter’s contribution via corresponding eigenvalue magnitude. - Set thresholds according to desired sparsity level. - Zero out weights linked to insignificant contributions (smaller than threshold). This process effectively reduces redundancy while maintaining essential features necessary for optimal functioning[^2]. However, direct computation becomes computationally expensive due to high dimensionality involved especially in large-scale problems like those encountered using deeplearning4j framework mentioned earlier . Therefore alternative strategies such as approximations must be considered where applicable. One common approximation method is diagonalizing only parts of the overall structure rather than computing every single element explicitly – thus reducing complexity from O(n³) down towards more manageable levels depending upon specific implementations chosen. Another approach could involve leveraging low-rank updates that allow incremental adjustments instead of recalculating entire structures repeatedly throughout iterative processes commonly found within stochastic gradient descent variants utilized extensively across various applications including but not limited to computer vision tasks involving monocular depth estimation under self-supervised settings described previously .
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