https://terms-en.ai-term-hub.com/zh/tags/math/Recent content in Math on 中文AI术语词典Hugozh-cnSat, 18 Jul 2026 11:44:45 +0000https://terms-en.ai-term-hub.com/zh/terms/tensor/Sat, 18 Jul 2026 11:35:54 +0000https://terms-en.ai-term-hub.com/zh/terms/tensor/<h2 id="definition">Definition</h2> <p>在计算机科学和深度学习中，张量是一种数学对象，它将标量、向量和矩阵推广到更高维度。它由其秩（维度数量）和形状等特征定义。</p> <h3 id="summary">Summary</h3> <p>一种多维数组，是深度学习框架中的基本数据结构。</p> <h2 id="key-concepts">Key Concepts</h2> <ul> <li>秩</li> <li>形状</li> <li>维度</li> <li>广播机制</li> </ul> <h2 id="use-cases">Use Cases</h2> <ul> <li>图像处理（4D张量）</li> <li>神经网络权重存储</li> <li>批量数据输入</li> </ul> <h2 id="code-example">Code Example</h2> <div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-python" data-lang="python"><span style="display:flex;"><span><span style="color:#f92672">import</span> torch </span></span><span style="display:flex;"><span>t <span style="color:#f92672">=</span> torch<span style="color:#f92672">.</span>tensor([[<span style="color:#ae81ff">1</span>, <span style="color:#ae81ff">2</span>], [<span style="color:#ae81ff">3</span>, <span style="color:#ae81ff">4</span>]]) </span></span></code></pre></div><h2 id="related-terms">Related Terms</h2> <ul> <li><a href="https://terms-en.ai-term-hub.com/en/terms/matrix-%E7%9F%A9%E9%98%B5/">Matrix (矩阵)</a></li> <li><a href="https://terms-en.ai-term-hub.com/en/terms/vector-%E5%90%91%E9%87%8F/">Vector (向量)</a></li> <li><a href="https://terms-en.ai-term-hub.com/en/terms/deep-learning-%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0/">Deep Learning (深度学习)</a></li> <li><a href="https://terms-en.ai-term-hub.com/en/terms/numpy-%E6%95%B0%E5%80%BC%E8%AE%A1%E7%AE%97%E5%BA%93/">NumPy (数值计算库)</a></li> </ul>https://terms-en.ai-term-hub.com/zh/terms/softmax/Sat, 18 Jul 2026 11:02:04 +0000https://terms-en.ai-term-hub.com/zh/terms/softmax/<h2 id="definition">Definition</h2> <p>Softmax 广泛用于多分类任务中神经网络的输出层。它接收原始对数几率（logits）向量并对其进行归一化，使每个元素代表一个概率值。</p> <h3 id="summary">Summary</h3> <p>一种数学函数，将任意实数值分数向量转换为概率分布。</p> <h2 id="key-concepts">Key Concepts</h2> <ul> <li>概率分布</li> <li>对数几率 (Logits)</li> <li>归一化</li> <li>多分类</li> </ul> <h2 id="use-cases">Use Cases</h2> <ul> <li>图像分类的输出层</li> <li>语言模型的词元预测</li> <li>多标签分类</li> </ul> <h2 id="code-example">Code Example</h2> <div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-python" data-lang="python"><span style="display:flex;"><span><span style="color:#f92672">import</span> torch </span></span><span style="display:flex;"><span><span style="color:#f92672">import</span> torch.nn.functional <span style="color:#66d9ef">as</span> F </span></span><span style="display:flex;"><span>logits <span style="color:#f92672">=</span> torch<span style="color:#f92672">.</span>tensor([<span style="color:#ae81ff">1.0</span>, <span style="color:#ae81ff">2.0</span>, <span style="color:#ae81ff">3.0</span>]) </span></span><span style="display:flex;"><span>probs <span style="color:#f92672">=</span> F<span style="color:#f92672">.</span>softmax(logits, dim<span style="color:#f92672">=</span><span style="color:#ae81ff">0</span>) </span></span><span style="display:flex;"><span>print(probs) </span></span></code></pre></div><h2 id="related-terms">Related Terms</h2> <ul> <li><a href="https://terms-en.ai-term-hub.com/en/terms/argmax-%E5%8F%96%E6%9C%80%E5%A4%A7%E5%80%BC%E7%B4%A2%E5%BC%95/">Argmax (取最大值索引)</a></li> <li><a href="https://terms-en.ai-term-hub.com/en/terms/%E4%BA%A4%E5%8F%89%E7%86%B5%E6%8D%9F%E5%A4%B1-cross-entropy-loss/">交叉熵损失 (Cross-Entropy Loss)</a></li> <li><a href="https://terms-en.ai-term-hub.com/en/terms/%E5%AF%B9%E6%95%B0%E5%87%A0%E7%8E%87-logits/">对数几率 (Logits)</a></li> <li><a href="https://terms-en.ai-term-hub.com/en/terms/%E7%A5%9E%E7%BB%8F%E7%BD%91%E7%BB%9C-neural-network/">神经网络 (Neural Network)</a></li> </ul>https://terms-en.ai-term-hub.com/zh/terms/high_dimensional/Sat, 18 Jul 2026 10:56:36 +0000https://terms-en.ai-term-hub.com/zh/terms/high_dimensional/<h2 id="definition">Definition</h2> <p>高维是指包含海量属性或特征的 dataset 或向量空间。在人工智能中，这常见于文本嵌入、图像像素或基因表达数据。虽然高维数据蕴含丰富信息，但也带来了“维度灾难”，即随着维度增加，数据变得极其稀疏，距离度量失效，且计算复杂度急剧上升。</p> <h3 id="summary">Summary</h3> <p>描述具有大量特征或维度的数据空间，通常导致稀疏性和计算挑战。</p> <h2 id="key-concepts">Key Concepts</h2> <ul> <li>维度灾难</li> <li>特征空间</li> <li>稀疏性</li> <li>降维</li> </ul> <h2 id="use-cases">Use Cases</h2> <ul> <li>自然语言处理（词嵌入）</li> <li>计算机视觉（像素数组）</li> <li>推荐系统</li> </ul> <h2 id="related-terms">Related Terms</h2> <ul> <li><a href="https://terms-en.ai-term-hub.com/en/terms/embedding-%E5%B5%8C%E5%85%A5/">embedding (嵌入)</a></li> <li><a href="https://terms-en.ai-term-hub.com/en/terms/pca-%E4%B8%BB%E6%88%90%E5%88%86%E5%88%86%E6%9E%90/">PCA (主成分分析)</a></li> <li><a href="https://terms-en.ai-term-hub.com/en/terms/sparsity-%E7%A8%80%E7%96%8F%E6%80%A7/">sparsity (稀疏性)</a></li> <li><a href="https://terms-en.ai-term-hub.com/en/terms/feature_engineering-%E7%89%B9%E5%BE%81%E5%B7%A5%E7%A8%8B/">feature_engineering (特征工程)</a></li> </ul>https://terms-en.ai-term-hub.com/zh/terms/first_order/Sat, 18 Jul 2026 10:56:36 +0000https://terms-en.ai-term-hub.com/zh/terms/first_order/<h2 id="definition">Definition</h2> <p>在人工智能和数学中，“一阶”通常描述不涉及高阶交互的直接、线性关系系统或操作。在优化领域，它指的是仅利用目标函数的一阶导数（梯度）信息来寻找极值的方法，例如梯度下降法。与二阶方法相比，一阶方法计算成本较低，但收敛速度可能较慢。</p> <h3 id="summary">Summary</h3> <p>指涉及直接关系或线性近似概念，如一阶逻辑或一阶导数。</p> <h2 id="key-concepts">Key Concepts</h2> <ul> <li>梯度下降</li> <li>一阶逻辑</li> <li>线性近似</li> <li>导数</li> </ul> <h2 id="use-cases">Use Cases</h2> <ul> <li>通过反向传播训练神经网络</li> <li>符号AI中的知识表示</li> <li>如随机梯度下降（SGD）等优化算法</li> </ul> <h2 id="related-terms">Related Terms</h2> <ul> <li><a href="https://terms-en.ai-term-hub.com/en/terms/second-order-%E4%BA%8C%E9%98%B6/">second-order (二阶)</a></li> <li><a href="https://terms-en.ai-term-hub.com/en/terms/gradient-%E6%A2%AF%E5%BA%A6/">gradient (梯度)</a></li> <li><a href="https://terms-en.ai-term-hub.com/en/terms/logic-%E9%80%BB%E8%BE%91/">logic (逻辑)</a></li> <li><a href="https://terms-en.ai-term-hub.com/en/terms/optimization-%E4%BC%98%E5%8C%96/">optimization (优化)</a></li> </ul>