From e30934c198997de308a239097fafc8006174a388 Mon Sep 17 00:00:00 2001 From: Lbruh Date: Sat, 31 Oct 2026 20:49:39 +0800 Subject: [PATCH] feat: init my blog --- .github/workflows/deploy.yml | 64 +++++ .gitignore | 4 + .gitmodules | 3 + archetypes/default.md | 5 + assets/css/extended/custom.css | 116 +++++++++ content/archives.md | 6 + content/posts/LSTM/index.md | 404 ++++++++++++++++++++++++++++++ content/posts/first/001.png | Bin 0 -> 598064 bytes content/posts/first/index.md | 11 + content/posts/second.md | 8 + content/search.md | 7 + hugo.toml | 72 ++++++ layouts/partials/extend_head.html | 18 ++ themes/PaperMod | 1 + 14 files changed, 719 insertions(+) create mode 100644 .github/workflows/deploy.yml create mode 100644 .gitignore create mode 100644 .gitmodules create mode 100644 archetypes/default.md create mode 100644 assets/css/extended/custom.css create mode 100644 content/archives.md create mode 100644 content/posts/LSTM/index.md create mode 100644 content/posts/first/001.png create mode 100644 content/posts/first/index.md create mode 100644 content/posts/second.md create mode 100644 content/search.md create mode 100644 hugo.toml create mode 100644 layouts/partials/extend_head.html create mode 160000 themes/PaperMod diff --git a/.github/workflows/deploy.yml b/.github/workflows/deploy.yml new file mode 100644 index 0000000..6b0b5d4 --- /dev/null +++ b/.github/workflows/deploy.yml @@ -0,0 +1,64 @@ +name: Hugo Blog + +on: + push: + branches: + - main + - master + workflow_dispatch: + +permissions: + contents: read + pages: write + id-token: write + +concurrency: + group: "pages" + cancel-in-progress: false + +defaults: + run: + shell: bash + +jobs: + build: + runs-on: ubuntu-latest + env: + HUGO_VERSION: 0.140.0 + steps: + - name: Install Hugo CLI + run: | + wget -O ${{ runner.temp }}/hugo.deb https://github.com/gohugoio/hugo/releases/download/v${HUGO_VERSION}/hugo_extended_${HUGO_VERSION}_linux-amd64.deb \ + && sudo dpkg -i ${{ runner.temp }}/hugo.deb + - name: Checkout + uses: actions/checkout@v4 + with: + submodules: recursive + fetch-depth: 0 + - name: Setup Pages + id: pages + uses: actions/configure-pages@v5 + - name: Build with Hugo + env: + HUGO_CACHEDIR: ${{ runner.temp }}/hugo_cache + HUGO_ENVIRONMENT: production + run: | + hugo \ + --gc \ + --minify \ + --baseURL "${{ steps.pages.outputs.base_url }}/" + - name: Upload artifact + uses: actions/upload-pages-artifact@v3 + with: + path: ./public + + deploy: + environment: + name: github-pages + url: ${{ steps.deployment.outputs.page_url }} + runs-on: ubuntu-latest + needs: build + steps: + - name: Deploy to GitHub Pages + id: deployment + uses: actions/deploy-pages@v4 diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..1204b85 --- /dev/null +++ b/.gitignore @@ -0,0 +1,4 @@ +# Hugo build directory +public/ +resources/_gen/ +.hugo_build.lock diff --git a/.gitmodules b/.gitmodules new file mode 100644 index 0000000..89af1b0 --- /dev/null +++ b/.gitmodules @@ -0,0 +1,3 @@ +[submodule "themes/PaperMod"] + path = themes/PaperMod + url = https://github.com/adityatelange/hugo-PaperMod.git diff --git a/archetypes/default.md b/archetypes/default.md new file mode 100644 index 0000000..25b6752 --- /dev/null +++ b/archetypes/default.md @@ -0,0 +1,5 @@ ++++ +date = '{{ .Date }}' +draft = true +title = '{{ replace .File.ContentBaseName "-" " " | title }}' ++++ diff --git a/assets/css/extended/custom.css b/assets/css/extended/custom.css new file mode 100644 index 0000000..c7138d5 --- /dev/null +++ b/assets/css/extended/custom.css @@ -0,0 +1,116 @@ +/* 列表页的背景与文章页不同,导航栏跟随当前页面配色。 */ +.list { + --nav-background: var(--code-bg); +} + +[data-theme="dark"] .list { + --nav-background: var(--theme); +} + +/* 窄屏时整栏吸顶;宽屏时仅站名与主题按钮固定在正文左侧。 */ +.header { + position: sticky; + top: 0; + z-index: 10; + background: var(--nav-background, var(--theme)); +} + +.header-nav { + max-width: calc(var(--nav-width) + var(--gap) * 2); + align-items: center; +} + +.logo { + flex-wrap: nowrap; + min-height: var(--header-height); +} + +.logo a { + font-size: 24px; + font-weight: 700; + white-space: nowrap; +} + +.logo-switches { + align-items: center; + min-height: 0; + flex-wrap: nowrap; +} + +#theme-toggle { + display: inline-flex; + align-items: center; + justify-content: center; + flex-shrink: 0; + min-height: 44px; + line-height: 1; +} + +#theme-toggle svg { + width: 24px; + height: 24px; + flex-shrink: 0; +} + +.menu a { + font-size: 16px; +} + +@media (min-width: 1200px) { + .header { + position: static; + } + + .header-nav { + justify-content: flex-end; + } + + .logo { + position: fixed; + top: 0; + right: calc((100% + var(--main-width)) / 2 + var(--gap)); + z-index: 10; + background: var(--nav-background, var(--theme)); + } +} + +@media (max-width: 599px) { + .header-nav { + column-gap: 12px; + } + + .menu { + max-width: 100%; + column-gap: 16px; + } +} + +/* 锚点跳转时为窄屏吸顶导航留出空间(菜单可能换到第二行)。 */ +@media (max-width: 1199px) { + html { + scroll-padding-top: calc(var(--header-height) * 2 + var(--gap)); + } +} + +/* 控制首页欢迎模块(Home-Info)与上下元素的距离 */ +.first-entry.home-info { + /* 1. 取消主题默认的 320px 最小高度限制,让上下间距完全由 margin 控制 */ + min-height: auto; + + /* 2. 与上方导航栏的距离(默认约为 24px,数值越大离导航栏越远) */ + margin-top: 40px; + + /* 3. 与下方第一篇文章的距离(默认约为 48px,数值越小文章越往上靠) */ + margin-bottom: 40px; + + /* 4. 欢迎模块内部上下的内边距(按需保留或设为 0) */ + padding-top: 10px; + padding-bottom: 10px; +} + +/* 数学公式排版优化:确保超长公式可平滑横向滚动,不溢出容器 */ +.katex-display { + overflow-x: auto; + overflow-y: hidden; + padding: 0.5rem 0; +} diff --git a/content/archives.md b/content/archives.md new file mode 100644 index 0000000..8e3d941 --- /dev/null +++ b/content/archives.md @@ -0,0 +1,6 @@ ++++ +title = 'Archive' +layout = 'archives' +url = '/archive/' +summary = 'archives' ++++ \ No newline at end of file diff --git a/content/posts/LSTM/index.md b/content/posts/LSTM/index.md new file mode 100644 index 0000000..54ef47a --- /dev/null +++ b/content/posts/LSTM/index.md @@ -0,0 +1,404 @@ ++++ +title = 'Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling' +date = 2026-01-14T07:07:07+01:00 +draft = false +tags = ['Test'] ++++ + +> **论文信息:** +> +> - **标题:** Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling(门控循环神经网络在序列建模上的实证评估) +> - **作者:** Junyoung Chung(郑浚英), Caglar Gulcehre, KyungHyun Cho(曹敬铉,GRU 主要发明人), Yoshua Bengio(深度学习三巨头之一,图灵奖得主) +> - **机构:** 蒙特利尔大学(Université de Montréal)与 CIFAR +> - **发表:** NIPS 2014 Deep Learning and Representation Learning Workshop (arXiv:1412.3555) +> - **开源代码:** [https://github.com/jych/librnn.git](https://github.com/jych/librnn.git) +> - **核心问题:** 相比传统无门控的 RNN,门控循环单元(LSTM 与 GRU)为什么具有决定性优势?在控制相同参数量的前提下,LSTM 与 GRU 到底谁的表现更好、收敛更快? + +--- + +## 一、研究背景与论文核心定位 + +### 1.1 历史背景:门控单元的崛起 + +2014 年前后,循环神经网络(RNN)在变长序列建模任务中迎来了爆发性突破: + +- **机器翻译(Machine Translation):** Sutskever 等人(Seq2Seq)与 Bahdanau、Cho 等人(Attention 机制)先后证明 RNN 可以达到甚至超越基于统计的传统翻译系统。 +- **语音识别(Speech Recognition):** Graves 等人将深度双向 LSTM 成功应用于大规模端到端语音识别。 + +然而作者敏锐地发现:**上述突破无一例外均未使用传统标准的 Vanilla RNN(基于 tanh 的简单循环单元),而是依赖带有门控机制的高级单元(LSTM 或最新提出的 GRU)。** + +### 1.2 核心研究动机与痛点 + +1. **理论与实践脱节:** LSTM(1997)早已确立了在捕捉长距离依赖中的统治地位;而 GRU(2014)刚由 Cho 等人提出用于神经机器翻译(NMT)。当时学术界并不知道:**GRU 的优秀表现究竟只是机器翻译特定任务的巧合,还是它在更通用的序列建模上本身就能与 LSTM 匹敌?** +2. **缺乏公平的受控对照(Controlled Benchmark):** GRU 的结构比 LSTM 更为紧凑(参数量约少 25%~33%)。以往研究往往直接指定相同隐藏单元数进行测试,这导致两者的模型参数总量不对等。 +3. **论文核心定位:** + +> **在严格控制网络总参数量基本一致的前提下,首个在多个代表性序列建模任务(包括离散复调音乐建模与极其严苛的长序列连续原始语音建模)上,对传统 tanh-RNN、LSTM、GRU 展开系统性实证评估与内部机制对比的研究。** + +--- + +## 二、Section 2 — 自回归序列建模与 RNN 背景 + +### 2.1 生成式自回归序列建模(Generative Sequence Modeling) + +本论文研究的核心任务是**序列生成建模(Sequence Modeling)**。给定长度为 $T$ 的可变长序列 $\mathbf{x} = (x_1, x_2, \dots, x_T)$,目标是学习其联合概率分布 $p(\mathbf{x})$。 + +根据概率链式法则,序列的联合概率可分解为条件概率的连乘积:$$p(x_1, x_2, \dots, x_T) = p(x_1) p(x_2 \mid x_1) p(x_3 \mid x_1, x_2) \cdots p(x_T \mid x_1, \dots, x_{T-1}) = \prod_{t=1}^T p(x_t \mid x_1, \dots, x_{t-1})$$ + +在时间步 $t$,模型利用历史信息预测当前元素 $x_t$。若输入为可变长序列,通常在末尾追加特殊的终止符(End-of-Sequence, ``)。 + +### 2.2 RNN 的核心机制 + +RNN 通过在内部维护一个时变但结构固定的**循环隐藏状态(Recurrent Hidden State)** $h_t \in \mathbb{R}^K$ 来总结历史: + +$$h_t = \begin{cases} \mathbf{0}, & t = 0 \\ \phi(h_{t-1}, x_t), & \text{otherwise} \end{cases}$$ + +模型利用隐藏状态计算条件概率分布:$$p(x_t \mid x_1, \dots, x_{t-1}) = g(h_t)$$ + +训练的目标是在训练集的所有序列 $\{ \mathbf{x}^n \}_{n=1}^N$ 上最大化对数似然(Log-Likelihood),即**最小化负对数似然(Negative Log-Likelihood, NLL)**:$$\max_{\theta} \frac{1}{N} \sum_{n=1}^N \sum_{t=1}^{T_n} \log p(x_t^n \mid x_1^n, \dots, x_{t-1}^n; \, \theta)$$ + +### 2.3 传统 tanh-RNN 的形式与致命缺陷 + +传统 Vanilla RNN 的状态转移函数采用单层仿射变换与饱和非线性激活:$$h_t = \tanh(W x_t + U h_{t-1} + b)$$ + + h_{t-1} ──────►[ × U ]──┐ + ├──►( + )──►[ tanh ]──► h_t + x_t ──────►[ × W ]──┘ + +#### 传统 RNN 的三大致命病灶: + +1. **状态强制覆写(Complete Overwrite):**在每个时间步,$h_{t-1}$ 被强行乘以递归矩阵 $U$ 并经过饱和非线性激活 $\tanh$ 覆写。即使遇到不需要更新的信息,也没有任何机制能让上一刻的状态“原样穿透”。 +2. **梯度消失与爆炸(Vanishing / Exploding Gradients):**根据随时间反向传播(BPTT)算法,从时间步 $T$ 向前传播到时间步 $t$ 的误差梯度涉及雅可比矩阵的连乘积:$$\frac{\partial h_T}{\partial h_t} = \prod_{k=t+1}^T \frac{\partial h_k}{\partial h_{k-1}} = \prod_{k=t+1}^T \operatorname{diag}\left(1 - h_k^2\right) U^\top$$ + +- 若 $U$ 的谱半径小于 1 且 $\tanh'$ 的导数值处于 $(0, 1]$,乘积随时间跨度 $T-t$ 呈**指数级衰减**趋近于 0(梯度消失); +- 若 $U$ 极大,乘积可能剧烈振荡爆炸。 + +3. **长程信号被短程掩盖(Signal Masking):**Bengio 等人(1994)指出,梯度下降优化的本质困境不仅在于梯度的数值缩放,还在于**远期依赖产生的微弱梯度信号,会被近期时步产生的大量局部梯度彻底淹没**。 + +### 2.4 破解梯度困境的两条技术路线 + +| 路线方向 | 代表方法 | 局限性与特点 | +| ---------------------------------------- | --------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------- | +| **路线一:改进优化算法** | - 梯度截断(Gradient Norm Clipping)
- 二阶 Hessian-free 优化(Martens & Sutskever) | 只能缓解梯度爆炸或部分数值条件,无法根本解决梯度消失所导致的记忆遗忘。 | +| **路线二:改进循环单元架构(本文核心)** | - LSTM(Hochreiter & Schmidhuber, 1997)
- GRU(Cho et al., 2014) | 从内部数学结构引入**加法直连跳跃路径(Additive Shortcuts)**与**门控调制(Gating)**,从根源上为梯度提供无损反向传播通道。 | + +--- + +## 三、Section 3.1 — LSTM(含 Peephole 窥孔连接) + +论文中采用的是 Alex Graves(2013)在其序列生成经典论文中提出的 **LSTM 变体**。该版本完整包含了**窥孔连接(Peephole Connections)**。 + +### 3.1 核心设计理念:记忆细胞与暴露状态分离 + +LSTM 不再将单一向量同时充当“特征提取”与“长期记忆”,而是实现了两者的解耦: + +- **细胞状态 $c_t$(Cell State):** 充当内部长期记忆传送带,主要执行线性累加操作,充当梯度的“高速公路”。 +- **隐藏状态 $h_t$(Hidden Activation):** 充当对外暴露的表征,由输出门选择性地从 $c_t$ 中读取。 + + ┌─── Peephole: V_f ───┐ + │ │ + ▼ ▼ + c_{t-1} ───────►( × )────────────────►( + )─────────────────────────► c_t + ▲ ▲ │ + │ 遗忘门 f_t │ 输入门 i_t │ + │ │ │ + x_t, h_{t-1} ──►[ f ] [ i ] │ + ▲ ▲ ▼ + │ ├─── Peephole: V_i [tanh] + │ │ │ + │ 候选记忆 \tilde{c}_t │ ▼ + x_t, h_{t-1} ────────────────────────►[ c ] ( × ) ◄───[ o ] ◄── Peephole: V_o + │ 输出门 o_t + ▼ + h_t + +### 3.2 论文采用的精确数学公式 + +设输入 $x_t \in \mathbb{R}^d$,隐藏单元数与记忆细胞数为 $K$。对于第 $j$ 个隐层单元($j \in \{1, \dots, K\}$): + +#### ① 输入门(Input Gate) + +决定当前输入的候选信息中有多少比例写入长期记忆细胞:$$i_t^j = \sigma\left( \left( W_i x_t + U_i h_{t-1} + V_i c_{t-1} \right)^j \right)$$ + +#### ② 遗忘门(Forget Gate) + +决定上一时刻记忆细胞中的旧历史有多少比例需要保留:$$f_t^j = \sigma\left( \left( W_f x_t + U_f h_{t-1} + V_f c_{t-1} \right)^j \right)$$ + +#### ③ 候选记忆内容(New Memory Content Candidate) + +由当前输入与上一刻外部状态合成的新候选知识:$$\tilde{c}_t^j = \tanh\left( \left( W_c x_t + U_c h_{t-1} \right)^j \right)$$ + +#### ④ 记忆细胞更新(Cell State Update) + +这是整个 LSTM **最关键的加法更新公式**:$$c_t^j = f_t^j c_{t-1}^j + i_t^j \tilde{c}_t^j$$向量形式为:$$\mathbf{c}_t = \mathbf{f}_t \odot \mathbf{c}_{t-1} + \mathbf{i}_t \odot \tilde{\mathbf{c}}_t$$ + +#### ⑤ 输出门(Output Gate) + +根据当前输入、上一刻隐藏状态以及**最新更新的记忆细胞**,决定记忆暴露程度:$$o_t^j = \sigma\left( \left( W_o x_t + U_o h_{t-1} + V_o c_t \right)^j \right)$$ + +#### ⑥ 隐藏状态输出(Hidden State) + +$$h_t^j = o_t^j \tanh(c_t^j)$$向量形式为:$$\mathbf{h}_t = \mathbf{o}_t \odot \tanh(\mathbf{c}_t)$$ + +### 3.3 关键细节分析:Peephole 窥孔连接的特殊机制 + +论文中明确强调: + +1. **$V_i, V_f, V_o$ 是对角矩阵(Diagonal Matrices):**窥孔连接是**按单元逐对(Element-wise)**作用的,即第 $j$ 个门的计算只查看第 $j$ 个 cell 的状态 $c^j$,不与其他单元产生全连接交互。这样不仅有效控制了参数量,还能让门精准获知自身当前记录的记忆幅度。 +2. **时间对齐差异(极其重要):** + +- 输入门 $i_t$ 与遗忘门 $f_t$ 查看的是**上一时刻的历史记忆 $c\_{t-1}$**(因为决定遗忘和写入时,当前的新状态尚未计算出来); +- 输出门 $o_t$ 查看的是**已经完成更新的当前时刻记忆 $c_t$**。 + +--- + +## 四、Section 3.2 — GRU(Gated Recurrent Unit) + +GRU 由 Cho 等人在 2014 年提出,其初衷是构建一个**既具备门控自适应捕捉多尺度时间依赖能力,又拥有更极简结构**的循环单元。 + +### 4.1 核心设计理念:基于 Leaky Integrator 的融合架构 + +与 LSTM 相比,GRU 的核心哲学在于**完全舍弃独立的细胞状态 $c_t$**: + +- 隐藏状态 $h_t$ 既是对外输出,又是内部记忆; +- 只有两个门:**更新门(Update Gate)**与**重置门(Reset Gate)**; +- 彻底取消输出门,隐藏状态在计算完成后 $100\%$ 暴露给下一层或下一个时间步。 + + ┌──────────────────────┐ + │ 重置门 r_t │ + h_{t-1} ──┴─►( × ) [ r ] ◄┼── x_t + │ │ + ▼ │ + [ tanh ] ◄──────────┤ (候选状态 \tilde{h}_t) + │ │ + │ ┌──────────────┘ + │ │ 更新门 z_t + ▼ ▼ + [ (1 - z_t) * h_{t-1} + z_t * \tilde{h}_t ] + │ + ▼ + h_t + +### 4.2 数学公式与论文重要标注(Footnote 1) + +#### ① 更新门(Update Gate) + +控制历史隐藏状态被保留的比例与新候选状态被采纳的比例:$$z_t^j = \sigma\left( \left( W_z x_t + U_z h_{t-1} \right)^j \right)$$ + +#### ② 重置门(Reset Gate) + +控制在生成新候选状态时,上一刻历史信息应当被遗忘/压制多少:$$r_t^j = \sigma\left( \left( W_r x_t + U_r h_{t-1} \right)^j \right)$$ + +#### ③ 候选激活状态(Candidate Activation) + +$$\tilde{h}_t^j = \tanh\left( \left( W x_t + U (r_t \odot h_{t-1}) \right)^j \right)$$ + +> 🔍 **论文注脚 1(Footnote 1)的重要技术细节:**在 Cho et al. (2014) 最初提出的 GRU 中,候选状态的计算公式为:$$\tilde{h}_t = \tanh\left( W x_t + r_t \odot (U h_{t-1}) \right)$$ 而在 Bahdanau et al. (2014) 和本文的实现中,重置门改为**先与 $h\_{t-1}$ 点乘,再乘以权重矩阵 $U$**:$$\tilde{h}_t = \tanh\left( W x_t + U (r_t \odot h_{t-1}) \right)$$作者在论文中指出:在预备实验中发现,**这两种变形的性能表现没有显著差异**。现代 PyTorch、TensorFlow 等主流框架均沿用了本文与 Bahdanau 版本的实现。 + +#### ④ 最终隐藏状态(Linear Interpolation) + +通过更新门 $z_t$ 对旧状态与候选状态进行**凸组合(线性插值)**:$$h_t^j = (1 - z_t^j) h_{t-1}^j + z_t^j \tilde{h}_t^j$$向量形式为:$$\mathbf{h}_t = (\mathbf{1} - \mathbf{z}_t) \odot \mathbf{h}_{t-1} + \mathbf{z}_t \odot \tilde{\mathbf{h}}_t$$ + +### 4.3 门的微观工作机理剖析 + +1. **重置门 $r_t \to 0$ 的物理意义:**若某个单元的 $r_t^j \to 0$,则 $U (r_t \odot h\_{t-1})^j \to 0$,此时候选状态 $\tilde{h}\_t^j \approx \tanh((W x_t)^j)$。这意味着该单元**完全忽略了所有过去的历史记忆,表现得如同刚刚读取序列的第一个符号一样**。这对于标识句子边界、乐句休止符或音频静音段至关重要。 +2. **更新门 $z_t \to 0$ 与 $z_t \to 1$ 的物理意义:** + +- 当 $z_t^j \to 0$ 时:$h_t^j \approx h_{t-1}^j$,历史状态无损跳跃传递到当前时刻,具备无限期的长期保存能力; +- 当 $z_t^j \to 1$ 时:$h_t^j \approx \tilde{h}_t^j$,单元全面刷新为当前候选内容。 + +--- + +## 五、Section 3.3 — 深度讨论:LSTM 与 GRU 的结构对比与数学共性 + +### 5.1 核心共性:加法更新(Additive Nature)构造的时间高速通道 + +为什么 LSTM 和 GRU 都能解决梯度消失,而传统 RNN 却不能?答案就在于两者在状态更新时均包含**加法项(Additive Component)**: + +- **LSTM:** $c_t = f_t \odot c_{t-1} + i_t \odot \tilde{c}_t$ +- **GRU:** $h_t = (1 - z_t) \odot h_{t-1} + z_t \odot \tilde{h}_t$ + +#### 梯度流的数学证明直觉: + +在反向传播计算局部导数时:$$\frac{\partial c_t}{\partial c_{t-1}} = \operatorname{diag}(f_t) + \text{包含输出门/候选状态导数的项}$$$$\frac{\partial h_t}{\partial h_{t-1}} = \operatorname{diag}(1 - z_t) + \text{包含候选状态对 } h_{t-1} \text{ 导数的项}$$ + +只要门控饱和接近 1(LSTM 中 $f_t \approx 1$;GRU 中 $z_t \approx 0$),主对角线上的导数就恒定保持在 $\approx 1$。**这就在跨越数十上百个时间步的长距离维度上构建了一条无损直连通道(Shortcut Paths),让梯度不再必须穿透层层有界压缩的激活函数,从而从数学上彻底抑制了梯度消失。** + +### 5.2 核心结构差异深度对比 + +| 比较维度 | LSTM(Graves 2013 变体) | GRU(Cho et al. 2014 / 本文版本) | +| --------------------------- | -------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------- | +| **内部状态体系** | 双状态:细胞状态 $c_t$ + 隐藏状态 $h_t$ | 单状态:仅维护隐藏状态 $h_t$ | +| **门的数量与类型** | 3 个门:输入门 $i_t$、遗忘门 $f_t$、输出门 $o_t$ | 2 个门:重置门 $r_t$、更新门 $z_t$ | +| **信息暴露机制** | **受控暴露:** 由输出门 $o_t$ 决定当前对外暴露多少细胞记忆 | **全量暴露:** 无输出门,计算出的 $h_t$ 100% 暴露给后续层 | +| **遗忘与写入的关系** | **独立解耦:** $f_t$ 与 $i_t$ 互不约束,可同时为 1(记忆暴增)或同时为 0(清空) | **互补耦合(凸组合):** 严格满足 $(1-z_t) + z_t = 1$,写入新信息必按相同比例挤掉旧信息 | +| **历史信息的过滤位置** | 在写入 cell 之后由输出门过滤,计算 $\tilde{c}_t$ 时使用完整的 $h_{t-1}$ | 在生成候选状态 $\tilde{h}_t$ **之前**,通过重置门 $r_t$ 预先对 $h_{t-1}$ 进行遮蔽 | +| **Peephole 窥孔** | 包含 3 组对角矩阵($V_i, V_f, V_o$),可直视 cell | 无窥孔机制 | +| **参数量(同维度 $K$ 下)** | $4(Kd + K^2) + 7K$(含 bias 与 peephole) | $3(Kd + K^2) + 3K$(约少 25% 参数) | + +--- + +## 六、Section 4 — 实验设计与严谨受控设置 + +### 6.1 为什么必须控制参数总量? + +在以往的评测中,若给 LSTM 和 GRU 赋予相同的隐藏单元数(例如均为 $K=200$),由于 GRU 每个单元只有 3 组仿射变换($z, r, \tilde{h}$),而 LSTM 有 4 组($i, f, o, \tilde{c}$),GRU 的参数量会比 LSTM 少近 $25\% \sim 33\%$。这会导致对比不公平。 + +**本论文的关键方法学原则:固定总参数量上限(Fixed Parameter Budget)。**因为 GRU 的单单元参数开销较小,在总参数预算相同的前提下,**GRU 可以分配到更多的隐层神经元(更多的状态维度)**。这正是架构设计紧凑性带来的天然红利。 + +### 6.2 实验规模与参数分配详情(Table 1) + +论文设计了两大具有代表性挑战的实验任务,模型均刻意设计得**足够小**,以防止严重过拟合干扰对循环单元本质特性的判定: + +| 实验任务 | 单元类型 | 隐藏单元数 $K$ | 矩阵与模型总参数量 | +| ------------------------------------------------------------------ | ------------------------------------------- | ----------------- | ----------------------------------------------------------------------------------------- | +| **任务一:复调音乐建模**
(参数预算 $\approx 20\text{k}$) | **tanh-RNN**
**GRU-RNN**
**LSTM-RNN** | 100
46
36 | $\approx 20.1 \times 10^3$
$\approx 20.2 \times 10^3$
$\approx 19.8 \times 10^3$ | +| **任务二:连续原始语音建模**
(参数预算 $\approx 169\text{k}$) | **tanh-RNN**
**GRU-RNN**
**LSTM-RNN** | 400
227
195 | $\approx 168.4 \times 10^3$
$\approx 168.9 \times 10^3$
$\approx 169.1 \times 10^3$ | + +> 📌 **观察:**在复调音乐任务中,20k 参数可以让 GRU 拥有 46 个隐层单元,而 LSTM 只有 36 个(多出 $27.8\%$ 单元数);在语音建模中,169k 参数让 GRU 拥有 227 个单元,LSTM 拥有 195 个(多出 $16.4\%$ 单元数)。tanh-RNN 因每个单元参数极少,单元数可多达 100 与 400。 + +### 6.3 评测数据集与输出层建模机制 + +#### 1. 复调音乐建模任务(Polyphonic Music Modeling) + +采用 Boulanger-Lewandowski et al. (2012) 整理的 4 个国际标准音乐评测数据集。每个时步的音符输入为高维二值向量(Binary Vector,对应钢琴键盘上是否有键按下): + +- **Nottingham:** 93 维二值向量(英国民谣乐谱 MIDI) +- **JSB Chorales:** 96 维二值向量(巴赫四声部圣咏曲) +- **MuseData:** 105 维二值向量(古典交响乐与管弦乐谱) +- **Piano-midi.de:** 108 维二值向量(古典钢琴演奏 MIDI 数据) +- **输出层配置:** 输出层使用 `Logistic Sigmoid` 单元,将每个音符建模为独立的伯努利分布,联合计算每个时间步的负对数似然。 + +#### 2. 原始音频信号建模任务(Speech Signal Modeling) + +采用育碧公司(Ubisoft)提供的两个真实工业级原始音频信号内部数据集(1 维连续采样点波形): + +- **时序滑动窗口预测机制:** 在每个时间步 $t$,RNN 查看**前 20 个连续连续音频采样点**($x_t \in \mathbb{R}^{20}$),目标是预测**接下来的 10 个连续音频采样点**($y_t \in \mathbb{R}^{10}$)。 +- **极端跨度挑战(Ubisoft A vs. Ubisoft B):** + - **Ubisoft A:** 序列长度为 500 时步,包含 7,230 条序列; + - **Ubisoft B:** 序列长度高达 **8,000 时步**,包含 800 条序列。序列跨度长达 8,000 步,是对 RNN 捕捉极限长距离依赖和防止梯度爆炸/消失的地狱级考验。 +- **输出层配置:** 对于连续信号的多峰分布,输出层采用包含 **20 个分量的高斯混合模型(Mixture of Gaussians, GMM)**。 + +### 6.4 训练、正则化与超参数调优协议 + +- **优化算法:** RMSProp(Hinton, 2012)。 +- **权重噪声正则化(Weight Noise):** 在训练阶段每次前向传播时向权重矩阵加入固定标准差 $\sigma = 0.075$ 的高斯噪声(Graves 2011 提出的变分推断近似技术),强力防止过拟合。 +- **梯度裁剪(Gradient Clipping):** 采用 Pascanu et al. (2013) 算法,若全局梯度的 $L_2$ 范数 $\|\nabla\|_2 > 1$,则按比例将其缩放截断为 1,确保训练不会发生梯度爆炸。 +- **随机搜索学习率(Random Search):** 依据 Bergstra & Bengio (2012),从对数均匀分布中随机抽取 10 个候选学习率:$\log_{10}(\text{lr}) \sim \mathcal{U}(-12, -6)$。 +- **模型选择机制:** 采用验证集(Validation Set)早停策略(Early Stopping),选取验证集损失最佳的超参数并在独立测试集上进行最终评价。 + +--- + +## 七、Section 5 — 实验结果深度解析 + +### 7.1 完整量化评测结果(Table 2) + +下表完整列出所有模型在测试集和训练集上的**平均负对数似然(Average Negative Log-Probability, NLL,数值越低代表模型越好)**: + +| 数据集类型 | 数据集名称 | 指标 | 传统 tanh-RNN | 门控 GRU-RNN | 门控 LSTM-RNN | 最优单元 | +| ------------------------------------- | ------------------------------------ | ----------------- | ------------- | -------------------- | -------------------- | ---------------------------------------- | +| **音乐数据集**
(Polyphonic Music) | **Nottingham** | Train
**Test** | 3.22
3.13 | **2.79**
3.23 | 3.08
**3.20** | **LSTM**(泛化略优)
GRU 拟合能力更强 | +| | **JSB Chorales** | Train
**Test** | 8.82
9.10 | **6.94**
**8.54** | 8.15
8.67 | **GRU 胜出**(显著领先) | +| | **MuseData** | Train
**Test** | 5.64
6.23 | **5.06**
**5.99** | 5.18
6.23 | **GRU 胜出**(测试集领先 0.24) | +| | **Piano-midi** | Train
**Test** | 5.64
9.03 | **4.93**
**8.82** | 6.49
9.03 | **GRU 胜出**(测试集领先 0.21) | +| **语音数据集**
(Ubisoft Raw Audio) | **Ubisoft A**
(序列长度 500) | Train
**Test** | 6.29
6.44 | 2.31
3.59 | **1.44**
**2.70** | **LSTM 胜出**(大幅领先 0.89) | +| | **Ubisoft B**
(序列长度 **8000**) | Train
**Test** | 7.61
7.62 | **0.38**
**0.88** | 0.80
1.26 | **GRU 胜出**(大幅领先 0.38) | + +--- + +### 7.2 三大核心结论剖析 + +#### 结论一:门控单元全面降维打击传统 tanh-RNN + +- **音乐任务:** 在 JSB Chorales、MuseData、Piano-midi 上,tanh-RNN 的测试集 NLL 明显劣于门控单元(JSB 上 9.10 vs 8.54/8.67)。 +- **语音任务:** 表现尤为悬殊。在 Ubisoft A 上,tanh-RNN 停滞在 6.44(门控单元达到 2.70~3.59);在长达 8000 步的 Ubisoft B 上,**tanh-RNN 停滞在 7.62 完全丧失优化动力**(学习曲线迅速平直,如 Fig. 3 所示),而门控单元则能够顺利学到深层连续依赖(GRU 达到 0.88)。 +- **本质结论:** 当序列跨度超过数十步时,传统 RNN 的结构缺陷是优化算法(即使搭配了梯度裁剪和 RMSProp)无法弥补的。**门控机制是处理长序列建模任务的不可或缺的前提。** + +#### 结论二:GRU 与 LSTM 各擅胜场,不存在“绝对霸主” + +论文的最核心论点是打破盲目迷信: + +- 在 4 个复调音乐数据集中,**GRU 在 3 个数据集(JSB Chorales、MuseData、Piano-midi)的测试集性能上均击败了 LSTM**,且在全部 4 个任务的训练集拟合程度上都明显更优;LSTM 则在 Nottingham 上微弱领先(3.20 vs 3.23)。 +- 在连续语音数据集中出现戏剧性反转: + - 在序列长度为 500 的 Ubisoft A 上,**LSTM 表现异常强劲**(测试 NLL 2.70,击败 GRU 的 3.59); + - 在序列长度高达 8000 的 Ubisoft B 上,**GRU 却全面压制 LSTM**(测试 NLL 0.88,击败 LSTM 的 1.26)。 +- **论文原话定调:** + + > _"Our results are not conclusive in comparing the LSTM and the GRU, which suggests that the choice of the type of gated recurrent unit may depend heavily on the dataset and corresponding task."_ + + (实证结果无法得出 GRU 优于 LSTM 或 LSTM 优于 GRU 的绝对结论,门控类型的选择极大程度上取决于具体的数据集和任务特性。) + +#### 结论三:收敛速度与计算效率的全面对比(Figure 2 & 3 学习曲线解读) + +论文通过 Figure 2(音乐建模)与 Figure 3(语音建模)记录了**迭代轮数(Per Epoch)**与**真实墙上钟时间(Wall Clock Time in Seconds)**两条学习曲线,展现了深刻的工程洞察: + + 训练进程对比示意(基于论文 Figures 2 & 3 趋势绘制): + + NLL (对数刻度, 越低越好) + │ + │ ────────────────────── tanh-RNN (早期停滞,无法取得实质性进展) + │ + │ \ + │ \ LSTM-RNN (稳步下降) + │ \ + │ \ GRU-RNN (斜率更陡峭,收敛更快达到极佳损失) + │ \________ + └────────────────────────────────────────► 墙上钟时间 (CPU Seconds) + +1. **更新效率(Per Update Progress):**虽然传统 tanh-RNN 每次参数更新的浮点运算量极低、单个 epoch 耗时最短,但由于缺乏跳跃路径,**每次更新所带来的有效损失下降极其微弱**,过早陷入鞍点或劣质局部极小。 +2. **GRU 的训练加速红利:** + +- 在相同参数预算下,GRU 凭借精简的门控流(无需计算独立的 cell state 和输出门),单个时间步的前向/反向计算开销显著小于带窥孔的 LSTM。 +- 在图 2 的 Nottingham 与 MuseData 学习曲线上,**无论是按照参数更新次数,还是按照真实 CPU 运行时间(Wall Clock Time),GRU 的下降曲线均明显陡峭于 LSTM**,能以更少的算力开销更快到达收敛区间。 + +--- + +## 八、理论升华:为什么在不同任务上表现会有差异? + +结合后续深度学习的发展(例如 Jozefowicz et al. 2015, Greff et al. 2015 的大规模架构搜索),我们可以对本论文中 GRU 与 LSTM 互有胜负的内在机理解读得更为透彻: + +### 1. 为什么 GRU 在 Ubisoft B(超长序列 8000 步)上反超 LSTM? + +- **更新门耦合的正则效应:** GRU 的更新机制是强约束的凸组合 $h_t = (1-z_t)h_{t-1} + z_t\tilde{h}_t$。这意味着状态的能量永远不会发生自发性指数膨胀,信息必须在“保留旧状态”与“吸收新状态”之间做守恒权衡。在长达 8000 步的反向传播中,这种**天然的范数稳定性**使得梯度反向流动更加平稳。 +- **更多隐层单元(227 vs 195):** 在固定的 169k 参数预算下,GRU 多出了 32 个隐层神经元(多出 16.4% 的特征容量),使得它能够在极长时序中保留更多不同尺度的特征模式。 + +### 2. 为什么 LSTM 在 Ubisoft A(连续语音 500 步)上表现最好? + +- **输出门(Output Gate)的解耦控制价值:** 连续语音的采样点具有极强的局部高频波动与复杂的泛音结构。LSTM 的细胞状态 $c_t$ 可以专注于无损累积底层高频声学特征,而**输出门 $o_t$ 能够根据需要,选择性地阻止未提炼的记忆污染当前预测**。GRU 缺乏输出门,所有中间特征必须全部暴露在 $h_t$ 中,在处理某些复杂连续谱建模时可能产生表征冲突。 +- **独立输入/遗忘机制的灵活性:** 当语音信号从元音快速切换到爆破音时,LSTM 可以同时让 $f_t \to 0$ 且 $i_t \to 1$;或者在静音段让 $f_t \to 0, i_t \to 0$。这种双门解耦赋予了 LSTM 在短序列复杂动态下更高的表征自由度。 + +--- + +## 九、总结与现代工程选型建议 + +### 9.1 全文核心知识脉络梳理 + + ┌── 传统 tanh-RNN ──► 无加法直连,状态强制覆写 ──► 梯度消失,无法处理长序列 + │ + 循环神经网络在序列建模中 ─┼── LSTM (1997) ──► 3个门 + Cell State + 输出门 ──► 控制精细,表征自由度高 + │ + └── GRU (2014) ──► 2个门 + 状态耦合 + 无输出门 ──► 结构精简,计算高效,参数利用率高 + +### 9.2 面对具体业务场景的选型心智模型 + +| 业务场景 / 约束条件 | 推荐单元 | 决策逻辑与理论支撑 | +| -------------------------------------------------------------------- | ------------ | --------------------------------------------------------------------------------------- | +| **算力/延迟受限(边缘端、移动端部署、实时音频推理)** | **GRU** | 参数少约 25%,相同参数下单元数更多;单步矩阵运算少,推理与训练耗时明显更短。 | +| **超长序列依赖建模(文本、长时间传感器信号序列)** | **GRU** | 更新门具备天然的凸组合约束,长时间步反向传播中数值更加稳定,收敛速度通常更快。 | +| **高维度多尺度复杂连续信号建模(如精细声学合成、高频金融微观结构)** | **LSTM** | 拥有独立记忆细胞 $c_t$ 与输出门 $o_t$,支持内部计算与外部暴露解耦,表征自由度上限更高。 | +| **标准 NLP / 分类 / 预测任务,追求工程鲁棒性** | **两者均可** | 建议优先以 GRU 作为 baseline 快速实验迭代;若验证集出现表征瓶颈再切换为 LSTM 验证。 | + +--- + +## 十、延伸思考:门控机制对后现代大模型架构的启示 + +Chung 等人在这篇 2014 年论文中的洞察,至今仍在现代前沿深度学习架构中产生深远回响: + +1. **加法直连跳跃的普遍真理:** LSTM/GRU 的加法更新机制直接启发了 CV 领域的 **ResNet 残差连接(He et al., 2015)**与 Transformer 的 Pre-LN 残差连接——本质都是通过加法构造恒等映射通道(Identity Mapping)来抵御梯度衰减。 +2. **门控机制在新一代 SSM / 线性注意力中的复兴:** 2023-2024 年爆火的现代状态空间模型(如 **Mamba** 中的 Selective State Spaces)以及线性 RNN 变体(如 **RWKV**、**Retention**、**Hawk/Griffin**),其核心数学骨架正是重拾了 GRU 这种带有时变衰减因子(Decay Gate)的极简门控一阶递推系统。 + +理解了 2014 年 Chung 等人对门控机制的这篇经典实证剖析,就真正掌握了从经典 RNN 到现代时序序列大模型演进的核心底层逻辑。 + +--- + +_本文档基于论文原文 arXiv:1412.3555 完整校订,涵盖论文全部公式推导、表格数据(Table 1 & 2)、学习曲线特征(Fig. 2 & 3)及深入的理论拓展。_ diff --git a/content/posts/first/001.png b/content/posts/first/001.png new file mode 100644 index 0000000000000000000000000000000000000000..fd5fda6208ff44ca9089087b959a0f39ecdd61b1 GIT binary patch literal 598064 zcmdSB^;=cn8wCi`EhP;iN_R+yARtIdcQ?`vl1i6K=M|JocXxM7cXxNgZ2WxZd1juO z`2*$$;BxQf+;jGMW4&vwO^AY=BnB!mDhvz^hSZ1miZC!w4-rL>5y6j&e3EAH1J+Sd zQWU0ekaQdT0&n(C_8kmNNfg?h0RjxnW3ANtcgk+Md-JYe@SGpIjwfABUCVO*h;E6) zFDt*tLqIr}8ww0Hv6hveb?YSs2<^S_ruvn<6?f?5r z$dvE*qG5jhf4pdq{PX`OuPKtaFtP1NoSSsU8dTFaZ?}wn`9&n6!(G%otPluS&&(M` zqLQe8IQCjbgsxfn{7UHC^NdV|UotYdFpDZf8`GYk#y5ke0M_f2O%}K9Y?FG1pHir0yh z?5dS>V0aO06h0H-f#KinXir~Rg7fWd|3KRw%mQ2R19J(3tUv&zAYbL^n+w&9&&FJ% z1TrN&yj(8#IFU0^binf!7-N|iqQO&?My1b1+asYw(Oj7$^ps)mUFma6ATr35n4hSr z->f6x#cmoV1bS8ccLy_INtI!S?c()c?_1R`K~mFy$NtGsc|AQz%8BbwW3hAZfK1tb z7~X39nEC@ls?(VATQkfy-1yPTcru zIJdbH>HZo=fy3WtasGu_2Alasp!s$5DVyR+67wC>uWRt&h-Pzkk~F3n#c5X$yek8j z$8TYnD(h)gKT)t#qk(w)Z=oeu!+YqCiHxbM;*TKDMaTT0yxr0VA`V|_y;Ryzsn3bo ziwR~_#cY)SMRYKtauLk05la@+FC`5%JqgDhgasEf$-6oB2Qc`e!HZ#m4ajs)OGS$Q zf4d&auC?;^&zf(Hr;`Joi@vAhO6Rf&vECcNkmOqV;b>%|_21FIDs00166U3#D(qjF zTMMr){aOf5$g@s`v@42ie>Cp#9tu=XW>#c2UHz!rrKUz6E{L~AYKP{_$wza?ZLTNsxFpPG)CcqTTylsULZ}! z{&VKvx{&_q|8tT3Rc3@s@@nXB$`I4PpnYGR4d*K%N@?!x>3BMN=jWA&#&PBYjzb)y zak;GW6g}pz|8KW+zH9BZD{(D!_Gz(6U(1e4Ib{8N{B*X?e?X1G8Q;d#+qjrQhj~WG z7deM{F`+r;Rf;sq`AK@24c`hCpA7fqyvdm6%B*Jm;mDMxs%}x6;9`uSW!}McQk3ZYY8ac|S;*iEV z7sk9Zw!`KsN(5ho0|b+1*p~dkH`;(j1%W!Y$gsvC!!cKs&x|7qsCVO^2Pp(57S%J@ z9K@dy6j`>Fk*pq(w3G>g(=t>c!|U^UgZ&txT;XG#g2`>I==nWu3_FWT2=9Rd)F0ND zgcoJcd{keu3J_*1@Q@w

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+date = 2026-01-14T07:07:07+01:00 +draft = false +tags = ['Test'] ++++ + +## first paper + +![图片](001.png) +[第二篇文章](../second) diff --git a/content/posts/second.md b/content/posts/second.md new file mode 100644 index 0000000..21a3d3c --- /dev/null +++ b/content/posts/second.md @@ -0,0 +1,8 @@ ++++ +title = 'My second Post' +date = 2026-01-14T07:07:07+01:00 +draft = false +hiddenInHomeList = true ++++ + +## second paper diff --git a/content/search.md b/content/search.md new file mode 100644 index 0000000..8abc3ee --- /dev/null +++ b/content/search.md @@ -0,0 +1,7 @@ ++++ +title = "Search" +layout = "search" +url = "/search/" +summary = "search" +placeholder = "输入关键词搜索文章..." ++++ \ No newline at end of file diff --git a/hugo.toml b/hugo.toml new file mode 100644 index 0000000..8086403 --- /dev/null +++ b/hugo.toml @@ -0,0 +1,72 @@ +baseURL = 'http://localhost:1313/' +locale = 'zh-cn' +title = "James'sLog" +theme = 'PaperMod' + +[params] +disableSpecial1stPost = true # 关闭首篇文章特殊高亮显示 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I’m documenting my learning notes in this blog since 2026." + +[[params.socialIcons]] +name = "twitter" +url = "https://twitter.com/" + +[[params.socialIcons]] +name = "other" +url = "https://example.com/" + +[[params.socialIcons]] +name = "rss" +url = "index.xml" + +[[params.socialIcons]] +name = "github" +url = "https://github.com/Liubruh" + +[[params.socialIcons]] +name = "instagram" +url = "https://instagram.com/" + +[markup] +[markup.goldmark] +[markup.goldmark.renderer] +unsafe = true # 允许渲染文章中的原生 HTML 标签 +[markup.goldmark.extensions] +[markup.goldmark.extensions.passthrough] +enable = true +[markup.goldmark.extensions.passthrough.delimiters] +block = [['\[', '\]'], ['$$', '$$']] +inline = [['\(', '\)'], ['$', '$']] + +[outputs] +home = ['HTML', 'RSS', 'JSON'] + +[menus] +[[menus.main]] +identifier = 'posts' +name = 'Posts' +url = '/' +weight = 1 + +[[menus.main]] +name = 'Archive' +url = '/archive/' +weight = 2 + +[[menus.main]] +identifier = 'search' +name = 'Search' +url = '/search/' +weight = 4 + +[[menus.main]] +identifier = 'tags' +name = 'Tags' +url = '/tags/' +weight = 3 diff --git a/layouts/partials/extend_head.html b/layouts/partials/extend_head.html new file mode 100644 index 0000000..69a3055 --- /dev/null +++ b/layouts/partials/extend_head.html @@ -0,0 +1,18 @@ +{{ if or .Params.math .Site.Params.math }} + + + + +{{ end }} diff --git a/themes/PaperMod b/themes/PaperMod new file mode 160000 index 0000000..1181196 --- /dev/null +++ b/themes/PaperMod @@ -0,0 +1 @@ +Subproject commit 118119693d8b5ac211b939775678310973bcb232

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