https://blog.techlover.shop/ Recent content on My Blog Hugo en-us https://blog.techlover.shop/posts/beiyesi/ Mon, 01 Jan 0001 00:00:00 +0000 https://blog.techlover.shop/posts/beiyesi/ <p><img alt="image-20251215122710714" loading="lazy" src="beiyesi/image-20251215122710714.png"></p> <p><img alt="image-20251215135300419" loading="lazy" src="beiyesi/image-20251215135300419.png"></p> <p><img alt="image-20251215140018151" loading="lazy" src="beiyesi/image-20251215140018151.png"></p> <p>贝叶斯概率：学习局部概率分享参数</p> <p><img alt="image-20251215141518465" loading="lazy" src="beiyesi/image-20251215141518465.png"></p> <p>所以naive模型认为看看是个正面评价</p> <p>参数一般是梯度下降得来的，但是naive贝叶斯是数出来的</p> <p><img alt="image-20251215142210247" loading="lazy" src="beiyesi/image-20251215142210247.png"></p> <p>数出来normalize之后就是最大似然</p> <p><img alt="image-20251215142355830" loading="lazy" src="beiyesi/image-20251215142355830.png"></p> <p><img alt="image-20251215142456817" loading="lazy" src="beiyesi/image-20251215142456817.png"></p> <p><img alt="image-20251215143152825" loading="lazy" src="beiyesi/image-20251215143152825.png"></p> <p><img alt="image-20251215144940522" loading="lazy" src="beiyesi/image-20251215144940522.png"></p> <p>相当于supervised里面的标签数据</p> <p><img alt="image-20251215150127821" loading="lazy" src="beiyesi/image-20251215150127821.png"></p> <p>m-step通过左边调整右边的参数</p> <p><img alt="image-20251215150148849" loading="lazy" src="beiyesi/image-20251215150148849.png"></p> <p><img alt="image-20251215150216571" loading="lazy" src="beiyesi/image-20251215150216571.png"></p> https://blog.techlover.shop/posts/gnn/ Mon, 01 Jan 0001 00:00:00 +0000 https://blog.techlover.shop/posts/gnn/ <h1 id="gnn">GNN</h1> <p><img alt="image-20251114165612672" loading="lazy" src="gnn/image-20251114165612672.png"></p> <p>聚合的过程就是把邻居的信息贴到自己的身上来</p> <h4 id="更新">更新</h4> <p>A的邻居信息为</p> <p><img alt="image-20251114165718185" loading="lazy" src="gnn/image-20251114165718185.png"></p> <p>a b c 都是可以训练的</p> <p><img alt="image-20251114165921881" loading="lazy" src="gnn/image-20251114165921881.png"></p> <p>A的信息为自己的特征加上 阿尔法 倍的邻居特征</p> <h4 id="多层">多层</h4> <p><img alt="image-20251114170503670" loading="lazy" src="gnn/image-20251114170503670.png"></p> <p><img alt="image-20251114170619116" loading="lazy" src="gnn/image-20251114170619116.png"></p> https://blog.techlover.shop/posts/lstmandattention/ Mon, 01 Jan 0001 00:00:00 +0000 https://blog.techlover.shop/posts/lstmandattention/ <h2 id="lstmimage-20251102140227071">lstm<img alt="image-20251102140227071" loading="lazy" src="lstm/image-20251102140227071.png"></h2> <p>lstm除了传递 hidden state以外还会传递memory cell</p> <p>lstm的计算非常冗长</p> <p><img alt="image-20251102141215244" loading="lazy" src="lstm/image-20251102141215244.png"></p> <ol> <li>更稳的梯度传递</li> </ol> <ul> <li>LSTM 有“细胞状态”（cell state）走<strong>加性通路</strong>，再配合输入门/遗忘门/输出门，能保留或丢弃信息，显著缓解梯度消失；普通 RNN 的递推是乘性累积，长序列上梯度很容易衰减或爆炸。</li> </ul> <ol> <li>记忆与选择性更新</li> </ol> <ul> <li>通过三种门控： • <strong>遗忘门</strong>：决定保留多少旧记忆； • <strong>输入门</strong>：决定当前时刻写入多少新信息； • <strong>输出门</strong>：决定暴露多少内部记忆到隐藏状态。</li> <li>这让模型能<strong>长期存储关键信息</strong>、<strong>屏蔽噪声</strong>，比 RNN 更擅长跨长距离依赖的任务（如机器翻译、语音、长文本建模等）。</li> </ul> <p><img alt="image-20251102141355585" loading="lazy" src="lstm/image-20251102141355585.png"></p> <p>所有的t都指的是时间点</p> <p><img alt="image-20251102142508862" loading="lazy" src="lstm/image-20251102142508862.png"></p> <p><img alt="image-20251102142603439" loading="lazy" src="lstm/image-20251102142603439.png"></p> <p><img alt="image-20251102142722883" loading="lazy" src="lstm/image-20251102142722883.png"></p> <p><img alt="image-20251102142731601" loading="lazy" src="lstm/image-20251102142731601.png"></p> <p>​ <img alt="image-20251102144029191" loading="lazy" src="lstm/image-20251102144029191.png"></p> <p><img alt="image-20251102144042023" loading="lazy" src="lstm/image-20251102144042023.png"></p> <p>计算新的hidden state</p> <p><img alt="image-20251102144058760" loading="lazy" src="lstm/image-20251102144058760.png"></p> <p>反向传播</p> <p><img alt="image-20251102145126628" loading="lazy" src="lstm/image-20251102145126628.png"></p> <p><img alt="image-20251102145146882" loading="lazy" src="lstm/image-20251102145146882.png"></p> <p><img alt="image-20251102145327624" loading="lazy" src="lstm/image-20251102145327624.png"></p> <h2 id="attention">attention</h2> <p><img alt="image-20251102145616212" loading="lazy" src="lstmandattention/image-20251102145616212.png"></p> <table> <thead> <tr> <th><strong>标记</strong></th> <th><strong>完整名称 (英文)</strong></th> <th><strong>完整名称 (中文)</strong></th> <th><strong>在模型中的作用</strong></th> </tr> </thead> <tbody> <tr> <td>$\text{BOS}$</td> <td><strong>B</strong>egin <strong>O</strong>f <strong>S</strong>equence</td> <td>序列开始标记</td> <td><strong>解码器的</strong>第一个<strong>输入</strong>，启动生成过程。</td> </tr> <tr> <td>$\text{EOS}$</td> <td><strong>E</strong>nd <strong>O</strong>f <strong>S</strong>equence</td> <td>序列结束标记</td> <td><strong>解码器的</strong>预测<strong>输出</strong>，用于<strong>终止</strong>生成过程。</td> </tr> </tbody> </table> <p><img alt="image-20251102211943127" loading="lazy" src="lstmandattention/image-20251102211943127.png"></p> <p>上要给时间节点的输出会当作下一个时间节点的输入</p> <h4 id="attention-概览">attention 概览</h4> <p>句子长的话</p> <p><img alt="image-20251102212338069" loading="lazy" src="lstmandattention/image-20251102212338069.png"></p> <p>context vector 为告诉解码器对齐的词是什么</p> <h4 id="attention-细节">attention 细节</h4> <p><img alt="image-20251102214337137" loading="lazy" src="lstmandattention/image-20251102214337137.png"></p> https://blog.techlover.shop/posts/rnn/ Mon, 01 Jan 0001 00:00:00 +0000 https://blog.techlover.shop/posts/rnn/ <p><img alt="image-20251031134852606" loading="lazy" src="rnn/image-20251031134852606.png"></p> <p><img alt=" image-20251031134918744" loading="lazy" src="rnn/image-20251031134918744.png"></p> <p><img alt="image-20251031135306643" loading="lazy" src="rnn/image-20251031135306643.png"></p> <p><img alt="image-20251031135352922" loading="lazy" src="rnn/image-20251031135352922.png"></p> <p><img alt="image-20251031135553040" loading="lazy" src="rnn/image-20251031135553040.png"></p> <p><img alt="image-20251031140054080" loading="lazy" src="rnn/image-20251031140054080.png"></p> <p><img alt="image-20251031140443703" loading="lazy" src="rnn/image-20251031140443703.png"></p> <p>注：初始参数为随机生成</p> <p><img alt="image-20251031142050061" loading="lazy" src="rnn/image-20251031142050061.png"></p> <p><img alt="image-20251031213225065" loading="lazy" src="rnn/image-20251031213225065.png"></p> <p><img alt="image-20251031213234625" loading="lazy" src="rnn/image-20251031213234625.png"></p> <p><img alt="image-20251031213257410" loading="lazy" src="rnn/image-20251031213257410.png"></p> <p>以上为正向传播过程</p> <p>接下来为反向传播过程</p> <h4 id="反向">反向</h4> <p><img alt="image-20251031213457258" loading="lazy" src="rnn/image-20251031213457258.png"></p> <p><img alt="image-20251031214409367" loading="lazy" src="rnn/image-20251031214409367.png"></p> <h5 id="穿越时">穿越时</h5> <p><img alt="image-20251031214503189" loading="lazy" src="rnn/image-20251031214503189.png"></p> <p><img alt="image-20251031214530032" loading="lazy" src="rnn/image-20251031214530032.png"></p> <p>第一轮的训练结果，默认学习率为1的情况下第一列减去第二列就是一次训练的结果</p> <p><img alt="image-20251031214726615" loading="lazy" src="rnn/image-20251031214726615.png"></p> https://blog.techlover.shop/posts/%E5%87%BD%E6%95%B0/%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/ Mon, 01 Jan 0001 00:00:00 +0000 https://blog.techlover.shop/posts/%E5%87%BD%E6%95%B0/%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/ <h3 id="softmax">softmax</h3> <p><img alt="image-20250727205830679" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250727205830679.png"></p> <p><img alt="image-20250727210056516" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250727210056516.png"></p> <p>归一化</p> <p><img alt="image-20250727212449071" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250727212449071.png"><img alt="image-20250727212533918" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250727212533918.png"></p> <p><img alt="image-20250727213127638" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250727213127638.png"></p> <p>hard max 非常粗暴设置成1000 softmax 更加优雅，设置为数值</p> <h3 id="一元线性回归">一元线性回归</h3> <p><img alt="image-20250728160013047" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250728160013047.png"></p> <p>回归：指回归到均值</p> <h3 id="一元线性回归增加偏置值">一元线性回归增加偏置值</h3> <p><img alt="image-20250728190621921" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250728190621921.png"></p> <p><img alt="image-20250728193201993" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250728193201993.png"></p> <p><img alt="image-20250728193209707" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250728193209707.png"></p> <p><img alt="image-20250728195336133" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250728195336133.png"></p> <h3 id="梯度下降">梯度下降</h3> <p><img alt="image-20250729151052538" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250729151052538.png"></p> <p>loss 函数位于最小值的附近，f&rsquo; 导数越来越小，趋于平缓，此时 x - f&rsquo; 的会越来越趋近于最小值，且加减的幅度越来越精细，方便进行微调，达到全局最低点</p> <p><img alt="image-20250729151521303" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250729151521303.png">学习率防止步长过大或者过小</p> <p><img alt="image-20250729154447829" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250729154447829.png"></p> <p><img alt="image-20250729162733234" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250729162733234.png"></p> <p>学习率需要人工矫正</p> <p><img alt="image-20250729163845560" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250729163845560.png"></p> <p>参数足够大的话，一般不会下降到局部的小坑中</p> <h4 id="2">2</h4> <p><img alt="image-20250729164455023" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250729164455023.png"></p> <p>两个feature一个偏置</p> <p><img alt="image-20250729165846098" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250729165846098.png"></p> <p><img alt="image-20250729165930801" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250729165930801.png"></p> <p><img alt="image-20250729165955772" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250729165955772.png"></p> <p><img alt="image-20250729200641735" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250729200641735.png"></p> <p><img alt="image-20250729200649767" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250729200649767.png"></p> <h3 id="pytorch">pytorch</h3> <table> <thead> <tr> <th></th> <th>线性层 / 本例中的 <code>inputs @ w</code></th> <th>卷积层 / filter</th> </tr> </thead> <tbody> <tr> <td><strong>输入形状</strong></td> <td><code>[batch, features]</code> (这里 5 × 2)</td> <td><code>[batch, channels, H, W]</code> (例如图像)</td> </tr> <tr> <td><strong>权重形状</strong></td> <td><code>[features, out_dim]</code> (这里 2 × 1)</td> <td><code>[out_channels, in_channels, kH, kW]</code></td> </tr> <tr> <td><strong>运算方式</strong></td> <td>对 <strong>整行特征一次性</strong> 做向量点积 → 得到输出标量（或向量）</td> <td>在输入张量上 <strong>滑动窗口</strong>，每次取一个局部 patch，与卷积核做元素乘加，再把结果放到对应输出位置</td> </tr> <tr> <td><strong>权重共享</strong></td> <td><strong>不共享</strong>：每个特征都有自己唯一的权重系数</td> <td><strong>共享</strong>：同一个卷积核在整幅图像（或序列）上重复使用</td> </tr> <tr> <td><strong>几何结构</strong></td> <td>忽略空间关系，只把特征当作独立维度</td> <td>保留空间/时序结构，用局部感受野提取模式</td> </tr> <tr> <td><strong>结果尺寸</strong></td> <td><code>[batch, out_dim]</code>（这里 5 × 1）</td> <td><code>[batch, out_channels, H', W']</code></td> </tr> </tbody> </table> <h3 id="一元逻辑回归">一元逻辑回归</h3> <p><img alt="image-20250730105302930" loading="lazy" src="%E5%90%84%E7%B1%BB%E5%87%BD%E6%95%B0/image-20250730105302930.png"></p> https://blog.techlover.shop/posts/%E5%8A%A0%E5%AF%86%E6%B5%81%E9%87%8F%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB%E5%8F%AF%E8%A1%8C%E6%80%A7/ Mon, 01 Jan 0001 00:00:00 +0000 https://blog.techlover.shop/posts/%E5%8A%A0%E5%AF%86%E6%B5%81%E9%87%8F%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB%E5%8F%AF%E8%A1%8C%E6%80%A7/ <p>下面从<strong>可行性</strong>与<strong>性能</strong>两条主线，把“隐马尔可夫模型（HMM）用于网络加密流量识别”做一次尽量全面、细致、深入的拆解（偏研究与工程落地视角）。内容默认用于<strong>合法合规</strong>的网络运维、安全检测与研究评测场景。</p> <hr> <h2 id="1-问题到底在识别什么">1) 问题到底在“识别”什么</h2> <p>“加密流量识别”通常不等同于“解密”，而是基于<strong>可观测的侧信道/元数据</strong>去做分类或检测。常见目标层级（难度递增）：</p> <ol> <li><strong>协议/隧道层</strong>：TLS/QUIC/SSH/VPN/Tor…（相对更可行）</li> <li><strong>应用/服务层</strong>：YouTube/Zoom/网盘/IM…（中等难度）</li> <li><strong>细粒度内容/网站指纹</strong>：同一CDN下的网站、同一APP内不同功能（最难、最不稳）</li> </ol> <p>综述类工作普遍指出：HTTP/2、QUIC、多路复用、流量伪装/隧道会显著抬高难度与不确定性。<a href="https://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2016187/">京东在线+1</a></p> <hr> <h2 id="2-加密后还剩下什么信息hmm为什么对口">2) 加密后还剩下什么信息？HMM为什么“对口”</h2> <p>即便负载加密，网络侧通常仍能拿到一些序列信号，例如：</p> <ul> <li><strong>包长序列</strong>（packet length sequence）</li> <li><strong>方向序列</strong>（上行/下行）</li> <li><strong>到达间隔/时序</strong>（inter-arrival time）</li> <li><strong>突发/静默结构</strong>（burstiness）</li> <li><strong>握手阶段的可见字段/长度结构</strong>（例如 TLS 的部分握手交互“形状”；QUIC则更受限）</li> </ul> <p>这些恰好是<strong>时序/序列数据</strong>。HMM的强项就是：</p> <blockquote> <p>用一组“隐状态”（可理解为通信的阶段/模式）去生成观测序列，从而用“序列整体的概率”来做分类。</p> </blockquote> <p>早期经典工作就展示了：仅用“包大小与时序”的序列建模，HMM可在加密/隧道背景下推断协议行为并做分类。<a href="https://jmlr.org/papers/volume7/wright06a/wright06a.pdf">机器学习研究杂志</a></p> <hr> <h2 id="3-hmm在加密流量识别中的典型建模方式">3) HMM在加密流量识别中的典型建模方式</h2> <h3 id="31-观测序列怎么设计决定上限">3.1 观测序列怎么设计（决定上限）</h3> <p>常见做法是把一个流/会话映射为长度为 TTT 的序列 O1:TO_{1:T}O1:T：</p> <ul> <li><strong>离散HMM</strong>：把包长、时间间隔分桶（binning），或向量量化（VQ）</li> <li><strong>连续HMM（GaussianHMM / GMM-HMM）</strong>：直接用连续值建模观测分布；若同一隐状态下观测是多峰分布，用GMM更合适</li> <li><strong>双向流</strong>：把方向编码进符号（例如“上行包长为正、下行为负”），或做“上下行各一条序列再融合”</li> </ul> <p>Wright 等人在协议行为推断中使用了<strong>profile HMM</strong>并扩展了向量量化以融合包长+时序，这个思路对“加密流量=只能看形状”非常典型。<a href="https://jmlr.org/papers/volume7/wright06a/wright06a.pdf">机器学习研究杂志</a></p> <h3 id="32-分类策略生成式的优势">3.2 分类策略（生成式的优势）</h3> <p>加密流量识别里常见是“每类一个HMM”：</p> <ul> <li>训练：对每个类别 ccc 训练参数 θc\theta_cθc</li> <li>推断：对未知序列算对数似然 log⁡p(O∣θc)\log p(O|\theta_c)logp(O∣θc)，取最大者 或做阈值判断（低于阈值当作未知类/异常）</li> </ul> <p>这类生成式框架对<strong>样本量较小</strong>、<strong>需要解释性/可审计</strong>、<strong>需要在线打分</strong>的场景很友好。</p> <hr> <h2 id="4-可行性分析hmm到底适合哪些加密识别任务">4) 可行性分析：HMM到底适合哪些“加密识别任务”</h2> <h3 id="更可行工程上更容易做稳">更可行（工程上更容易做稳）</h3> <ol> <li><strong>粗粒度：协议族/隧道识别</strong>（TLS vs SSH vs Tor vs VPN…）</li> <li><strong>场景固定：企业网/园区网内“已知应用集合”识别</strong></li> <li><strong>恶意加密流量检测</strong>：例如“加密C2/恶意通信”相对更像“行为模式”问题</li> </ol> <p>例如《软件学报》有工作用 <strong>profile HMM</strong>做“跨协议的加密恶意流量检测”，强调在不同条件下有效、且设计了规避检测对抗并验证抗规避能力。<a href="https://jos.org.cn/html/2022/7/6282.htm">软件学报</a></p> <h3 id="中等可行能做但要接受漂移与误差">中等可行（能做，但要接受漂移与误差）</h3> <ul> <li><strong>应用级分类</strong>：尤其当不同应用的交互节奏差异明显（VoIP、视频、下载、聊天等）</li> <li>可以借助<strong>握手可见交互字段</strong>增强：例如有研究利用 SSL 交互阶段字段作为观测序列并用HMM做应用识别，报告其对典型加密应用有更好的性能与鲁棒性。<a href="https://www.ecice06.com/CN/Y2020/V46/I4/151">易采网</a></li> </ul> <h3 id="很难做稳hmm不占优甚至整体方法论都很难">很难做稳（HMM不占优，甚至整体方法论都很难）</h3> <ul> <li><strong>同CDN下细粒度网站/内容指纹</strong></li> <li><strong>强对抗/强伪装</strong>：主动padding、定速整形、随机化分片策略</li> <li><strong>QUIC/HTTP3 多路复用 + 频繁网络环境变化</strong>：序列“形状”本身会被链路条件改变</li> </ul> <hr> <h2 id="5-性能分析准确率之外更关键的是稳不稳">5) 性能分析：准确率之外，更关键的是“稳不稳”</h2> <h3 id="51-经典结果能说明什么">5.1 经典结果能说明什么</h3> <p>Wright 等的JMLR论文报告：对若干协议在混合流量中分类准确率可超过 90%，在“单连接细粒度分类”上多数协议也能超过 80%，并能在某些加密隧道场景估计连接数，平均误差优于约 20%。<a href="https://jmlr.org/papers/volume7/wright06a/wright06a.pdf">机器学习研究杂志</a> 这些结果的意义在于：<strong>序列形状确实携带可分信息，HMM能捕捉“阶段性结构”。</strong></p> https://blog.techlover.shop/posts/%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/ Mon, 01 Jan 0001 00:00:00 +0000 https://blog.techlover.shop/posts/%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/ <h2 id="likelihood">likelihood</h2> <p><img alt="image-20251215152126276" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251215152126276.png"></p> <p><img alt="image-20251215152132029" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251215152132029.png"></p> <p><img alt="image-20251215152138202" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251215152138202.png"></p> <p><img alt="image-20251215152352472" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251215152352472.png"></p> <p><img alt="image-20251215163856080" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251215163856080.png"></p> <p><img alt="image-20251215194405358" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251215194405358.png"></p> <p><img alt="image-20251215194232466" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251215194232466.png"></p> <p><img alt="image-20251215195021191" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251215195021191.png"></p> <p><img alt="image-20251215195122014" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251215195122014.png"></p> <p>横轴为tracitions</p> <p><img alt="image-20251215195208989" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251215195208989.png"></p> <p>数轴为emissions</p> <p>两个表格初始为随机生成的</p> <p><img alt="image-20251216205941011" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251216205941011.png"></p> <p><img alt="image-20251216205952361" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251216205952361.png"></p> <p>全概率公式</p> <p><img alt="image-20251216211049319" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251216211049319.png"></p> <p>应该使用动态规划去优化</p> <p><img alt="image-20251216211235928" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251216211235928.png"></p> <h2 id="decoding">decoding</h2> <p><img alt="image-20251216213503906" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251216213503906.png"></p> <p>max（1，2，3）</p> <p>得到最大的，然后把线路高亮</p> <p><img alt="image-20251216214500728" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251216214500728.png"></p> <p><img alt="image-20251216214610452" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251216214610452.png"></p> <h2 id="inference">inference</h2> <p><img alt="image-20251216220637868" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251216220637868.png"></p> <p><img alt="image-20251216220645644" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251216220645644.png"></p> <p><img alt="image-20251217133901246" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251217133901246.png"></p> <p><img alt="image-20251217135615981" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251217135615981.png"></p> <p><img alt="image-20251217135625999" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251217135625999.png"></p> <p><img alt="image-20251217135739904" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251217135739904.png"></p> <p><img alt="image-20251217135744855" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251217135744855.png"></p> <p><img alt="image-20251217140755695" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251217140755695.png"></p> <p><img alt="image-20251217153927364" loading="lazy" src="%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB/image-20251217153927364.png"></p> <h2 id="learning">learning</h2>