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      "tex": "\\text{参考信息}\n\\rightarrow\n\\text{运动对齐的特征上下文}\n\\rightarrow\n\\begin{cases}\n\\text{帮助形成表示}\\\\\n\\text{帮助图像重建}\\\\\n\\text{帮助概率估计}\n\\end{cases}",
      "display": true
    },
    {
      "tex": "\\hat x_t=\nf_{\\mathrm{dec}}\\!\\left(\nQ\\!\\left(f_{\\mathrm{enc}}(x_t-\\tilde x_t)\\right)\n\\right)+\\tilde x_t .\n\\tag{1}",
      "display": true
    },
    {
      "tex": "Q",
      "display": false
    },
    {
      "tex": "\\hat x_t=\nf_{\\mathrm{dec}}\\!\\left(\nQ(f_{\\mathrm{enc}}(x_t\\mid\\tilde x_t))\n\\mid\\tilde x_t\n\\right).\n\\tag{2}",
      "display": true
    },
    {
      "tex": "\\hat x_t=\nf_{\\mathrm{dec}}\\!\\left(\nQ(f_{\\mathrm{enc}}(x_t\\mid\\bar x_t))\n\\mid\\bar x_t\n\\right).\n\\tag{3}",
      "display": true
    },
    {
      "tex": "m_t",
      "display": false
    },
    {
      "tex": "\\hat m_t",
      "display": false
    },
    {
      "tex": "\\hat m_t",
      "display": false
    },
    {
      "tex": "\\bar x_t",
      "display": false
    },
    {
      "tex": "y_t",
      "display": false
    },
    {
      "tex": "\\hat x_t",
      "display": false
    },
    {
      "tex": "R(\\hat y_t)\\ge\n\\mathbb E_{\\hat y_t\\sim q}\n[-\\log_2p(\\hat y_t)].\n\\tag{4}",
      "display": true
    },
    {
      "tex": "q",
      "display": false
    },
    {
      "tex": "p",
      "display": false
    },
    {
      "tex": "\\begin{aligned}\nH(q,p)\n&=-\\sum_u q(u)\\log_2p(u)\\\\\n&=H(q)+D_{\\mathrm{KL}}(q\\Vert p).\n\\end{aligned}",
      "display": true
    },
    {
      "tex": "(\\mu_{t,i},\\sigma_{t,i})=\nf_{\\mathrm{pf}}\\!\\left(\nf_{\\mathrm{hpd}}(\\hat z_t),\nf_{\\mathrm{ar}}(\\hat y_{t,<i}),\nf_{\\mathrm{tpe}}(\\bar x_t)\n\\right).",
      "display": true
    },
    {
      "tex": "\\hat y_{t,<i}",
      "display": false
    },
    {
      "tex": "p(\\hat y_t\\mid\\bar x_t,\\hat z_t)\n=\n\\prod_i\n\\left[\n\\mathcal L(\\mu_{t,i},\\sigma_{t,i}^{2})\n*\\mathcal U(-\\tfrac12,\\tfrac12)\n\\right](\\hat y_{t,i}).\n\\tag{5}",
      "display": true
    },
    {
      "tex": "k",
      "display": false
    },
    {
      "tex": "p(\\hat y=k)\n=\n\\int_{k-1/2}^{k+1/2}f(u)\\,du\n=\nF(k+1/2)-F(k-1/2).",
      "display": true
    },
    {
      "tex": "p(\\hat y=0)=1-e^{-0.5}\\approx0.39347.",
      "display": true
    },
    {
      "tex": "f(0)=0.5",
      "display": false
    },
    {
      "tex": "\\sigma^2",
      "display": false
    },
    {
      "tex": "(\\mu,\\sigma)=\nf_{\\mathrm{pf}}\\!\\left(\nf_{\\mathrm{hpd}}(\\hat z_t),\nf_{\\mathrm{tpe}}(\\bar x_t)\n\\right).",
      "display": true
    },
    {
      "tex": "\\bar x_t=\nf_{\\mathrm{cr}}\\!\\left(\n\\operatorname{warp}\n\\left(f_{\\mathrm{fe}}(\\hat x_{t-1}),\\hat m_t\\right)\n\\right).\n\\tag{6}",
      "display": true
    },
    {
      "tex": "\\text{参考图像}\n\\rightarrow\\text{特征提取}\n\\rightarrow\\text{运动对齐}\n\\rightarrow\\text{上下文细化}.",
      "display": true
    },
    {
      "tex": "0.75\\times10+0.25\\times14=11.",
      "display": true
    },
    {
      "tex": "L=\\lambda D+R.\n\\tag{7}",
      "display": true
    },
    {
      "tex": "\\lambda",
      "display": false
    },
    {
      "tex": "\\lambda",
      "display": false
    },
    {
      "tex": "10^{-4}",
      "display": false
    },
    {
      "tex": "10^{-5}",
      "display": false
    },
    {
      "tex": "256\\times256",
      "display": false
    },
    {
      "tex": "26\\%-9\\%=17\\%",
      "display": true
    },
    {
      "tex": "1-\\frac1{1.054}\\approx5.12\\%.",
      "display": true
    },
    {
      "tex": "x_t:[B,3,H,W],\\qquad\nc_t:[B,64,H,W].",
      "display": true
    },
    {
      "tex": "[x_t,c_t]:[B,67,H,W].",
      "display": true
    },
    {
      "tex": "y_t:[B,96,H/16,W/16].",
      "display": true
    },
    {
      "tex": "1/256",
      "display": false
    },
    {
      "tex": "\\hat y_t",
      "display": false
    },
    {
      "tex": "\\hat z_t",
      "display": false
    },
    {
      "tex": "\\hat g_t",
      "display": false
    },
    {
      "tex": "\\hat s_t",
      "display": false
    },
    {
      "tex": "R_{\\mathrm{P}}\n=\nR(\\hat y_t)+R(\\hat z_t)\n+R(\\hat g_t)+R(\\hat s_t).",
      "display": true
    },
    {
      "tex": "\\boxed{\n\\text{条件怎样表示}\n\\quad+\\quad\n\\text{条件在哪些环节使用}\n\\quad+\\quad\n\\text{条件怎样学得}\n}",
      "display": true
    },
    {
      "tex": "1920\\times1080",
      "display": false
    },
    {
      "tex": "1920\\times1024",
      "display": false
    },
    {
      "tex": "x_t",
      "display": false
    },
    {
      "tex": "\\hat x_{t-1}",
      "display": false
    },
    {
      "tex": "v_i=\\frac{u_i}{\\sqrt{\\beta_i+\\sum_j\\gamma_{ij}u_j^2}}.",
      "display": true
    },
    {
      "tex": "q=\\operatorname{round}(y-\\mu),\\qquad\np(q)=F_b(q+1/2)-F_b(q-1/2).",
      "display": true
    },
    {
      "tex": "F_b",
      "display": false
    },
    {
      "tex": "-\\log_2p",
      "display": false
    },
    {
      "tex": "P(q=0)=F(0.5)-F(-0.5)=1-e^{-0.5}\\approx0.39347.",
      "display": true
    },
    {
      "tex": "\\mathrm{bpp}_{file}=\\mathrm{bpp}_{payload}+\\frac{24\\times8}{HW}.",
      "display": true
    },
    {
      "tex": "L=R_y+R_z+R_{mv_y}+R_{mv_z}+\\lambda D(x_t,\\hat x_t).",
      "display": true
    },
    {
      "tex": "c_0=0,\\qquad c_{s+1}=c_s+f_s,\\qquad\nf_s>0,\\qquad \\sum_s f_s=M.",
      "display": true
    },
    {
      "tex": "x'=M\\left\\lfloor\\frac{x}{f_s}\\right\\rfloor\n +(x\\bmod f_s)+c_s.",
      "display": true
    },
    {
      "tex": "x'\\bmod M=r+c_s\\in[c_s,c_s+f_s).",
      "display": true
    },
    {
      "tex": "x=f_s\\left\\lfloor\\frac{x'}{M}\\right\\rfloor\n +(x'\\bmod M)-c_s.",
      "display": true
    },
    {
      "tex": "r_t=x_t-\\tilde x_t.",
      "display": true
    },
    {
      "tex": "\\hat x_t=\\tilde x_t+\\hat r_t.",
      "display": true
    },
    {
      "tex": "H(x_t-\\tilde x_t)\\ge H(x_t\\mid\\tilde x_t).",
      "display": true
    },
    {
      "tex": "H(R)=-\\sum_r p(r)\\log_2 p(r),\n\\qquad\nH(R\\mid P)=\\sum_p p(p)H(R\\mid P=p).",
      "display": true
    },
    {
      "tex": "p(R=r\\mid P=p)=p(X=r+p\\mid P=p).",
      "display": true
    },
    {
      "tex": "H(R\\mid P=p)=H(X\\mid P=p).",
      "display": true
    },
    {
      "tex": "H(R\\mid P)=H(X\\mid P).",
      "display": true
    },
    {
      "tex": "I(R;P)=H(R)-H(R\\mid P)\\ge0.",
      "display": true
    },
    {
      "tex": "\\boxed{H(X-P)=H(X\\mid P)+I(X-P;P)\\ge H(X\\mid P).}",
      "display": true
    },
    {
      "tex": "H(R)=-\\frac12\\log_2\\frac12\n-2\\cdot\\frac14\\log_2\\frac14=1.5\\ \\text{bit}.",
      "display": true
    },
    {
      "tex": "H(R\\mid P)=\\frac12\\cdot0+\\frac12\\cdot1=0.5\\ \\text{bit}.",
      "display": true
    },
    {
      "tex": "c_t:=\\bar x_t,\\qquad\ny_t=E_\\theta(x_t,c_t),\\qquad\n\\hat y_t=Q(y_t),\\qquad\n\\hat x_t=D_\\phi(\\hat y_t,c_t).",
      "display": true
    },
    {
      "tex": "\\ell(\\hat y_t,c_t)\\approx-\\log_2 p_\\psi(\\hat y_t\\mid c_t,\\ldots).",
      "display": true
    },
    {
      "tex": "\\hat x_t=f_{\\rm dec}\\!\\left(Q\\!\\left(f_{\\rm enc}(x_t-\\tilde x_t)\\right)\\right)+\\tilde x_t,\n\\qquad \\tilde x_t=f_{\\rm predict}(\\hat x_{t-1}).\\tag{1}",
      "display": true
    },
    {
      "tex": "\\hat x_t=f_{\\rm dec}\\!\\left(Q(f_{\\rm enc}(x_t\\mid\\tilde x_t))\\mid\\tilde x_t\\right),\n\\qquad\\tilde x_t=f_{\\rm predict}(\\hat x_{t-1}).\\tag{2}",
      "display": true
    },
    {
      "tex": "\\hat x_t=f_{\\rm dec}\\!\\left(Q(f_{\\rm enc}(x_t\\mid\\bar x_t))\\mid\\bar x_t\\right),\n\\qquad \\bar x_t=f_{\\rm context}(\\hat x_{t-1}).\\tag{3}",
      "display": true
    },
    {
      "tex": "R(\\hat y_t)\\geq\\mathbb E_{\\hat y_t\\sim q_{\\hat y_t}}\n[-\\log_2p_{\\hat y_t}(\\hat y_t)].\\tag{4}",
      "display": true
    },
    {
      "tex": "H(q,p)=-\\sum_uq(u)\\log_2p(u)\n=H(q)+D_{\\rm KL}(q\\Vert p).",
      "display": true
    },
    {
      "tex": "p_{\\hat y_t}(\\hat y_t\\mid\\bar x_t,\\hat z_t)\n=\\prod_i\\left[\\mathcal L(\\mu_{t,i},\\sigma_{t,i}^{2})\n*\\mathcal U(-\\tfrac12,\\tfrac12)\\right](\\hat y_{t,i}),\\tag{5}",
      "display": true
    },
    {
      "tex": "(\\mu_{t,i},\\sigma_{t,i})=\nf_{\\rm pf}\\!\\left(f_{\\rm hpd}(\\hat z_t),\nf_{\\rm ar}(\\hat y_{t,<i}),f_{\\rm tpe}(\\bar x_t)\\right).",
      "display": true
    },
    {
      "tex": "f(u)=\\frac1{2b}e^{-|u-\\mu|/b},\\qquad\np(\\hat y=k)=\\int_{k-1/2}^{k+1/2}f(u)\\,du\n=F(k+1/2)-F(k-1/2).",
      "display": true
    },
    {
      "tex": "(\\mu_{t,i},\\sigma_{t,i})=f_{\\rm pf}\n\\left(f_{\\rm hpd}(\\hat z_t),f_{\\rm tpe}(\\bar x_t)\\right).",
      "display": true
    },
    {
      "tex": "\\bar x_t=f_{\\rm cr}\\!\\left(\n\\operatorname{warp}(f_{\\rm fe}(\\hat x_{t-1}),\\hat m_t)\n\\right).\\tag{6}",
      "display": true
    },
    {
      "tex": "L=\\lambda D+R.\\tag{7}",
      "display": true
    },
    {
      "tex": "x_t:[B,3,H,W],\\quad c_t:[B,64,H,W],",
      "display": true
    },
    {
      "tex": "\\operatorname{concat}(x_t,c_t):[B,67,H,W],\n\\quad y_t:[B,96,H/16,W/16].",
      "display": true
    },
    {
      "tex": "v_i=\\frac{u_i}{\\sqrt{\\beta_i+\\sum_j\\gamma_{ij}u_j^2}}.",
      "display": true
    },
    {
      "tex": "L_{\\rm me}=\\lambda D(x_t,\\tilde x_t)+R(\\hat g_t)+R(\\hat s_t),",
      "display": true
    },
    {
      "tex": "L_{\\rm reconstruction}=\\lambda D(x_t,\\hat x_t),",
      "display": true
    },
    {
      "tex": "L_{\\rm contextual\\_coding}=\\lambda D(x_t,\\hat x_t)+R(\\hat y_t)+R(\\hat z_t),",
      "display": true
    },
    {
      "tex": "L_{\\rm all}=\\lambda D(x_t,\\hat x_t)+R(\\hat y_t)+R(\\hat z_t)+R(\\hat g_t)+R(\\hat s_t).",
      "display": true
    }
  ],
  "missing_local_links": [],
  "heading_count": 170,
  "input_markdown_sha256": "b3c79ea715d817f9e6ddb265258c967fbfe2434588981360cd9e5a2e9b8915b6",
  "output_html_sha256": "de91619a821b4a3df5a8cb8a77d01eec8819b5ac5fea43f6ccb83d766a1cf724",
  "html_generation": "Rendered directly from the saved canonical Markdown with local Markdown-it and KaTeX HTML+MathML; no separate prose rewriting.",
  "deduplication": "task_complete.last_agent_message duplicates response_item; only response_item retained. Saved lecture files are preserved separately because their contents differ from chat finals.",
  "code_lecture_status": "Complete Python inference and active C++ entropy-path lectures; independent Python rANS reference verified, no official extension or trained model execution."
}