File size: 1,188 Bytes
675525d | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | {
"renderer": "matplotlib mathtext, STIX fonts, vector paths",
"formulas": {
"decision-distribution": [
"p_d(a_i\\mid x,A)=\\frac{\\exp(z_{d,i})}{\\sum_{j=1}^{K}\\exp(z_{d,j})}"
],
"joint-depth-objective": [
"\\mathcal{L}_{\\mathrm{decision}}=0.5\\,\\mathrm{CE}(q,p_{\\mathrm{low}})+0.5\\,\\mathrm{CE}(q,p_{\\mathrm{high}})",
"\\qquad +0.1\\,\\mathrm{KL}\\!\\left(\\mathrm{stopgrad}(p_{\\mathrm{high}})\\,\\Vert\\,p_{\\mathrm{low}}\\right)"
],
"dcrl-objective": [
"\\mathcal{L}_{\\mathrm{DCRL}}=\\frac{1}{|\\mathcal{D}|}\\sum_{d\\in\\mathcal{D}}\\left[\\mathrm{NLL}(q,p_d)+\\lambda_B\\,\\mathrm{Brier}(q,p_d)\\right]",
"\\qquad +\\lambda_{\\mathrm{ref}}\\,\\mathrm{KL}(p_{\\mathrm{high}}\\,\\Vert\\,p_{\\mathrm{reference}})",
"\\qquad +\\lambda_U\\,\\mathcal{L}_{\\mathrm{utility}}(p_{\\mathrm{low}})"
],
"expected-utility": [
"\\mathcal{L}_{\\mathrm{utility}}=-\\sum_{a\\in A(x)}p_{\\mathrm{low}}(a)\\,u(a)"
],
"candidate-projection": [
"z_C=W[C]h_d+b[C]=(Wh_d+b)[C]"
],
"projection-cost": [
"\\mathrm{Full\\ vocabulary}:\\ O(HV)\\qquad\\mathrm{Candidate\\ rows}:\\ O(HK)"
]
}
}
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