The degree d(H)of a subgraph H of a graph G is|u∈∪V(H)N(u)-V(H)|,where N(u)denotes the neighbor set of the vertex u of G.In this paper,we prove the following result on the condition of the degrees of subgraphs.Let G...The degree d(H)of a subgraph H of a graph G is|u∈∪V(H)N(u)-V(H)|,where N(u)denotes the neighbor set of the vertex u of G.In this paper,we prove the following result on the condition of the degrees of subgraphs.Let G be a 2-connected claw-free graph of order n with minimum degreeδ(G)≥3.If for any three non-adjacent subgraphs H1,H2,H3 that are isomorphic to K1,K1,K2,respectively,there is d(H1)+d(H2)+d(H3)≥n+3,then for each pair of vertices u,v∈G that is not a cut set,there exists a Hamilton path between u and v.展开更多
近几年卷积神经网络作为深度学习最重要的技术,在图像分类、物体检测、语音识别等领域均有所建树。在此期间,由多层卷积神经网络组成的深度神经网络横空出世,在各种任务准确性方面具有显著提升。然而,神经网络的权重往往被限定在单精度...近几年卷积神经网络作为深度学习最重要的技术,在图像分类、物体检测、语音识别等领域均有所建树。在此期间,由多层卷积神经网络组成的深度神经网络横空出世,在各种任务准确性方面具有显著提升。然而,神经网络的权重往往被限定在单精度类型,使网络体积相较于特定硬件平台上的内存空间更大,且floating point 16、INT 8等单精度类型已无法满足现在一些模型推理的现实需求。为此,提出一种以子图为最小单位,通过判断相邻结点之间的融合关系,添加了丰富比特位的混合精度推理算法。首先,在原有单精度量化设计的搜索空间中增加floating point 16半精度的比特配置,使最终搜索空间变大,为寻找最优解提供更多机会。其次,使用子图融合的思想,通过整数线性规划将融合后的不同子图精度配置,根据模型大小、推理延迟和位宽操作数3个约束对计算图进行划分,使最后累积的扰动误差减少。最终,在ResNet系列网络上验证发现,所提模型精度相较于HAWQ V3的损失没超过1%的同时,相较于其他混合精度量化方法在推理速度方面得到了提升,在ResNet18网络中推理速度分别提升18.15%、19.21%,在ResNet50网络中推理速度分别提升13.15%、13.70%。展开更多
基金supported by the National Natural Science Foundation of China(No.11871398)the Natural Science Basic Research Plan in Shaanxi Province of China(Program No.2018JM1032)+1 种基金the Fundamental Research Funds for the Central Universities(No.3102019ghjd003)the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(No.ZZ2019031)
文摘The degree d(H)of a subgraph H of a graph G is|u∈∪V(H)N(u)-V(H)|,where N(u)denotes the neighbor set of the vertex u of G.In this paper,we prove the following result on the condition of the degrees of subgraphs.Let G be a 2-connected claw-free graph of order n with minimum degreeδ(G)≥3.If for any three non-adjacent subgraphs H1,H2,H3 that are isomorphic to K1,K1,K2,respectively,there is d(H1)+d(H2)+d(H3)≥n+3,then for each pair of vertices u,v∈G that is not a cut set,there exists a Hamilton path between u and v.
文摘近几年卷积神经网络作为深度学习最重要的技术,在图像分类、物体检测、语音识别等领域均有所建树。在此期间,由多层卷积神经网络组成的深度神经网络横空出世,在各种任务准确性方面具有显著提升。然而,神经网络的权重往往被限定在单精度类型,使网络体积相较于特定硬件平台上的内存空间更大,且floating point 16、INT 8等单精度类型已无法满足现在一些模型推理的现实需求。为此,提出一种以子图为最小单位,通过判断相邻结点之间的融合关系,添加了丰富比特位的混合精度推理算法。首先,在原有单精度量化设计的搜索空间中增加floating point 16半精度的比特配置,使最终搜索空间变大,为寻找最优解提供更多机会。其次,使用子图融合的思想,通过整数线性规划将融合后的不同子图精度配置,根据模型大小、推理延迟和位宽操作数3个约束对计算图进行划分,使最后累积的扰动误差减少。最终,在ResNet系列网络上验证发现,所提模型精度相较于HAWQ V3的损失没超过1%的同时,相较于其他混合精度量化方法在推理速度方面得到了提升,在ResNet18网络中推理速度分别提升18.15%、19.21%,在ResNet50网络中推理速度分别提升13.15%、13.70%。
