Theory of Cognitive Relativity — The Road to Strong Artificial Intelligence
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摘要: 人工智能(AI)的发展如火如荼，大有超越人类之势，以致很多人认为奇点就要来临，强人工智能即将实现。这是一种对强人工智能的误解，因为强人工智能的核心并不在于其功能是否强大，而在于它是否具有意识。该文首先解释了强人工智能的内涵，讨论了与之相关的意识问题；然后，阐述了旨在揭开意识奥秘的认知相对论思想，包括：世界的相对性原理和符号的相对性原理，以及世界、语言和心灵的关系。接着，提出了另一条新原理，即意识的等效原理，用以说明意识从物质产生所需要的物理条件，解决主观体验或现象意识的困难问题，推导意识能力受限于感觉能力且以感觉容量为上界的认知基本定理，并分析意识在哪里和自我是什么的可能性。最后，在认知相对论的框架下，给出了研究意识问题的新纲领和实现机器意识的新思路，并展望了强人工智能的未来。Abstract: Artificial Intelligence(AI) develops in full swing with a great potential to surpass human, leading many people to believe that a singularity is imminent and that strong AI is about to be realized. This is a misconception of strong AI, because the core of strong AI is not whether it is powerful, but whether it has consciousness. In this article, firstly, the connotation of strong AI is explained, and the related problem of consciousness is discussed; Then, the ideas of Theory of Cognitive Relativity is elucidated, aimed at revealing the secret of consciousness, including the Principle of World’s Relativity, the Principle of Symbol’s Relativity, together with the relationships between world, language and mind. Subsequently, another new principle is expounded, namely the Principle of Consciousness’ Equivalence, to show the physical conditions required for arising of consciousness from matter, and to solve the hard problem of subjective experience or phenomenal consciousness, and to establish the fundamental theorem of cognition that conscious ability is limited by sensory ability with the upper bound of sensory capacity, and to analyze the possibility of where consciousness is as well as what self is. Finally, under the framework of the theory of cognitive relativity, a new creed for solving the puzzle of consciousness and a new guide for implementing machine consciousness are presented, with the future of strong AI envisioned.
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1. 引言
作为2维平面结构的超材料，超表面[1,2]通过精心设计亚波长尺寸的单元结构可以调控电磁波的幅度、相位和极化方式，具有低剖面、重量轻、易于制作等优点，被广泛应用于极化转化器[3,4]、涡旋发生器[5,6]、图像处理器[7]、天线[8,9]等领域。而随着现代集成系统的迅速发展，功能单一的超表面已无法满足集成系统的需求。相对于有源超表面(如可重构超表面)[10,11]为实现多功能进行的复杂控制系统设计，无源超表面通过改变入射波的极化、频率和角度等实现多种功能的集成，极大降低了系统的损耗和成本。2018年，文献[12]基于P-B相位在微波波段提出了一款3层金属结构堆叠的双功能超表面；同年，Zhuang等人[13]利用一种基于反射和透射结构的多层超表面实现3种不同的功能；2019年，文献[14]研制了一款集成共振和几何相位的级联多功能超表面，以独立操控反射和透射电磁波；2021年，Shang等人[15]利用一组双层交叉型反射单元设计了一款2 bit编码超表面，在不同极化波作用下实现两幅独立的全息图像。上述研制的多功能超表面，大多数采用多层结构堆叠的形式实现360°相位覆盖，并不是研制低成本和集成化功能性器件的最佳解决方案。
惠更斯超表面[16-19]通过合理构建电偶极子和磁偶极子，能够对电场和磁场产生响应，从而实现对入射电磁波的自由调控，相对于只调控极化电流的超表面，它既能保证高的透射效率，又能保证全相位覆盖，且制作工艺简单，能显著提高超表面效率，一直是人工电磁领域的研究热点。文献[20]提出了一款极化不敏感的惠更斯超表面，在远场产生高效率的全息图像。2018年，Wang等人[21]在微波波段研制了4款惠更斯超表面全息图，并在y极化电磁波的激励下呈现不同的图像。之后，该研究团队设计了一款宽频段的惠更斯超表面，y极化电磁波经过超表面的调制实现3维全息图像[22]。目前大多数研究的惠更斯超表面极化模式单一，并且需要在物理结构上同时构建电、磁偶极子，设计过程相对复杂，极大限制了在实际工程中的应用。因此，围绕惠更斯超表面开展结构简单的新型极化复用电磁集成器件的研究方兴未艾。
本文提出一种极化复用的聚焦惠更斯超表面，可通过改变相应的物理参数实现x极化和y极化独立调控，35 GHz频率下具有较小的传输损耗和较高的聚焦质量。超表面单元由一层厚度为0.17λ的介质基板和位于两侧的两个不对称电偶极子元件组成，物理结构上没有单独的磁偶极子元件，而是通过反向流动的表面电流诱导磁流，使单元结构更加紧凑。利用全息理论，设计了在x极化波和y极化波作用下具有独立聚焦特性的极化复用超表面，仿真和实测结果基本一致，验证了所提出的惠更斯超表面具有极化复用的可行性。
2. 超表面单元设计
惠更斯超表面来源于等效原理，该原理通过无穷小的薄型表面电流密度Js和磁流密度Ms来满足边界条件[16,17]。当入射波激励惠更斯表面时，会同时感应表面电流和磁流密度，产生依赖于电流和磁流密度的反射波和透射波，如图1所示。对于区域1中的入射场，区域2中的任意场可以通过在超表面上引入电流和磁流密度来确定。电磁场和表面电磁流密度满足边界条件为
Js=n×(H2−H1) (1) Ms=−n×(E2−E1) (2) 其中，n为朝向区域2的单位法向向量，E和H为电场和磁场。在实际应用中，通过取表面电磁流密度与表面平均切向场的比值，得到特定表面电磁流密度与表面电导纳
ˉˉYes 和磁阻抗ˉˉZms 之间的关系Js=ˉˉYes⋅Etan,av|S (3) Ms=ˉˉZms⋅Htan,av|S (4) 其中，Etan,av和Htan,av分别是表面上的平均切向电场和磁场。
ˉˉYes 和ˉˉZms 为张量，表示为ˉˉYes = (YxxesYxyesYyxesYyyes) (5) ˉˉZms = (ZxxmsZxymsZyxmsZyyms) (6) 由场分布得到表面阻抗后，将超表面离散为单元。根据反射系数(R)和透射系数(T)确定特定单元的表面阻抗
Yes=2η⋅1−T−R1+T+R (7) Zms=2η⋅1−T+R1+T−R (8) 其中，η为自由空间的波阻抗，对于无反射、全透射的惠更斯超表面，即
R=0 ,T=ejφt 满足Yes=−j2η⋅tan(φt2) (9) Zms=−j2η⋅tan(φt2) (10) 由式(9)和式(10)可以看出，表面阻抗与传输相位
φt 有关，对于每个特定的传输相位，都有相应的表面阻抗。此外，如果归一化的表面电导纳和磁阻抗相等且为纯虚数(Yesη = Zms/η)，则会激发电磁共振，获得高传输幅度。图2说明了本文利用的透射型惠更斯单元结构，分别由x方向和y方向的金属结构线性叠加构成，具有4种不同叠加方式。当y极化波入射时，调控y方向的金属结构可产生轴向表面电流，实现传输幅度接近1的宽带传输谱和360°相位覆盖，而不改变x极化波的传输相位和幅度。同理，x方向的金属结构可对x极化波进行波束调控，而对y极化波不产生响应，单元实现极化复用特性。
图3(a)和图3(b)为对y极化波响应的单元结构E_1和E_2，由印刷在1.5 mm厚的介质基板(介电常数2.22，tanδ = 0.001)两侧的不对称金属贴片(电偶极子)构成，其中P = 4.8 mm, h = 1.5 mm, w = 0.2 mm。通过建立归一化电导纳Yesη与磁阻抗Zms/η同单元传输幅度之间的关系分析其工作原理，如图4(a)所示，谐振点31.5 GHz和34.2 GHz处，Yesη与Zms/η的虚部相等，实部趋于0，实现电磁共振，形成两个传输幅度峰值。两电磁共振频率之间形成一个通频带，传输幅度优于0.9。谐振点34.2 GHz处的表面电流在矩形金属贴片上流动，假设上、下层金属贴片的电流分别为Iup和Ilow，他们具有相同的电流密度但具有不同的相位，即Ilow =Iupexp(jΔ
φ )，Δφ 代表延迟相位。图4(b)给出了随时间相位因子θ = ωt变化的表面电流分布，灰色部分的上、下金属贴片的表面电流方向相反，在单元侧面形成电流环，即构成磁偶极子，诱导出垂直于电流的磁流，与表面电流相互作用激发电磁共振。因此，可通过调控单元E_1的贴片长度L1和单元E_2的贴片弧长L2获得所需的电磁共振，实现360°相位覆盖和高传输幅度。y极化电磁波垂直入射到超表面单元，L1从1 mm变化到4.8 mm，共极化透射波Tyy的传输幅度均优于0.90，传输相位在445°～105°之间变化，实现340°相位积累，L1的变化对交叉极化透射波Txy的传输相位几乎没有影响，可独立实现对x极化波和y极化波的相位调控，如图5(a)所示。由图5(b)可知，L2从0.95 mm变化到1.40 mm，共极化透射波Tyy的传输幅度优于0.90，传输相位在105°～85°之间变化，相位积累达到20°，L2的变化使交叉极化透射波Txy的传输相位偏移7°左右，偏移量较小，可以在后续超表面的阵列排布中进行修正。结合图5(a)和图5(b)的分析，通过改变单元E_1和单元E_2的金属参数L1和L2，在中心频率35 GHz处实现360°的相位覆盖。
3. 超表面设计与测试
本文利用全息理论[18,23]，设计了在x极化和y极化波作用下具有独立聚焦特性的极化复用惠更斯超表面。为实现任意波前的再现，惠更斯超表面需要如下步骤得到相位补偿：首先，将所需要的波前看作物波，并记录相位补偿；其次，利用相同的参考波对全息图进行激励，再现物波。基于此思想，在超表面设计过程中，将期望的目标场分布和入射平面波分别视为物波和参考波。
图6是基于超表面的全息原理图，详细的相位补偿推导如下：超表面上的场分布来自目标场辐射的球面波的叠加。为了再现目标场，需要将目标场离散为多个虚拟点源。假设在Fn位置产生n个点源，则超表面的叠加E场表示为
E(xi,yi)=N∑n=1An(xi,yi)⋅exp(jk0Rn) (11) An(xi,yi) = AnRn (12) Rn=|Fn−ri| (13) (xi,yi)表示第i个超表面单元的中心坐标。常数An是第n个点源的振幅，Rn是第n个点源到第i个超表面单元的距离。k0为自由空间中的波数。Fn是第n个点源到原点的距离，ri是第i个单元到原点的距离，N为离散的点源总数目。参考波为正入射的平面波，到超表面上的振幅和相位恒定。假设相位是
φr ，超表面的相位补偿为φ(xi,yi)=φr−angleE(xi,yi) (14) 为了验证所设计的惠更斯超表面在35 GHz处具有极化复用特性，设置x极化波作用下，惠更斯超表面在焦距为40 mm和80 mm分别实现单焦点和4个焦点的3维聚焦。在y极化波作用下，焦距70 mm平面处再现字母“I”，图7为极化复用超表面的相位分布和尺寸分布。利用商用软件CST Microwave Studio进行模拟，得到在线极化波垂直入射下，经过惠更斯超表面调制的透射场分布。图8(a)为x极化波作用下，焦距为40 mm和80 mm的电场强度分布，实现了单个焦点和4个焦点的3维聚焦。而y极化波作用下，在焦距为70 mm的平面中心再现字母“I”，如图8(b)所示。焦点和图像“I”附近存在少量的衍射场，是电磁波通过惠更斯超表面产生了基于衍射光图案的高次谐波，可采取一些优化算法改善效果。
采用印刷电路板(Printed Circuit Board, PCB)工艺制作了超表面样品，以实验验证模拟的极化复用惠更斯超表面在中心频率处的性能，如图9(b)。设计的惠更斯超表面由729个单元组成，覆盖面积为129.6 mm×129.6 mm。利用喇叭天线发射线极化准平面波(通过调整端口方向以实现不同的极化方式)，并使其与超表面中心保持一致，用近场探针在指定焦距处测量透射电场，如图9(a)所示。图10分别为x极化波和y极化波入射下，频率为35 GHz的电场强度分布，从图中可以看出，x极化波经过惠更斯超表面调制后，在焦距为40 mm和80 mm平面处分别实现单焦点和4个焦点的3维聚焦。而y极化波经过超表面的调制后再现字母“I”。
为进一步验证实测与模拟结果的一致性，提取特定平面处x方向和y方向的电场强度，如图11所示。图11(a)显示利用极化复用惠更斯超表面调制x极化波后，提取焦距为40 mm，中心焦点x方向的模拟和实测电场强度分布，以及焦距为80 mm, 4个焦点x方向和y方向的电场强度分布，结果表明实测的单焦点聚焦和模拟结果一致，而4个焦点的实测结果相对于模拟结果有轻微的偏差。这样的偏差主要来自喇叭天线辐射的入射波并不是严格的平面波，在超表面上存在轻微离轴偏差。此外，相位补偿误差、加工缺陷和测量误差等也会造成焦点之间的偏差和微弱的强度变化。对于y极化，图11(b)展现了焦距为70 mm，x方向和y方向的模拟和实测结果，实测的峰值强度与模拟结果有一定的偏差，存在的主要原因是喇叭天线提供的非理想的平面波前，并且加工缺陷、测试误差也会造成一定影响。实测和模拟结果表明，所设计的惠更斯超表面能够实现对x极化波和y极化波的独立调控，具有极化复用特性。
超表面的聚焦效率η可以由聚焦平面处聚焦区域的能量总和P1与无超表面时该平面处的辐射功率P2的比值来确定，即η=P1/P2，P1和P2可通过相应区域的坡印廷矢量积分得到。对于x极化波，计算得中心频率35 GHz的聚焦效率为29.73%，y极化波的聚焦效率达到33.64%。
表1为本文设计的超表面与已有超表面的对比。通过比较发现，所设计的超表面具有双极化独立调控功能。与文献[25,26]相比，本文设计的惠更斯单元实现360°全相位覆盖和优于0.9的高传输幅度，且单层无金属过孔，具有低剖面和结构简单等特点，可印刷在价格低廉的PCB板两侧，降低加工难度。此外，所设计的惠更斯单元没有单独构建磁偶极子，在物理结构上消除了对磁性元件的需求，使超表面更加紧凑。
表 1 文献对比分析4. 结论
本文采用4种简单的单元编码实现一款极化复用的聚焦惠更斯超表面。通过调整电磁共振，实现了惠更斯超表面的高透射率、360°相位覆盖和极化控制。并在35 GHz处进行了实验验证，通过操纵入射电磁波的极化分量，超表面根据透射波的极化状态实现独立聚焦，实测和仿真结果吻合良好。所提出的超表面具有结构紧凑、极化调控、易加工等优点，可应用于信息复用、多通道图像显示、加密防伪、存储显示等领域。
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