TCI-Former: Thermal Conduction-Inspired Transformer for Infrared Small Target Detection Infrared small target detection (ISTD) is critical for national security and has been widely applied in military areas. ISTD aims to segment small target pixels from the background. Most ISTD networks focus on designing feature extraction blocks or fusion modules, but rarely describe the ISTD process from the feature map evolution perspective. In the ISTD process, the network attention gradually shifts towards target areas. This process is abstracted as the directional movement of feature map pixels to target areas through convolution, pooling, and interactions with surrounding pixels, analogous to the movement of thermal particles constrained by surrounding variables and particles. Based on the theoretical principles of thermal conduction, we propose the Thermal Conduction-Inspired Transformer (TCI-Former). According to the thermal conduction differential equation in heat dynamics, we derive the pixel movement differential equation (PMDE) in the image domain and further develop two modules: Thermal Conduction-Inspired Attention (TCIA) and Thermal Conduction Boundary Module (TCBM). TCIA incorporates the finite difference method with PMDE to extract target body features. TCBM is designed and supervised by boundary masks to refine target body features with fine boundary details. Experiments on IRSTD-1k and NUAA-SIRST demonstrate the superiority of our method. The paper introduces a novel research routine by analogizing the pixel movement during the ISTD process as thermal conduction in thermodynamics. Based on the thermal conduction differential equation, we derive the pixel movement differential equation (PMDE) in the image domain for ISTD. Our PMDE builds a spatial-temporal constraint to guide the pixel flow direction, so we design our network based on it. On one hand, we apply the finite difference method to PMDE and propose TCIA to help extract the main body features of targets. On the other hand, focusing only on the main body areas of targets can cause errors in segmenting boundary areas, so we devise TCBM to refine target body features with fine boundary details. Our contributions include: (1) We are the first to realize the intrinsic consistency between thermal micro-elements and image pixels during feature map evolution in ISTD, transferring heat conduction theories into ISTD network design and proposing TCI-Former. (2) Inspired by the thermal conduction differential equation, we derive our pixel movement differential equation (PMDE) to establish a link between spatial and temporal information of pixel values during ISTD process. (3) We incorporate the finite difference method to PMDE and propose TCIA to extract target main body features but bring slight errors to target boundary areas. As a complement, TCBM is also devised to supplement target body features with fine boundary details to make up for the errors. (4) Our method outperforms others on IRSTD-1k and NUAA-SIRST in terms of evaluation metrics.TCI-Former: Thermal Conduction-Inspired Transformer for Infrared Small Target Detection Infrared small target detection (ISTD) is critical for national security and has been widely applied in military areas. ISTD aims to segment small target pixels from the background. Most ISTD networks focus on designing feature extraction blocks or fusion modules, but rarely describe the ISTD process from the feature map evolution perspective. In the ISTD process, the network attention gradually shifts towards target areas. This process is abstracted as the directional movement of feature map pixels to target areas through convolution, pooling, and interactions with surrounding pixels, analogous to the movement of thermal particles constrained by surrounding variables and particles. Based on the theoretical principles of thermal conduction, we propose the Thermal Conduction-Inspired Transformer (TCI-Former). According to the thermal conduction differential equation in heat dynamics, we derive the pixel movement differential equation (PMDE) in the image domain and further develop two modules: Thermal Conduction-Inspired Attention (TCIA) and Thermal Conduction Boundary Module (TCBM). TCIA incorporates the finite difference method with PMDE to extract target body features. TCBM is designed and supervised by boundary masks to refine target body features with fine boundary details. Experiments on IRSTD-1k and NUAA-SIRST demonstrate the superiority of our method. The paper introduces a novel research routine by analogizing the pixel movement during the ISTD process as thermal conduction in thermodynamics. Based on the thermal conduction differential equation, we derive the pixel movement differential equation (PMDE) in the image domain for ISTD. Our PMDE builds a spatial-temporal constraint to guide the pixel flow direction, so we design our network based on it. On one hand, we apply the finite difference method to PMDE and propose TCIA to help extract the main body features of targets. On the other hand, focusing only on the main body areas of targets can cause errors in segmenting boundary areas, so we devise TCBM to refine target body features with fine boundary details. Our contributions include: (1) We are the first to realize the intrinsic consistency between thermal micro-elements and image pixels during feature map evolution in ISTD, transferring heat conduction theories into ISTD network design and proposing TCI-Former. (2) Inspired by the thermal conduction differential equation, we derive our pixel movement differential equation (PMDE) to establish a link between spatial and temporal information of pixel values during ISTD process. (3) We incorporate the finite difference method to PMDE and propose TCIA to extract target main body features but bring slight errors to target boundary areas. As a complement, TCBM is also devised to supplement target body features with fine boundary details to make up for the errors. (4) Our method outperforms others on IRSTD-1k and NUAA-SIRST in terms of evaluation metrics.