## 1 Introduction  
Intent is a complex, multi-level concept encompassing psychological, behavioral, and technological aspects [1, 2]. It reveals the underlying motivations, expectations, and goals of human behavior and decision-making, providing significant value in understanding target behavior and its causes, and predicting its outcomes [3]. By understanding and predicting the behavior, needs, and expectations of targets, the intelligence level of systems can be greatly enhanced, improving human-computer interaction and user experience. Additionally, in complex systems, intent recognition can provide crucial support for decision-making [4, 5]. In the fields of product design and user experience, the study of cognitive intent regarding product form characteristics holds significant importance. Research indicates that 80% of users are influenced by product form design in their purchasing decisions [6]. This demonstrates that product form is not only a key factor in attracting users but also an important element affecting their emotions and behaviors [7]. With increasing market competition and diverse user demands, deeply understanding users' cognitive intent regarding product form becomes crucial. This understanding aids designers in creating products that better meet user expectations [8]. Product form plays a crucial role in conveying design intent, suggesting product functions and usage methods. It not only attracts users and promotes consumption but also guides users to quickly recognize and correctly understand the product, enhancing the smoothness of the product experience, thereby influencing acceptance, satisfaction, and loyalty [9]. Accurate communication of intent is also related to product safety, especially in professional fields such as road traffic, aerospace, and aviation [10; 11]. Therefore, ensuring that the design intent of a product can be understood and recognized through its form characteristics is crucial to reducing safety risks from misuse, thereby enhancing user experience and trust in the product [12]. However, traditional design methods face numerous challenges in addressing the complexity of user intent recognition. Traditional approaches often rely on designers' experience and intuition, lacking systematic and scientific analytical tools. This results in a high degree of subjectivity and uncertainty in the design process [13]. In existing research, studies on the cognitive intent of product form characteristics are scarce, but there is a wealth of research on form imagery. For instance, [PERSON] et al. explored the visual imagery and user preferences of central control touch screens (CCTS) in new energy vehicles [14]. [PERSON] and [PERSON], using the analytic hierarchy process (AHP), quantified design imagery vocabulary and established relationships between design features and imagery vocabulary. They systematically evaluated human emotions and design features in new energy vehicle model designs using a fuzzy comprehensive evaluation method [15]. Currently, research on intent recognition and prediction mainly focuses on battlefield target recognition [16; 17], human-computer interaction [18; 19], motion behavior analysis [20], visual behavior studies [21], user search intent [22; 23], and emotional intent recognition [24]. For example, [PERSON] et al. proposed a novel neural network fusion model that combines information classification processing and information fusion functions to recognize target behavior intent in battlefield environments [25]. [PERSON] et al. proposed a human-machine interaction (HMI) model that uses Gaussian mixture distribution to identify user operation intent and designed a hybrid communication architecture to facilitate intent sharing, thereby improving industrial assembly efficiency and reducing error rates [26]. [PERSON] et al. analyzed survey data from 1,135 participants in industrial environments using regression models to explore the relationship between physical activity intent and actual behavior, providing a basis for improvements in ergonomic design [27].