Large-scale artificial intelligence models are transforming industries and redefining human machine collaboration. However, continued scaling exposes critical limitations in hardware, including constraints on computation, bandwidth, and memory. These dimensions are tightly interconnected, so improvements in one often create bottlenecks in others, making isolated optimizations less effective. Balancing them to maximize system efficiency remains a central challenge in scalable AI design. To address this challenge, we introduce {Computation-Bandwidth-Memory Trade-offs}, termed the {AI Trinity}, a unified paradigm that positions {computation}, {bandwidth}, and {memory} as coequal pillars for next-generation AI infrastructure. AI Trinity enables dynamic allocation of resources across these pillars, alleviating single-resource bottlenecks and adapting to diverse scenarios to optimize system performance. Within this framework, AI Trinity identifies three fundamental trade-offs: (1) {More Computation$\rightarrow$Less Bandwidth}, wherein computational resources are exploited to reduce data transmission under limited bandwidth conditions, (2) {More Bandwidth$\rightarrow$Less Memory}, which exploits abundant communication capacity to populate or refresh memory when local storage resources are constrained, and (3) {More Memory$\rightarrow$Less Computation}, whereby storage capacity are utilized to mitigate redundant computation when computational costs are prohibitive. We illustrate the effectiveness of AI Trinity through representative system designs spanning edge-cloud communication, large-scale distributed training, and model inference. The innovations embodied in AI Trinity advance a new paradigm for scalable AI infrastructure, providing both a conceptual foundation and practical guidance for a broad range of application scenarios.