Advances in hybrid bonding and packaging have driven growing interest in 3D DRAM-stacked accelerators with higher memory bandwidth and capacity. As LLMs scale to hundreds of billions or trillions of parameters, distributed inference across multiple 3D chips becomes essential. With cross-stack co-design increasingly critical, we propose DeepStack, an accurate and efficient performance model and tool to enable early-stage system-hardware co-design space exploration (DSE) for distributed 3D-stacked AI systems. At the hardware level, DeepStack captures fine-grained 3D memory semantics such as transaction-aware bandwidth, bank activation constraints, buffering limitations, and thermal-power modeling. At the system level, DeepStack incorporates comprehensive parallelization strategies and execution scheduling for distributed LLM inference. With novel modeling techniques such as dual-stage network abstraction and tile-level compute-communication overlap, we achieve up to 100,000x faster runtime over state-of-the-art simulators at comparable accuracy, cross-validated against our in-house 3D designs, NS-3 backend (2.12%), and vLLM serving on 8xB200 GPUs (12.18%). With hierarchical design space search, DeepStack enables efficient exploration over 2.5x10^14 design points spanning 3D-stacked DRAM layers, DRAM vertical connectivity, interconnect, compute-memory allocation, and distributed scheduling. Compared with baseline designs, DeepStack achieves up to 9.5x higher throughput through co-optimized parallelism and 3D architecture search. Our DSE further reveals that batch size drives a more fundamental architectural divide than the prefill/decode distinction, and that parallelism strategy and hardware architecture are tightly coupled -- incomplete schedule search leads to permanently suboptimal silicon irrecoverable by software tuning. We intend to open source DeepStack to support future research.

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