Deployment of dynamic neural networks on edge accelerators requires careful consideration of hardware constraints beyond conventional complexity metrics such as Multiply-Accumulate operations. In Early-Exiting Neural Networks (EENN), exit placement, quantization level, and hardware workload mapping interact in non-trivial ways, influencing memory traffic, accelerator utilization, and ultimately energy-latency trade-offs. These interactions remain insufficiently understood in existing Neural Architecture Search (NAS) approaches, which typically rely on proxy metrics or hardware-in-the-loop evaluation. This work presents a hardware-algorithm co-design framework for EENN that explicitly models the interplay between quantization, exit configuration, and multi-core accelerator mapping. Using analytical design space exploration, we characterize how small architectural variations can induce disproportionate changes in hardware efficiency due to tensor dimension alignment and dataflow effects. Building on this analysis, we formulate EENN deployment as a constrained multi-objective optimization problem balancing accuracy, energy-latency product, exit overhead, and dynamic inference behavior. Experimental results on CIFAR-10 demonstrate that the proposed framework identifies architectures achieving over 50\% reduction in energy-latency product compared to static baselines under 8-bit quantization. The results highlight the importance of deployment-aware co-design for dynamic inference on heterogeneous edge platforms.

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