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      For hardware that can exploit sparsity, increasing the amount of sparsity (i.e., decreasing the number of effectual operations out of (total) operations) can increase the number of operations per joule, which subsequently increases inferences per joule, as shown in Equation (3.6). While exploiting sparsity has the potential of increasing the number of (total) operations per joule, the additional hardware will decrease the effectual operations plus unexploited ineffectual operations per joule. In order to achieve a net benefit, the decrease in effectual operations plus unexploited ineffectual operations per joule must be more than offset by the decrease of effectual operations out of (total) operations.

      In summary, we want to emphasize that the number of MAC operations and weights in the DNN model are not sufficient for evaluating energy efficiency. From an energy perspective, all MAC operations or weights are not created equal. This is because the number of MAC operations and weights do not reflect where the data is accessed and how much the data is reused, both of which have a significant impact on the operations per joule. Therefore, the number of MAC operations and weights is not necessarily a good proxy for energy consumption and it is often more effective to design efficient DNN models with hardware in the loop. Techniques for designing DNN models with hardware in the loop are discussed in Chapter 9.

      In order to evaluate the energy efficiency and power consumption of the entire system, it is critical to not only report the energy efficiency and power consumption of the chip, but also the energy efficiency and power consumption of the off-chip memory (e.g., DRAM) or the amount of off-chip accesses (e.g., DRAM accesses) if no specific memory technology is specified; for the latter, it can be reported in terms of the total amount of data that is read and written off-chip per inference. As with throughput and latency, the evaluation should be performed on clearly specified, ideally widely used, DNN models.

3.4 HARDWARE COST

In order to evaluate the desirability of a given architecture or technique, it is also important to consider the hardware cost of the design. Hardware cost is used to indicate the monetary cost to build a system.⁷ This is important from both an industry and a research perspective to dictate whether a system is financially viable. From an industry perspective, the cost constraints are related to volume and market; for instance, embedded processors have a much more stringent cost limitations than processors in the cloud.

      One of the key factors that affect cost is the chip area (e.g., square millimeters, mm²) in conjunction with the process technology (e.g., 45 nm CMOS), which constrains the amount of on-chip storage and amount of compute (e.g., the number of PEs for custom DNN accelerators, the number of cores for CPUs and GPUs, the number of digital signal processing (DSP) engines for FPGAs, etc.). To report information related to area, without specifying a specific process technology, the amount of on-chip memory (e.g, storage capacity of the global buffer) and compute (e.g., number of PEs) can be used as a proxy for area.

      Another important factor is the amount of off-chip bandwidth, which dictates the cost and complexity of the packaging and printed circuit board (PCB) design (e.g., High Bandwidth Memory (HBM) [122] to connect to off-chip DRAM, NVLink to connect to other GPUs, etc.), as well as whether additional chip area is required for a transceiver to handle signal integrity at high speeds. The off-chip bandwidth, which is typically reported in gigabits per second (Gbps), sometimes including the number of I/O ports, can be used as a proxy for packaging and PCB cost.

      There is also an interplay between the costs attributable to the chip area and off-chip bandwidth. For instance, increasing on-chip storage, which increases chip area, can reduce off-chip bandwidth. Accordingly, both metrics should be reported in order to provide perspective on the total cost of the system.

      Of course reducing cost alone is not the only objective. The design objective is invariably to maximize the throughput or energy efficiency for a given cost, specifically, to maximize inferences per second per cost (e.g., $) and/or inferences per joule per cost. This is closely related to the previously discussed property of utilization; to be cost efficient, the design should aim to utilize every PE to increase inferences per second, since each PE increases the area and thus the cost of the chip; similarly, the design should aim to effectively utilize all the on-chip storage to reduce off-chip bandwidth, or increase operations per off-chip memory access as expressed by the roofline model (see Figure 3.1), as each byte of on-chip memory also increases cost.

3.5 FLEXIBILITY

      The merit of a DNN accelerator is also a function of its flexibility. Flexibility refers to the range of DNN models that can be supported on the DNN processor and the ability of the software environment (e.g., the mapper) to maximally exploit the capabilities of the hardware for any desired DNN model. Given the fast-moving pace of DNN research and deployment, it is increasingly important that DNN processors support a wide range of DNN models and tasks.

      We can define support in two tiers: the first tier requires that the hardware only needs to be able to functionally support different DNN models (i.e., the DNN model can run on the hardware). The second tier requires that the hardware should also maintain efficiency (i.e., high throughput and energy efficiency) across different DNN models.

      To maintain efficiency, the hardware should not rely on certain properties of the DNN models to achieve efficiency, as the properties cannot be guaranteed. For instance, a DNN accelerator that can efficiently support the case where the entire DNN model (i.e., all the weights) fits on-chip may perform extremely poorly when the DNN model grows larger, which is likely given that the size of DNN models continue to increase over time, as discussed in Section 2.4.1; a more flexible processor would be able to efficiently handle a wide range of DNN models, even those that exceed on-chip memory.

      The degree of flexibility provided by a DNN accelerator is a complex trade-off with accelerator cost. Specifically, additional hardware usually needs to be added in order to flexibly support a wider range of workloads and/or improve their throughput and energy efficiency. We all know that specialization improves efficiency; thus, the design objective is to reduce the overhead (e.g., area cost and energy consumption) of supporting flexibility while maintaining efficiency across the wide range of DNN models. Thus, evaluating flexibility would entail ensuring that the extra hardware is a net benefit across multiple workloads.

      Flexibility has become increasingly important when we factor in the many techniques that are being applied to the DNN models with the promise to make them more efficient, since they increase the diversity of workloads that need to be supported. These techniques include DNNs with different network architectures (i.e., different layer shapes, which impacts the amount of required storage and compute and the available data reuse that can be exploited), as described in Chapter 9, different levels of precision (i.e., different number of bits for across layers and data types), as described in Chapter 7, and different degrees of sparsity (i.e., number of zeros in the data), as described in Chapter 8. There are also different types of DNN layers and computation beyond MAC operations (e.g., activation functions) that need to be supported.

      Actually getting a performance or efficiency benefit from these techniques invariably requires additional hardware, because a simpler DNN accelerator design may not benefit from these techniques. Again, it is important that the overhead of the additional hardware does not exceed the benefits of these techniques. This encourages a hardware and DNN model co-design approach.

      To date, exploiting the flexibility of DNN hardware has relied on mapping processes that act like static per-layer compilers.

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