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Approximate computing

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Approximate computing is an emerging paradigm for energy-efficient and/or high-performance design.<a href="#cite_note-1">[1]</a> It includes a plethora of computation techniques that return a possibly inaccurate result rather than a guaranteed accurate result, and that can be used for applications where an approximate result is sufficient for its purpose.<a href="#cite_note-2">[2]</a> One example of such situation is for a search engine where no exact answer may exist for a certain search query and hence, many answers may be acceptable. Similarly, occasional dropping of some <a href="Frame_(video)" class="mw-redirect" title="Frame (video)">frames</a> in a video application can go undetected due to perceptual limitations of humans. Approximate computing is based on the observation that in many scenarios, although performing exact computation requires large amount of resources, allowing <a href="Approximation_theory" title="Approximation theory">bounded approximation</a> can provide disproportionate gains in performance and energy, while still achieving acceptable result accuracy. For example, in <a href="K-means_clustering" title="K-means clustering">k-means clustering</a> algorithm, allowing only 5% loss in classification accuracy can provide 50 times energy saving compared to the fully accurate classification.

The key requirement in approximate computing is that approximation can be introduced only in non-critical data, since approximating critical data (e.g., control operations) can lead to disastrous consequences, such as <a href="Program_crash" class="mw-redirect" title="Program crash">program crash</a> or erroneous output.

<div class="mw-heading mw-heading2"><h2 id="Strategies">Strategies</h2></div>

Several strategies can be used for performing approximate computing.

<dl><dt>Approximate circuits</dt>

<dd>Approximate arithmetic circuits:<a href="#cite_note-3">[3]</a> <a href="Adder_(electronics)" title="Adder (electronics)">adders</a>,<a href="#cite_note-4">[4]</a><a href="#cite_note-5">[5]</a> <a href="Binary_multiplier" title="Binary multiplier">multipliers</a><a href="#cite_note-6">[6]</a> and other <a href="Logical_circuit" class="mw-redirect" title="Logical circuit">logical circuits</a> can reduce hardware overhead.<a href="#cite_note-7">[7]</a><a href="#cite_note-8">[8]</a><a href="#cite_note-9">[9]</a> For example, an approximate multi-bit adder can ignore the <a href="Carry_chain" class="mw-redirect" title="Carry chain">carry chain</a> and thus, allow all its sub-adders to perform addition operation in parallel.<a href="#cite_note-10">[10]</a><a href="#cite_note-11">[11]</a></dd>

<dt>Approximate storage and memory</dt>

<dd>Instead of <a href="Computer_data_storage" title="Computer data storage">storing data</a> values exactly, they can be stored approximately, e.g., by <a href="Data_truncation" title="Data truncation">truncating</a> the lower-bits in <a href="Floating_point" class="mw-redirect" title="Floating point">floating point</a> data. Another method is to accept less reliable memory. For this, in <a href="DRAM" class="mw-redirect" title="DRAM">DRAM</a><a href="#cite_note-12">[12]</a> and <a href="EDRAM" title="EDRAM">eDRAM</a>, <a href="Refresh_rate" title="Refresh rate">refresh rate</a> assignments can be lowered or controlled.<a href="#cite_note-13">[13]</a> In <a href="Static_random-access_memory" title="Static random-access memory">SRAM</a>, supply voltage can be lowered<a href="#cite_note-14">[14]</a> or controlled.<a href="#cite_note-15">[15]</a> Approximate storage can be applied to reduce <a href="Magnetoresistive_random-access_memory" class="mw-redirect" title="Magnetoresistive random-access memory">MRAM</a>'s high write energy consumption.<a href="#cite_note-16">[16]</a> In general, any <a href="Error_detection_and_correction" title="Error detection and correction">error detection and correction</a> mechanisms should be disabled.</dd>

<dt>Software-level approximation</dt>

<dd>There are several ways to approximate at software level. <a href="Memoization" title="Memoization">Memoization</a> or fuzzy memoization (the use of a <a href="Vector_database" title="Vector database">vector database</a> for approximate retrieval from a cache, i.e. fuzzy caching) can be applied. Some <a href="Iteration" title="Iteration">iterations</a> of <a href="Loop_(computing)" class="mw-redirect" title="Loop (computing)">loops</a> can be skipped (termed as <a href="Loop_perforation" title="Loop perforation">loop perforation</a>) to achieve a result faster. Some tasks can also be skipped, for example when a run-time condition suggests that those tasks are not going to be useful (<a href="Task_skipping" title="Task skipping">task skipping</a>). <a href="Monte_Carlo_algorithm" title="Monte Carlo algorithm">Monte Carlo algorithms</a> and <a href="Randomized_algorithm" title="Randomized algorithm">Randomized algorithms</a> trade correctness for execution time guarantees.<a href="#cite_note-17">[17]</a> The computation can be reformulated according to paradigms that allow easily the acceleration on specialized hardware, e.g. a neural processing unit.<a href="#cite_note-18">[18]</a></dd>

<dt>Approximate system</dt>

<dd>In an approximate system,<a href="#cite_note-19">[19]</a> <a href="#cite_note-20">[20]</a> different subsystems of the system such as the processor, memory, sensor, and communication modules are synergistically approximated to obtain a much better system-level Q-E trade-off curve compared to individual approximations to each of the subsystems.</dd></dl>

<div class="mw-heading mw-heading2"><h2 id="Application_areas">Application areas</h2></div>

Approximate computing has been used in a variety of domains where the applications are error-tolerant, such as <a href="Multimedia" title="Multimedia">multimedia</a> processing, <a href="Machine_learning" title="Machine learning">machine learning</a>, <a href="Signal_processing" title="Signal processing">signal processing</a>, <a href="Computational_science" title="Computational science">scientific computing</a>. Therefore, approximate computing is mostly driven by applications that are related to human perception/cognition and have inherent error resilience. Many of these applications are based on statistical or probabilistic computation, such as different approximations can be made to better suit the desired objectives.<a href="#cite_note-21">[21]</a>

One notable application in <a href="Machine_learning" title="Machine learning">machine learning</a> is that Google is using this approach in their <a href="Tensor_processing_unit" class="mw-redirect" title="Tensor processing unit">Tensor processing units</a> (TPU, a custom <a href="Application-specific_integrated_circuit" title="Application-specific integrated circuit">ASIC</a>).<a href="#cite_note-22">[22]</a>

<div class="mw-heading mw-heading2"><h2 id="Derived_paradigms">Derived paradigms</h2></div>

The main issue in approximate computing is the identification of the section of the application that can be approximated. In the case of large scale applications, it is very common to find people holding the expertise on approximate computing techniques not having enough expertise on the application domain (and vice versa). In order to solve this problem, <a href="Programming_paradigm" title="Programming paradigm">programming paradigms</a><a href="#cite_note-23">[23]</a> have been proposed. They all have in common the clear role separation between application <a href="Programmer" title="Programmer">programmer</a> and application <a href="Domain_expert" class="mw-redirect" title="Domain expert">domain expert</a>. These approaches allow the spread of the most common <a href="Program_optimization" title="Program optimization">optimizations</a> and approximate computing techniques.

<ul><li><a href="Artificial_neural_network" class="mw-redirect" title="Artificial neural network">Artificial neural network</a></li>

<li><a href="Metaheuristic" title="Metaheuristic">Metaheuristic</a></li>

<li><a href="PCMOS" title="PCMOS">PCMOS</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<li id="cite_note-23"><a href="#cite_ref-23">^</a> <cite id="CITEREFNguyenLenharthPingali2013" class="citation book cs1">Nguyen, Donald; Lenharth, Andrew; Pingali, Keshav (2013). "A lightweight infrastructure for graph analytics". Proceedings of the Twenty-Fourth ACM Symposium on Operating Systems Principles. ACM. pp. 456–471. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F2517349.2522739">10.1145/2517349.2522739</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9781450323888</bdi>.</cite>

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