Internet of Things Devices } Internet of Things (IoT) devices } Have access to an abundance of raw data } In home, work, or vehicle
IoT: Raw Data & Processing } IoT is gaining ground with the widespread of } Embedded processors } Ubiquitous wireless networks } Access to raw data } Understand it! } Real-time constraints } Limited resources } Power } Compute
IoT: DNN-based Processing } With deep neural networks (DNNs): }With DNNs IoTs can } Process several new data types and } Understand behaviors }Speech, vision, video, and text } But, DNNs are resource hungry }Cannot met real-time constraints on IoT devices }Several DNNs cannot be executed on IoTs
Approach 1: Offload to Cloud } Send the request to cloud services } AWS } Google Cloud } Microsoft
Why Cloud is not Always a Solution }Unreliable connections to the cloud }Plus low bandwidth and high latency }Disconnected Devices }Privacy }Privacy preserving learning (eg, differential privacy) }Privacy preserving inference (eg homomorphic encryption) }Personalization } Federated learning
Approach : IoT Collaboration erver } Distribute computations with collaboration Home Home Network } To meetsdemandsnetwork of DNNs } On top of common DNN User techniques for constrained Secure Domain devices (eg, pruning) (b) In-Home Server Home Alerts User Secure Domain (c) Musical Chair?! Balloon S Computation Domain (a) Single Robot Computation Domain (b) Collaborative Robots
IoT Collaboration Pros & Cons } Assuming DNN performance barrier is solved with collaboration among IoT devices Pros Not Dependent on Cloud Privacy Preserving Enables Personalized Insight Cons Unreliable Latencies Accuracy Drop due to Data Loss & Device Failure
Challenges Impact: Unreliable Latencies } Histogram of arrival times in -node system performing AlexNet (model parallelism) Compute Time Tail Latency Latency Data Points 0ms Computation <100ms % <10ms % } Long Tail and Max Latency -> Straggler Problem
Challenges Impact: Accuracy Drop } Common to loose data parts due to Accuracy (top-1) Accuracy (top-1) 10 08 0 0 0 00 1 08 0 0 0 0 000 00 Increasing loss 000 00 008 01 01 00 0 08 Increasing loss 008 01 01 00 0 0 0 00 0 08 0 0 00 0 Percentage of Data Loss (only in one layer) (a) 10-class digit recognition (LeNet-) 08 0 0 00 0 08 0 0 00 0 Percentage of Data Loss (only in one layer) (b) 1000-class image recognition (Inception v) } High Accuracy Drop Accuracy Drop 08 0 0 080 08 088 09 09 100 08 0 0 080 08 088 09 09 100
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sha1_base="8udf8dveqnsaqmiynnbydvdus=">aaabhicbzbns8naeiyn9avwrphltf8fqsefqifl1bmf+qbvkzjtp1yxcjlnbfmwdil9sd8nbhlt1hywhdbymtdibnfgdb+dwtrxuzwcbu0suf1a+pgrpofummywwseoevkpgepugggdrcgnaohtyhwqefugkeywczsdcpfdykdnqrnwzcrbtwdiycl0mfctxa/eigzphniwqbxuemi/iwqwnaaamxakwog9mhdi1kgqhs/miujmnqejywfngtu/piakt1japsz0tnsc/xzuz/twqwms/zjjduq+chmbtexmv1nblwhmjigtlfaejaiiznhssjyeb/nkvwhdvdljctktapowgncarnmev1oaetaebgjp8apvzqpzrwhvwgppphmmfoz8/jm+mwq==</latexit> sha1_base="8udf8dveqnsaqmiynnbydvdus=">aaabhicbzbns8naeiyn9avwrphltf8fqsefqifl1bmf+qbvkzjtp1yxcjlnbfmwdil9sd8nbhlt1hywhdbymtdibnfgdb+dwtrxuzwcbu0suf1a+pgrpofummywwseoevkpgepugggdrcgnaohtyhwqefugkeywczsdcpfdykdnqrnwzcrbtwdiycl0mfctxa/eigzphniwqbxuemi/iwqwnaaamxakwog9mhdi1kgqhs/miujmnqejywfngtu/piakt1japsz0tnsc/xzuz/twqwms/zjjduq+chmbtexmv1nblwhmjigtlfaejaiiznhssjyeb/nkvwhdvdljctktapowgncarnmev1oaetaebgjp8apvzqpzrwhvwgppphmmfoz8/jm+mwq==</latexit> K 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sha1_base="i0jzreoqzlhpokx8gyh90e=">aaabhicbzbns8naeiyn9avwrphltf8fqsefry9cjacf+qbvkzjtp1yxcjlnbfmwdil9sd8nbhlt1hywhdbymtdibnfgdb+dwtrxuzwcbu0suf1a+pgrpofummywwseoevkpgepugggdrcgnaohtyhwqefugkeywczsdcpfdykdnqrnwcrbtwdiycl0mfctxa/eigzphniwqbxuemi/iwqwnaaamxakwog9mhdi1kgqhs/miujmnqejywfngtu/piakt1japsz0tnsc/xzuz/twqwms/zjjduq+chmbtexmv1nblwhmjigtlfaejaiiznhssjyeb/nkvwhdvdljctksapowgncarnmev1oaotaebgjp8apvzqpzrwhvwgppphmmfoz8/ogemzw==</latexit> sha1_base="i0jzreoqzlhpokx8gyh90e=">aaabhicbzbns8naeiyn9avwrphltf8fqsefry9cjacf+qbvkzjtp1yxcjlnbfmwdil9sd8nbhlt1hywhdbymtdibnfgdb+dwtrxuzwcbu0suf1a+pgrpofummywwseoevkpgepugggdrcgnaohtyhwqefugkeywczsdcpfdykdnqrnwcrbtwdiycl0mfctxa/eigzphniwqbxuemi/iwqwnaaamxakwog9mhdi1kgqhs/miujmnqejywfngtu/piakt1japsz0tnsc/xzuz/twqwms/zjjduq+chmbtexmv1nblwhmjigtlfaejaiiznhssjyeb/nkvwhdvdljctksapowgncarnmev1oaotaebgjp8apvzqpzrwhvwgppphmmfoz8/ogemzw==</latexit> Computation of DNNs } Each layer s computations can be represented as matrix-matrix multiplication (GEMM kernels) Layer Layer Fully-connected layer: Layer 1 w 1 sha1_base="9ij/nmfdhhuntmscpsybs8/w=">aaab8xicbzdlsgmxfibp1futtpln8eiucozvdbl0ylcvacvgyaaynzsrdklhkmg/hxouibn0bdnatslbf0h8pgfc8gfxbzporfjufldw19yizmlredrx/0niyuyqiersdqkskwecng0znhzirxeucnooxtftevurkskudotmporhgowmokntefhtja1k/pvkxfrrhvdya0dfofcjvje/egnjkogkqzjwuuusfftrawjngalxqjpjmkydnxosar1xzhdj9yzofaq+rbm/friojrsdrydsjbezsty1/t1exne+iktcwkoipopwoqji9h0fdrgihldjxywuczuisgik0ymdalkq/awt1gvqqwb9r9sv8jikcathcaoexeadbqabtsagblecrzovznzmwwtopnmif+r8/ga0lzcy</latexit> a = w X k=1 wka l 1 k + b l Conv layer: F C F C WH = sha1_base="8udf8dveqnsaqmiynnbydvdus=">aaabhicbzbns8naeiyn9avwrphltf8fqsefqifl1bmf+qbvkzjtp1yxcjlnbfmwdil9sd8nbhlt1hywhdbymtdibnfgdb+dwtrxuzwcbu0suf1a+pgrpofummywwseoevkpgepugggdrcgnaohtyhwqefugkeywczsdcpfdykdnqrnwzcrbtwdiycl0mfctxa/eigzphniwqbxuemi/iwqwnaaamxakwog9mhdi1kgqhs/miujmnqejywfngtu/piakt1japsz0tnsc/xzuz/twqwms/zjjduq+chmbtexmv1nblwhmjigtlfaejaiiznhssjyeb/nkvwhdvdljctktapowgncarnmev1oaetaebgjp8apvzqpzrwhvwgppphmmfoz8/jm+mwq==</latexit> First channel, unrolled WH W k F C I F C WH = O K WH
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sha1_base="/cmi1uxs9gjdz+qvloxkouays=">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</latexit> 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sha1_base="/cmi1uxs9gjdz+qvloxkouays=">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</latexit> sha1_base="/cmi1uxs9gjdz+qvloxkouays=">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</latexit> Computation Distribution of DNNs } Methods distributing computation of a model* Fully-connected Layers Output splitting: Input splitting: Hadidi, Ramyad, et al "Collaborative Execution of Deep Neural Networks on Internet of Things Devices" arxiv preprint arxiv:19010 (019) w 11 w 1 w 1k w 1 w w k w 1 w w k w m1 w m w mk Weights (divided among nodes) w 11 w 1 w 1k w 1 w w k w 1 w w k w m1 w m w mk Weights (divided among nodes) m k m k } Same can be applied on conv layers* } Channel, spatial, and filter splitting a 0 1 a 0 a 0 a 0 k k 1 Inputs (every node needs a copy) a 0 1 a 0 a 0 a 0 k = k 1 = a 1 a a a m m 1 Outputs (each node independently) Inputs Outputs (divided among nodes) (each node calculates partial sums) a 1 a m a 1 a m m 1 m 1 = a 1 a a a m m 1
Coded Distributed Computing (CDC) } Designed for MapReduce workloads (018)* } Preforming redundant or coded computer per node to reduce communication This work: DNNs on IoT More Compute / Node = More Reliability * Li, Songze, et al "A fundamental tradeoff between computation and communication in distributed computing" IEEE Transactions on Information Theory 1 (018): 109-18
Using CDC for Robustness } Add column-wise summation of the weights: } The new weights are constant, so done in offline } Distribute outputs among nodes }Thus, applicable only to output-splitting methods
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sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> How to Distribute CDC and Recover? } Add column-wise summation of the weights: }Simple example (one output/device) }Recovery } Subtraction vs Multiplication } You also needs the weights, that X X X X X X X X X you would not have in the final node }Multiple out/device: Just create a new weight matrix [ sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> X X X Output Splitting for nodes One Failure Tolerance [ sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> X X X X X X [ [ [ sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> Output Splitting for nodes Two Failures Tolerance [ sha1_base="mmilieak1suevxtmwgdhaxvu=">aaabhicbzbns8naeiynftbvfxozbeinkoighlxjyyj8gdwwznbrrnuwuxfkc/wkerr/kb/bt0ovrcwsmm+zmgaca+o8a+sbm1nzppyt9wwdkbuskuwxblbgjozuo+aswybgd1uiy1dgz1wfdurdqazibznjmyjpupkimqs1ftlapbc+ciq+avuivcjxlqzdiwbajnexqrxptuquuezgt9zknkwvjoktfoqqxicflzol9yzkchr9klduvizzgwk/i0hbg1iz0cm1m/lfzmxpdbdmxawzqssvhusaiscjsajlgcpkrewuukwjwxefwxgzloixjlj9c+lmwwevevrrwloiuzuaaprqeod9cafjbaeizxehmenrfnflytkxcwj/jhz+qo/fzv</latexit> [ [