[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82018-en":3,"doc-seo-82018-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},82018,7971461740886,"Theodore","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","A Theoretical Framework for Stochastic Activity Prediction in Tensor Accelerator Wallace-Tree Multipliers","Tensor accelerator multipliers consume dynamic power on every clock cycle even when sparse operands trigger minimal internal switching. Existing methods fail to cover this active-but-sparse regime: zero-detection needs exactly-zero inputs, structural power gating requires an idle multiplier, and offline selection cannot react to runtime operand statistics. Stochastic Activity Prediction (SAP) predicts low switching from operands’ Hamming weight and freezes inputs once a Safety Controller verifies correctness. Three formal results bound prediction error, retain information, and establish Bernoulli-encoder optimality.","A Theoretical Framework for Stochastic Activity Prediction in Tensor Accelerator Wallace-Tree  \nMultipliers  \nPrashanthi Metku, Chandra Gandu  \nQualcomm Technologies, Inc., USA  \n{pmetku, chandras}@qti.qualcomm.com  \narXiv :2607 .08002v 1 [ cs .AR] 9 Jul 2026  \nAbstract—Tensor accelerator multipliers burn dynamic power on every clock cycle, even when sparse operands require very little internal switching. No existing technique addresses this: zero-detection requires exactly-zero operands, structural power gating requires an idle multiplier, and offline weight selection cannot respond to runtime data. This paper introduces Stochastic Activity Prediction (SAP), which closes this gap by examining the Hamming weight of arriving operands before the multiplier executes, predicting low switching activity, and freezing the inputs when a deterministic Safety Controller independently confirms the reuse is correct. Mispredictions cause missed savings, never wrong answers. Three formal results underpin SAP: (i) a Spectral Contraction Lemma proving that Wallace-tree activity depends on operand bit density, not bit position, establishing Lipschitz constant Lφ = 3/2 and prediction error below 10 −13 for a 256-cycle window; (ii) an Information Retention Theorem showing ηI ≥ 1 − O(log n/n), so one bit per cycle captures nearly all predictive information about O (n2 ) internal nodes; and (iii) a Bernoulli Optimality Theorem proving the chosen encoding is shown to be optimal, within the family of calibrated one-bit encoders of Hamming-weight statistics considered. SAP addresses the specific layer of the tensor accelerator power stack that existing techniques do not cover.  \nIndex Terms—Wallace Tree Multiplier, Tensor Accelerators, LowPower VLSI, Stochastic Activity Prediction, Operand Isolation, Energy-Efficient Computing, Information Theory, Bernoulli Optimality.  \nI. INTRODUCTION  \nThe rapid growth of deep learning has placed energy efficiency atthe centre of hardware design. Tensor accelerators, the silicon engines that power modern AI inference in data centres, edge devices, and mobile platforms, achieve their throughput by replicating Multiply– Accumulate (MAC) units at massive scale. A contemporary TPU contains 256 ×256 = 65 ,536 MAC units operating in parallel [1]–[3], and the dominant cost of running a neural network layer on such a device is the dynamic power burned inside those units [5] . That power is governed by Pdyn ∝ α·Ceff ·V2 ·f, where voltage and frequency are fixed by the process node, leaving the switching activity α as the only quantity that varies with the workload at runtime. Reducing α is therefore the primary lever available to a power-conscious hardware designer once the chip has been fabricated.  \nInside each MAC unit, the multiplication is implemented as a Wallace-tree reduction network: a logarithmic cascade of carry-save adders that compresses n2 partial products into two final carrypropagate inputs [2]–[4] . Tensor accelerators arrange these units in systolic arrays [6], where operands flow through a grid of MAC units in lock-step, enabling massive parallelism with minimal control overhead. Every gate in this tree toggles in proportion to how many  \nactive bits (logical 1s) flow through it each cycle. When both operands are dense, the tree works hard and consumes its full switching budget. When both operands are sparse, most stages barely move, yet the tree runs unconditionally and burns power regardless. This mismatch between the information content of the inputs and the energy expended on them is the inefficiency this work addresses.  \nThe problem is practically important because quantized AI inference is dominated by sparse operands. Post-training quantization [7]–[9] concentrates weight values near zero: an INT8 weight of value +2 is represented as 00000010: seven zeros and one one. Weight pruning and compression techniques [10] push this concentration further, leaving the majority of weights with very few acti","cbCaipvyXq3g9R7A","https://ap.wps.com/l/cbCaipvyXq3g9R7A","pdf",319289,5,1,6,"English","en",105,"# Introduction\n## Motivation: dynamic power vs. operand sparsity\n## Limitations of existing power-management techniques\n## Proposed framework: Stochastic Activity Prediction (SAP)","[{\"question\":\"What power inefficiency does the paper target in tensor accelerator multipliers?\",\"answer\":\"Wallace-tree multipliers burn full switching power each cycle even when operands are sparse but non-zero, creating wasted internal activity relative to the information content of the inputs.\"},{\"question\":\"How does Stochastic Activity Prediction (SAP) reduce multiplier switching activity?\",\"answer\":\"SAP computes the operands’ combined Hamming weight before execution, predicts low switching activity, and freezes the multiplier inputs after a deterministic Safety Controller confirms the reuse is correct.\"},{\"question\":\"What ensures correctness when SAP freezes inputs?\",\"answer\":\"A deterministic Safety Controller independently confirms that the reuse is correct; mispredictions only lead to missed savings rather than wrong answers.\"}]",1784177604,15,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"a-theoretical-framework-for-stochastic-activity-prediction-in-tensor-accelerator-wallace-tree-multipliers","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/a-theoretical-framework-for-stochastic-activity-prediction-in-tensor-accelerator-wallace-tree-multipliers/82018/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-29","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What power inefficiency does the paper target in tensor accelerator multipliers?","Question",{"text":76,"@type":77},"Wallace-tree multipliers burn full switching power each cycle even when operands are sparse but non-zero, creating wasted internal activity relative to the information content of the inputs.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does Stochastic Activity Prediction (SAP) reduce multiplier switching activity?",{"text":81,"@type":77},"SAP computes the operands’ combined Hamming weight before execution, predicts low switching activity, and freezes the multiplier inputs after a deterministic Safety Controller confirms the reuse is correct.",{"name":83,"@type":74,"acceptedAnswer":84},"What ensures correctness when SAP freezes inputs?",{"text":85,"@type":77},"A deterministic Safety Controller independently confirms that the reuse is correct; 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