cs.LGAug 1, 2023

Learning from Hypervectors: A Survey on Hyperdimensional Encoding

Authors: Sercan Aygun, Mehran Shoushtari Moghadam, M. Hassan Najafi, Mohsen Imani

Organizations: Sch. Comp. and Info., Univ. of Louisiana at Lafayette, 70503 Lafayette, LA, USA · Comp. Sci. and Eng., Univ. of California Irvine, 92697 Irvine, CA, USA

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Abstract

Hyperdimensional computing (HDC) is an emerging computing paradigm that imitates the brain's structure to offer a powerful and efficient processing and learning model. In HDC, the data are encoded with long vectors, called hypervectors, which typically range from 1,000 to 10,000 in length. The literature provides several encoding methods to generate orthogonal or correlated hypervectors, based on the application. Existing surveys focus on overall HDC system aspects like inputs, primary computations, and outputs. However, this study takes a more specific approach. It zeroes in on the HDC system input and the generation of hypervectors, directly influencing the hypervector encoding. This survey brings together various hypervector generation and encoding methods, exploring the limitations, challenges, and potential benefits they entail.

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Figure 1. Overview of an HDC system for classification, together with a compact reference for the representation and operation conventions used throughout this survey. The main stages are: I encoding incoming data, II training with the input dataset, and III computing similarity between class-based HV\boldsymbol{\mathcal{HV}} s ( CclassC_{\mathrm{class}} ) and the query HV\boldsymbol{\mathcal{HV}} . The right-side quick reference summarizes binary / bipolar domains, binding operators, bundling and thresholding conventions, and permutation notation.
Figure 2. PRISMA-inspired literature search, screening, and inclusion workflow used in this survey.
Figure 3. Comparison of learning : HDC vs. NNs, together with a compact summary of HDC encoding and ML-based representation learning.
TargetSOTA WorksTargetSOTA Works
Image Processing/Computer Vision( Morris et al., 2022b ; Poduval et al., 2022 ; Imani et al., 2020a ; Kang et al., 2022b ; Imani et al., 2019f ; Mitrokhin et al., 2020 ; Imani et al., 2019d ; Ma et al., 2023a ; Kleyko et al., 2018b ; Duan et al., 2022 ; Ma and Jiao, 2022 ; Zhao et al., 2022 ; Khaleghi et al., 2022 ; Kovalev et al., 2022 ; Montone et al., 2017 ; Kirilenko et al., 2021 ; Hersche et al., 2020 ; Watkinson et al., 2021 ; Duan et al., 2022 ; Miranda and d’Aliberti, 2022 ; Dutta et al., 2022 ; Peter Sutor et al., 2022 ; Ma et al., 2023c ; Hersche et al., 2023b ; Wilson et al., 2023 ; Neubert et al., 2021 ; Menet et al., 2023 ; Hersche et al., 2023a ; Aygun et al., 2024 ; Moghadam et al., 2023 ; Imani et al., 2022 ; Redding et al., 2023 ; Kim et al., 2021a ; Yu et al., 2022 ; Moghadam et al., 2026 ; Masum et al., 2025 )Language/Text Processing( Wu et al., 2018a ; Rahimi et al., 2016b ; Räsänen, 2015 ; Kleyko et al., 2018b ; Karunaratne et al., 2021b ; Moraliyage et al., 2022 ; Kovalev et al., 2022 ; Montone et al., 2017 ; Kirilenko et al., 2021 ; Mohammad Navaz et al., 2023 ; Liu et al., 2022 ; Aygun et al., 2023 ; Moghadam et al., 2026 )
Biomedical/Biometrics( Imani et al., 2018a ; Nazemi et al., 2020 ; Rahimi et al., 2019 ; Zou et al., 2022a ; Burrello et al., 2019 ; Chang et al., 2019 ; Imani et al., 2020a ; Kang et al., 2022b ; Imani et al., 2019f ; Imani et al., 2020b ; Imani et al., 2019d ; Rahimi et al., 2016a ; Burrello et al., 2020 ; Burrello et al., 2018 ; Menon et al., 2022a ; Basaklar et al., 2021 ; Moin et al., 2018 ; Watkinson et al., 2021 ; Hersche et al., 2018 ; Gupta et al., 2022 ; Thomann et al., 2023 ; Rahimi et al., 2020 ; Schindler and Rahimi, 2021 ; Pale et al., 2022 ; Xu et al., 2023a ; Yang et al., 2022 ; Pinge et al., 2023 ; Kim et al., 2021a ; Moghadam et al., 2026 ; Masum et al., 2026 ; Masum et al., 2025 )Cross-paradigm Computing †( Poduval et al., 2021b ; Liu et al., 2019 ; Bosch et al., 2019 ; Hao et al., 2021 ; Moghadam et al., 2023 ; Aygun et al., 2023 ; Orchard and Jarvis, 2023 ; Zou et al., 2022b ; Bent et al., 2022 ; Zhang et al., 2023 ; Aygun et al., 2024 ; Imani et al., 2022 ; Fayza et al., 2023 ; Moghadam et al., 2026 ; Masum et al., 2026 ; Yu et al., 2026 )
Security/Reliability Issues( Amrouch et al., 2022 ; Ma et al., 2023a ; Ma et al., 2023b ; Cai et al., 2022 ; Yang and Ren, 2020b ; Moraliyage et al., 2022 ; Gungor et al., 2022 ; Gungor et al., 2023a ; Wang et al., 2023a ; Khaleghi et al., 2020a ; Yang and Ren, 2020a ; Wang et al., 2022 ; Ma et al., 2021 ; Wang and Jiao, 2022 ; Chen and Li, 2021 ; Gungor et al., 2023b ; Genssler et al., 2024a ; Barkam et al., 2023a ; Barkam et al., 2023b ; Park et al., 2023 ; Kleyko et al., 2018a ; Kumar et al., 2022 ; Nam et al., 2023 ; Yu et al., 2023 ; Guirado et al., 2023 ; Liu et al., 2023 ; Khaleghi et al., 2024 ; Zhang et al., 2025 ; Jeong et al., 2025 ; Barkam et al., 2024 ; Justus Rajappa et al., 2026 )Graph Processing( Poduval et al., 2022 ; Nunes et al., 2022 ; Kang et al., 2022c ; Amrouch et al., 2022 ; Zhou et al., 2021 ; Chen et al., 2023 ; Cornell et al., 2022 ; Nickel et al., 2016 ; Yi and Achour, 2023 )
Memory-centric Computing( Morris et al., 2022a ; Poduval et al., 2022 ; Poduval et al., 2021b ; Imani et al., 2020b ; Karunaratne et al., 2020a ; Kazemi et al., 2021 ; Li and others, 2016 ; Imani et al., 2020 ; Dutta et al., 2022 ; Karunaratne et al., 2021a ; Poduval et al., 2021a ; Karunaratne et al., 2020b ; Langenegger et al., 2023 ; Guirado et al., 2023 ; Karunaratne et al., 2022 ; Guirado et al., 2022 ; Thomann et al., 2022 ; Cai et al., 2022 ; Yang et al., 2023 ; Gupta et al., 2022 ; Liu et al., 2019 ; Teeters et al., 2023 ; Genssler et al., 2023 ; Mohammad Navaz et al., 2023 ; Kazemi et al., 2022b ; Wang et al., 2023e ; Masum et al., 2025 ; Yun et al., 2026b )DNA - Genome Application( Kim et al., 2020 ; Imani et al., 2018b ; Cumbo et al., 2020 ; Zou et al., 2022c ; Poduval et al., 2021c ; Chen and Imani, 2022 ; Barkam et al., 2023b )
IoT & Edge AI( Gungor et al., 2023b ; Khaleghi et al., 2021 ; Datta et al., 2019 ; Kim et al., 2018 ; Gungor et al., 2023a ; Amrouch et al., 2022 ; Zou et al., 2021a ; Khaleghi et al., 2022 ; Basaklar et al., 2021 ; Kandaswamy et al., 2022 ; Genssler et al., 2022 ; Yu et al., 2023 ; Taheri et al., 2022 ; Huang et al., 2025 ; Ding et al., 2026 ; Zhang et al., 2026 ; Yu et al., 2026 ; Yun et al., 2026b ; Tang et al., 2026 ; Yun et al., 2026a ; Justus Rajappa et al., 2026 )Robotics( Menon et al., 2022b ; Hassan et al., 2024 ; Mitrokhin et al., 2019 ; Neubert et al., 2019 ; McDonald et al., 2021 ; Neubert et al., 2021 )
Table 1. First Glance of Prior HDC Works Classified based on Prominent Targets
HV TypeDomainBindingUnbindingBundlingBinarizationSimilarity
Binary{0,1}D\{0,1\}^{D}XOR : (ha⊕hb)i(\mathbf{h}_{a}\oplus\mathbf{h}_{b})_{i}XOR againMajority vote / pop-countMajority thresholdHamming Distance: 1D∥ha⊕hb∥1\frac{1}{D}\|\mathbf{h}_{a}\oplus\mathbf{h}_{b}\|_{1}
Bipolar{−1,+1}D\{-1,+1\}^{D}Hadamard: (ha⊙hb)i=ha,ihb,i(\mathbf{h}_{a}\odot\mathbf{h}_{b})_{i}=h_{a,i}h_{b,i}Hadamard again∑khk\sum_{k}\mathbf{h}_{k}sgn(⋅)\text{sgn}(\cdot)Cosine: 1D∑iha,ihb,i\frac{1}{D}\sum_{i}h_{a,i}h_{b,i}
Real-valuedRD\mathbb{R}^{D} (unit-norm)HadamardApproximate (re-normalize)1n∑khk\frac{1}{n}\sum_{k}\mathbf{h}_{k}sgn(⋅)\text{sgn}(\cdot) or quantizeCosine: ha⋅hb/(∥ha∥∥hb∥)\mathbf{h}_{a}\cdot\mathbf{h}_{b}/(\|\mathbf{h}_{a}\|\|\mathbf{h}_{b}\|)
Complex (phasor)CD\mathbb{C}^{D} (∣hj∣=1)(|h_{j}|=1)Phase add: (ha⊙hb)j=ei(θa,j+θb,j)(\mathbf{h}_{a}\odot\mathbf{h}_{b})_{j}=e^{i(\theta_{a,j}+\theta_{b,j})}Conj. mult.: hc⊙hb‾\mathbf{h}_{c}\odot\overline{\mathbf{h}_{b}}Superposition →\rightarrow renormalize: ∑khk,j∣∑khk,j∣\frac{\sum_{k}h_{k,j}}{|\sum_{k}h_{k,j}|}Normalize to unit circleInner product: 1DRe(ha⋅hb‾)\frac{1}{D}\text{Re}(\mathbf{h}_{a}\cdot\overline{\mathbf{h}_{b}})
Table 2. Summary of HV\boldsymbol{\mathcal{HV}} Types and Operations
HDC SurveysYearVector MappingRandom Source Variety DiscussionOpen-source Platform DiscussionCross-paradigm ComputingApplication Classifications
Gritsenko et al. ( Gritsenko et al., 2017 )2017• • • • • • •• • • • • • •• • • • • • •• • • • • • •• • • • • • •
Lulu and Parhi ( Ge and Parhi, 2020 )2020• • • • • • •• • • • • • •• • • • • • •• • • • • • •• • • • • • •
Thomas et al. ( Thomas et al., 2021 )2021• • • • • • •• • • • • • •• • • • • • •• • • • • • •• • • • • • •
Kleyko et al. (part 1) ( Kleyko et al., 2022 )2022• • • • • • •• • • • • • •• • • • • • •• • • • • • •• • • • • • •
Kleyko et al. (part 2) ( Kleyko et al., 2023 )2022• • • • • • •• • • • • • •• • • • • • •• • • • • • •• • • • • • •
Hassan et al. ( Hassan et al., 2022 )2022• • • • • • •• • • • • • •• • • • • • •• • • • • • •• • • • • • •
Table 3. Comparison of Previous SOTA Surveys for Key Contributions of This Survey
Figure 4. An overview of the comprehensive multi-stage encoding pipeline taxonomy.
HV\boldsymbol{\mathcal{HV}} SourceDimensionality of HV\boldsymbol{\mathcal{HV}} s ( D\mathbf{D} )Run-to-run reproducibilityExecutions for validationSecurity-critical deploymentHardware generator complexityHigh- D\mathbf{D} scaling overheadCurrent validation gaps
Pseudo-RandomEffective at sufficiently large DD ; near-orthogonality holds with high probabilityReproducible with fixed seed; seed-dependent otherwiseUsually needs multiple seeds for statistical confidenceSuitable if seeds are protected and entropy is sufficientLow–Medium: LFSR+comparatorUsually modest; depends on parallelism and generator periodStandard baseline, but seed- and workload-dependent
True RandomEffective at large DD ; task- and technology-dependentWeak unless stored or replayedRequires repeated trials or stored realizationsUnpredictable; attractive for security-sensitive settingsDepends on entropy source or emerging deviceDepends on generation, storage, and readout costLimited HDC-specific validation across workloads and hardware
LD SequencesReported benefits mainly at moderate DD ; task-dependentDeterministic and reproducible by constructionMay reduce repeated seed trials; validation remains task-dependentPotentially vulnerable if the generator is knownMedium–High: LUT/counter or deterministic logicImplementation-dependent; LUT/counter overhead may grow with DDBroader validation needed across tasks, datasets, dimensions, and hardware
Table 4. Qualitative Tradeoffs of LD Sequences vs. Pseudo-Random and True-Random Initializations
Figure 5. Text and image processing pipelines in HDC. (a) Text Processing: Letters are converted into orthogonal symbol vectors via a pseudo-random source and a comparator, followed by NN -gram encoding: shifting-and-rotating , XOR , and accumulate operations. (b) Image Processing: Pixel values are processed using intensity ( LL , level) and symbol-based position ( PP ) vector encoding.
EncodingAccuracy vs. DimensionalityHardware CostBest-Suited Domain
♣ Record-based ( Imani et al., 2018a ; Datta et al., 2019 ; Rahimi et al., 2016a ; Ge and Parhi, 2020 )MediumLowMultivariate sensor streams
♣ N-gram ( Rahimi et al., 2016b ; Ge and Parhi, 2020 ; Datta et al., 2019 )High (text)MediumLanguage and other symbol sequences
◆ RBF (cosine) ( Hernández-Cano et al., 2021b ; Zou et al., 2021a ; Wang et al., 2023c ; Zou et al., 2021b )High (continuous)HighRegression or continuous-valued data
◆ Random projection ( Cannings and Samworth, 2015 ; Hersche et al., 2018 ; Imani et al., 2019f ; Morris et al., 2022b )MediumMedium–HighGeneral-purpose vision tasks
▲ Cellular automaton ( Menon et al., 2022a ; Neubert et al., 2021 )MediumVery LowSpatio-temporal signal processing
◆ Sigmoidal activation function ( Hernández-Cano et al., 2021b ; Zou et al., 2021a )MediumMediumAnalog/continuous sensor data
Table 5. Selection Guideline on HDC Encoding Methods with Hardware Cost and Taxonomy Symbols
Representative StudiesDominant Encoding Stage
 ◼ Feature◆ Mapping♣ Composition▲ HV\boldsymbol{\mathcal{HV}} Source
VoiceHD ( Imani et al., 2017b ) , AdaptHD ( Imani et al., 2019e ) , PRID ( Hernández-Cano et al., 2021a ) , MIMHD ( Kazemi et al., 2021 ) , Dynamic-HDC ( Chuang et al., 2023 ) , HyperGRAF ( Chen et al., 2023 ) , SemiHD ( Imani et al., 2019b ) , BinHD ( Imani et al., 2019d ) , QubitHD ( Bosch et al., 2019 ) , QuantHD ( Imani et al., 2020a ) , HDC-IM ( Liu et al., 2019 ) , EnHDC ( Wang et al., 2023d ) , HDCluster ( Imani et al., 2019c ) , TP-HDC ( Chang et al., 2020 ) , LeHDC ( Duan et al., 2022 ) , XCelHD ( Kang et al., 2022a ) , MulTa-HDC ( Chang et al., 2021 ) , HyperRec ( Guo et al., 2021 ) , ScaleHD ( Zhang et al., 2022 ) , HyperSpec ( Xu et al., 2023a ) , Imani et al. ( Kim et al., 2018 ) , Nazemi et al. ( Nazemi et al., 2020 ) , Montone et al. ( Montone et al., 2017 )∗\ast∗\astC1, C2P. Random
ST-HDC ( Karunaratne et al., 2021a ) , RelHD ( Kang et al., 2022c ) , LookHD ( Imani et al., 2021 ) , SHDC ( Huch et al., 2023 ) , DOMINO ( Wang et al., 2023b ) , GENERIC ( Khaleghi et al., 2022 ) , BioHD ( Zou et al., 2022c ) , GrapHD ( Poduval et al., 2022 ) , HAM ( Imani et al., 2017c ) , PartialHD ( Taheri et al., 2023 ) , Rahimi et al. ( Rahimi et al., 2016b ) , Datta et al. ( Datta et al., 2019 ) , Li et al. ( Li and others, 2016 ) , Wu et al. ( Wu et al., 2018b ) , Karunaratne et al. ( Karunaratne et al., 2020a ) , Rahimi et al. ( Rahimi et al., 2017 ; Rahimi et al., 2020 ) , Kovalev et al. ( Kovalev et al., 2022 )∗\ast∗\astC1, C2, C3P. Random
FebHD ( Hernández-Cano et al., 2021b ) , DistHD ( Wang et al., 2023c ) , DUAL ( Imani et al., 2020 ) , TempHD ( Ni et al., 2022 ) , NeuralHD ( Zou et al., 2021a ) , RE-FHDC ( Zeulin et al., 2023 ) , ManiHD ( Zou et al., 2021b ) , HD-I-IoT ( Gungor et al., 2023b ) , CascadeHD ( Kim et al., 2021b ) , SupportHD ( Safa et al., 2023 ) , CyberHD ( Wang et al., 2023a ) , Yu et al. ( Yu et al., 2022 )∗\astM1∗\astGaussian
SparseHD ( Imani et al., 2019h ) , F5-HD ( Salamat et al., 2019 ) , compHD ( Morris et al., 2019 ) , HD-Core ( Salamat et al., 2020 ) , HoloGN ( Kleyko et al., 2017 ) , Kleyko et al. ( Kleyko et al., 2018a ; Kleyko et al., 2018b )∗\ast∗\astC2, C3P. Random
SecureHD ( Imani et al., 2019a ) , OnlineHD ( Hernández-Cano et al., 2021c ) , FACH ( Imani et al., 2019g ) , SHEARer ( Khaleghi et al., 2020b ) , SearcHD ( Imani et al., 2020b )∗\ast∗\astC1, C2Gaussian
Table 6. Representative Studies Categorized by the Multi-Stage HDC Encoding Taxonomy
HDC ProjectsRelevant Taxonomy StagesEncoding-Relevant Details ( HV\boldsymbol{\mathcal{HV}} source, mapping, composition, or encoder realization)
TorchHD ( Chandrasekaran and Heddes, 2022 ; Heddes and others, 2023 )◼ ▲ ◆ ♣General HDC framework supporting random, level, thermometer, circular, RBF-kernel, N-gram-based , and Record-based encoding.
DistHD ( Wang et al., 2023c )▲ ◆Gaussian HV\boldsymbol{\mathcal{HV}} source and RBF-style mapping for distance-preserving continuous-feature encoding.
OpenHD ( Kang and Kim, 2022 )◆ ♣ ✸GPU-oriented framework support for mapping, composition, and encoder execution.
HDTorch ( Simon et al., 2022 )▲ ◆Random, sandwich, and scale-with-radius encoding for HDC model construction.
Hyperdimensional Computing Library ( , 2019 )▲ ♣ ✸Random HV\boldsymbol{\mathcal{HV}} source and N-gram-based composition with CPU/GPU-oriented encoder support.
Laelaps ( Burrello et al., 2019 )⚫ ◼ ♣ ✸LBP-based feature extraction with composition-oriented encoder realization ( Kaya et al., 2014 ) .
Table 7. Representative HDC Frameworks and Implementations Mapped to the Encoding Taxonomy
Year, AuthorsContributionApplication, Dataset (Accuracy, D)EncodingEnvironment , Model , or Hardware DetailsHardware Efficiency
2015, Räsänen ★ ( Räsänen, 2015 )Vector generation for non-discrete dataSpoken word classification CAREGIVER Y2 UK corpus ( >97>97 %, DD =4,000)S-WARP Mapping and Weighted Accumulation of Random Projections ◼ ◆No information givenNo hardware implementation
2018, Wu et al. ❆ ( Wu et al., 2018a )Exploring the opportunities of HDC for next generation devices (nanotubes, RRAM)21 European languages classification Europarl (98%)Evenly spaced time-delay encoding ◆ ♣ ✸Synopsys Design Compiler CNFET and RRAM-based design# of CNFET (1952) # of RRAM (224)
2018, Imani et al. ♠ ( Imani et al., 2018a )Decreasing classification costSpeech recognition ISOLET (95.9%, DD =10,000)Random-Bipolar HV\boldsymbol{\mathcal{HV}} Bit-flipping applied Hierarchical multi-encoder: I. Record-based II. N-gram-based ▲ ♣ ✸Synopsys Design Compiler (TSMC 45nm)Energy (6.6×) Speed (6.3×)
2019, Chang et al. ❃ ( Chang et al., 2019 )HV\boldsymbol{\mathcal{HV}} embedding using random non-linearityGalvanic Skin Response, Electroencephalogram, Electrocardiogram dataset (AMIGOS) binary emotion classification (76.6%, DD =10,000)Multiplexer-based ternary (-1, 0, +1) feature mapping into hyperspace ◼ ◆No information givenOnly system block diagram is given
2019 Liu et al. ✥ ( Liu et al., 2019 )RRAM-based HDC in-memory architectureISOLET (92.1%, DD =8,192)Block generation of HV\boldsymbol{\mathcal{HV}} s on crossbar, XOR -summation encoding ▲ ♣ ✸RRAM, CPU, and GPU separately2.28 J Energy (in-memory) 3960 J Energy (CPU)
2020, Nazemi et al. ❣ ( Nazemi et al., 2020 )Automatic feature extractionHAR (96.44%, DD =10,240) ISOLET (96.67%, DD =10,240)Random seed HV\boldsymbol{\mathcal{HV}} Bit-flipping Binding and Bundling ◼ ▲ ♣ ✸FPGA (Xilinx UltraScale+ VU9P)BRAMs (1.8%) DSPs (15%) FFs (0.8%) LUTs (5.1%) Latency (23.3 us) Power (5.3 W)
Table 8. Summary of Noticeable SOTA Works Highlighting Applications, HV\boldsymbol{\mathcal{HV}} Mapping, and Hardware
TermDescription
Associative Memory (AM)A memory for storing learned class hypervectors used for similarity-based classification.
Binary Spatter CodingA foundational VSA model using high-dimensional dense binary vectors; binding is performed via XOR and bundling via majority rule.
BinarizationTransforms real-valued bundles into bipolar form (e.g., sign() to get ±1\pm 1 ) or into binary form (e.g., majority thresholding to get 00 or 11 ).
BindingCombines hypervectors (e.g., via XOR, circular convolution) to represent relationships or associations.
Bit-Flipping EncodingGenerates hypervectors for neighboring scalar values by flipping a small number of bits.
BundlingAggregates multiple hypervectors into one, typically by majority vote or summation + sign thresholding.
Table 9. Glossary of Key Terms in Hyperdimensional Computing (HDC)
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