Superposed Inference for Hyperdimensional Computing

Quanling Zhao; Nilesh Prasad Pandey; Ye Tian; Tajana Rosing

cs.LGSep 26, 2026

Superposed Inference for Hyperdimensional Computing

Authors: Quanling Zhao, Nilesh Prasad Pandey, Ye Tian, Tajana Rosing

Organizations: University of California San Diego

Abstract

Hyperdimensional computing (HDC) is attractive for efficient and robust learning, but conventional inference still encodes every query independently, repeatedly paying the cost of high-dimensional projection. We introduce SupHDC, a new inference paradigm that processes multiple queries through a shared encoding computation. SupHDC assigns lightweight random slot keys, superposes the keyed queries before encoding, and uses slot-specific classifiers to recover their individual predictions. A random-feature kernel view explains why exact recovery of each hypervector is unnecessary: inference only needs to preserve the class evidence that determines the prediction. Across ten datasets, SupHDC achieves 1.39x analytical speedup with no average accuracy loss, and up to 2.08x speedup with only a 2.67 percentage-point mean accuracy loss. On a Raspberry Pi~5, it delivers 2.01x measured wall-clock speedup with a 2.26 percentage-point loss in mean prediction accuracy. SupHDC shows that high-dimensional redundancy can be used not only for robustness, but also as capacity for shared inference.

Figures & tables

Figure 1: Motivation for SupHDC. (Left) Conventional HDC independently encodes each query into a high-dimensional distributed representation (hypervector), repeating the dominant encoding operation. SupHDC multiplexes multiple queries and amortizes the encoding cost through one shared encoding while retaining separate predictions. (Right) Profiling at $D=10{,}000$ shows that encoding dominates inference latency across different workloads, motivating SupHDC to amortize this cost.

Figure 2: SupHDC adaptation and selective fallback. (a) Superposition-aware training adapts only the slot-specific prototype banks while keeping the base encoder fixed. (b) Margin-gated fallback selectively re-encodes low-confidence queries through the clean inference path.

Figure 3: SupHDC provides an efficiency knob complementary to representation dimension and numerical precision. (a) Accuracy change of SupHDC with prototype adaptation and 20% margin-gated fallback across representation dimensions. Larger $D$ supports more aggressive superposition with smaller accuracy degradation. (b) SupHDC under different numerical precisions, always compared against Plain HDC at the same precision. The upper axis reports the analytical speedup introduced by SupHDC, showing that quantization and superposed inference can be applied jointly.

Method	$K$	Acc. (%)	$\Delta$ Acc. (pp)	Analyt. speedup
Plain	1	84.39	0.00	$1.00\times$
SupHDC + Adapt.	2	83.30	$-1.09\pm 0.81$	$1.92\times$
+ FB	2	84.76	$\mathbf{+0.37\pm 0.42}$	$1.39\times$
SupHDC + Adapt.	3	80.17	$-4.21\pm 0.87$	$2.78\times$
+ FB	3	83.22	$\mathbf{-1.16\pm 0.51}$	$1.78\times$
SupHDC + Adapt.	4	77.27	$-7.11\pm 0.97$	$3.58\times$

Table 1: Accuracy–compute tradeoff at

D=10{,}000

and full precision. Adapt. denotes prototype adaptation and FB denotes 20% margin-gated fallback.

\Delta

Acc. is relative to Plain.

\pm

denotes standard error of the mean(SEM) across dataset-level means.

Figure 4: From key separation to prediction accuracy. (a) On the actual $\ell_{2}$ -normalized benchmark inputs, cross-slot alignment closely follows the $\sqrt{(K-1)/d}$ dependence predicted by Proposition 1 ; dashed curves show the theoretical values without fitting. (b) During full SupHDC inference, relative score distortion increases with superposition factor $K$ , while larger random-feature dimension $D$ reduces the finite-feature contribution to this distortion. (c) Across the shown $(D,K)$ operating points, larger score distortion strongly corresponds to greater accuracy degradation.

Setting	Meas.	Analyt.	$\Delta$ Acc.
	speedup	speedup	(pp)
$K=2$ , Adapt.	$1.79\times$	$1.90\times$	$-2.58$
$K=2$ , Adapt. + FB	$1.19\times$	$1.38\times$	$-0.47$
$K=4$ , Adapt.	$3.36\times$	$3.45\times$	$-6.66$
$K=4$ , Adapt. + FB	$2.01\times$	$2.04\times$	$-2.26$

Table 2: Raspberry Pi 5 deployment.

D=10{,}000

, full precision, one CPU thread.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning
$x\in\mathbb{R}^{d}$	Input query in the original feature space.
$d$	Original input dimension.
$D$	Hyperdimensional / random-feature representation dimension.
$C$	Number of classes.
$K$	Superposition factor; number of queries processed through one shared encoding.
$W\in\mathbb{R}^{D\times d}$	Fixed random-feature projection matrix.

Appendix

Table 3: List of notations.

Parameter	Setting	Description
Kernel bandwidth $\sigma$	$1$	RBF/ORF bandwidth
Hypervector dimension $D$	$\{1000,2000,5000,10000\}$	Random-feature dimension
Superposition factor $K$	$\{2,\ldots,10\}$	Queries encoded jointly
Base training epochs	$20$	Prototype refinement epochs
Base learning rate $\eta$	$1.0$	Error-driven prototype update
Adaptation epochs	$100$	Superposition-aware refinement

Appendix

Table 4: Hyperparameters used in the main SupHDC experiments.

Dataset	Domain	$\mathbf{N_{\mathrm{tr}}}$	$\mathbf{N_{\mathrm{te}}}$	$\mathbf{d}$	$\mathbf{C}$	Input representation
HAR	Activity	7,352	2,947	561	6	Activity feature vector
ISOLET	Speech	6,238	1,559	617	26	Acoustic feature vector
CIFAR-10	Vision	50,000	10,000	2,048	10	ResNet-50 feature
Airline Sentiment	Text	9,228	2,307	64	2	Word2Vec feature
AG News	Text	120,000	7,600	64	4	Word2Vec feature
IMDB	Text	25,000	25,000	512	2	Word2Vec feature

Appendix

Table 5: Datasets and input representations used in the SupHDC experiments.

N_{\mathrm{tr}}

and

N_{\mathrm{te}}

denote the number of training and test examples after preprocessing,

d

is the input dimension, and

C

is the number of classes.

Figure 5: Extended SupHDC variant sweep at $D=10{,}000$ and full precision. Accuracy change relative to paired Plain HDC is shown for $K=2,\ldots,10$ . Direct superposition degrades progressively as the interference load increases. Superposition-aware adaptation substantially improves accuracy without adding inference-time encoding operations, while selective fallback further recovers prediction fidelity by cleanly recomputing low-confidence queries. Shaded regions denote SEM across dataset-level means.

Figure 6: Extended accuracy–compute landscape at $D=10{,}000$ and full precision. Each point corresponds to a superposition factor $K\in\{2,\ldots,10\}$ . Adaptation improves accuracy at essentially unchanged inference cost, whereas fallback deliberately trades part of the analytical speedup for clean recomputation of uncertain queries. The Plain HDC operating point is shown at $(1\times,0)$ . Error bars denote SEM across dataset-level accuracy changes.

Figure 7: Dimension dependence of superposed inference. SupHDC remains effective across $D\in\{1{,}000,2{,}000,5{,}000,10{,}000\}$ , while larger random-feature representations tolerate stronger superposition and therefore support more aggressive $K$ . Accuracy change is shown for SupHDC with superposition-aware adaptation and $20\%$ selective fallback over $K=2,\ldots,10$ at full precision. Shaded regions denote SEM across dataset-level means.

Figure 8: Complete full-precision SupHDC sweep. Each panel shows all four SupHDC variants over $K=2,\ldots,10$ for one representation dimension. The ordering among methods and the progressive degradation with increasing $K$ are consistent across $D=1$ K, $2$ K, $5$ K, and $10$ K, indicating that the trends observed in the main operating regime are not specific to a single representation dimension.

Figure 9: Per-dataset sensitivity to the superposition factor. Paired accuracy change for SupHDC with adaptation and $20\%$ selective fallback at $D=10{,}000$ and full precision. Each cell reports the accuracy change in percentage points relative to the corresponding Plain HDC model, averaged over five paired seeds. Moderate superposition is broadly tolerated, whereas larger $K$ produces increasingly heterogeneous degradation across workloads.

Figure 10: Convergence of superposition-aware adaptation. (a) Accuracy change relative to paired Plain HDC as the number of adaptation epochs increases. Most of the improvement occurs early, with diminishing gains after approximately 20 epochs. (b) Fraction of the final 100-epoch improvement recovered as a function of relative adaptation cost. Both adaptation alone and adaptation combined with fallback recover most of their final gain using only a fraction of the full adaptation budget.

Figure 11: Ablation of margin-gated selective fallback. (a) Fraction of pre-fallback errors captured when queries are ranked by their top-two classification margin. Low-margin selection captures substantially more errors than random selection at the same fallback budget. (b) Accuracy–compute tradeoff as the fallback fraction is varied. Increasing fallback improves accuracy by selectively recomputing more uncertain queries, while giving back part of the analytical speedup. Percent labels indicate the fallback fraction.

Figure 12: Persistent storage overhead of SupHDC. Mean persistent model storage relative to Plain HDC across the ten datasets at $D=10{,}000$ and full precision. The projection matrix is shared across slots, while slot-specific prototype banks account for the additional storage. Selective fallback retains an additional clean prototype bank for each slot.

Method	$K$	Storage (MiB)	Relative to Plain
Plain	–	25.19	$1.00\times$
SupHDC	2	25.90	$1.04\times$
SupHDC	4	27.30	$1.13\times$
SupHDC + FB	2	27.30	$1.13\times$
SupHDC + FB	4	30.11	$1.29\times$

Appendix

Table 6: Storage cost at representative operating points. Values are averaged across the ten datasets at

D=10{,}000

and full precision.

Figure 13: Analytical versus measured Raspberry Pi 5 speedup. Each point corresponds to adapted SupHDC with fallback fraction $q\in\{0,5,10,20\}\%$ for $K=2$ or $K=4$ . “Raw” denotes the adapted SupHDC model without selective fallback ( $q=0$ ), rather than unadapted direct superposition. Speedups are aggregated across HAR, ISOLET, CIFAR-10, and AG News. The dashed line denotes ideal agreement between analytical and measured speedup. Increasing fallback reduces acceleration because more low-confidence queries are individually recomputed.

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Overparameterized machine learning (ML) methods such as neural networks may be prohibitively resource intensive for devices with limited computational capabilities. Hyperdimensional computing (HDC) is an emerging resource efficient and low-complexity ML method that allows hardware efficient implementations of (re-)training and inference procedures. In this paper, we propose a maximum-margin HDC classifier, which significantly outperforms baseline HDC methods on several benchmark datasets. Our method leverages a formal relation between HDC and support vector machines (SVMs) that we established for the first time. Our findings may inspire novel HDC methods with potentially more hardware-oriented implementations compared to SVMs, thus enabling more efficient learning solutions for various intelligent resource-constrained applications.

Abstract

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