ConformalHDC: Uncertainty-Aware Hyperdimensional Computing with Application to Neural Decoding

Ziyi Liang; Hamed Poursiami; Zhishun Yang; Keiland Cooper; Akhilesh Jaiswal; Maryam Parsa; Norbert Fortin; Babak Shahbaba

stat.MLFeb 24, 2026

ConformalHDC: Uncertainty-Aware Hyperdimensional Computing with Application to Neural Decoding

Authors: Ziyi Liang, Hamed Poursiami, Zhishun Yang, Keiland Cooper, Akhilesh Jaiswal, Maryam Parsa, Norbert Fortin, Babak Shahbaba

Organizations: Department of Statistics, UC Irvine, Irvine, CA, USA · Department of Electrical and Computer Engineering, George Mason University, Fairfax, VA, USA · Center for the Neurobiology of Learning and Memory, UC Irvine, Irvine, CA, USA · Department of Neurobiology and Behavior, UC Irvine, Irvine, CA, USA · Department of Electrical and Computer Engineering, University of Wisconsin Madison, Madison, WI, USA

Abstract

Hyperdimensional Computing (HDC) offers a computationally efficient paradigm for neuromorphic learning. Yet, it lacks rigorous uncertainty quantification, leading to open decision boundaries and, consequently, vulnerability to outliers, adversarial perturbations, and out-of-distribution inputs. To address these limitations, we introduce ConformalHDC, a unified framework that combines the statistical guarantees of conformal prediction with the computational efficiency of HDC. For this framework, we propose two complementary variations. First, the set-valued formulation provides finite-sample, distribution-free coverage guarantees. Using carefully designed conformity scores, it forms enclosed decision boundaries that improve robustness to non-conforming inputs. Second, the point-valued formulation leverages the same conformity scores to produce a single prediction when desired, potentially improving accuracy over traditional HDC by accounting for class interactions. We demonstrate the broad applicability of the proposed framework through evaluations on multiple real-world datasets. In particular, we apply our method to the challenging problem of decoding non-spatial stimulus information from the spiking activity of hippocampal neurons recorded as subjects performed a sequence memory task. Our results show that ConformalHDC not only accurately decodes the stimulus information represented in the neural activity data, but also provides rigorous uncertainty estimates and correctly abstains when presented with data from other behavioral states. Overall, these capabilities position the framework as a reliable, uncertainty-aware foundation for neuromorphic computing.

Figures & tables

Figure 1: ConformalHDC enables rigorous uncertainty quantification and principled abstention through enclosed decision regions. Unlike the open partitions of standard HDC, our framework produces bounded regions where overlaps explicitly characterize predictive uncertainty. Furthermore, the enclosed geometry allows the model to identify and abstain when encountering non-conforming inputs, such as the OOD samples denoted by triangles. Scatter points represent three classes, and colored regions indicate boundaries.

Figure 2: Decision boundary comparison between standard HDC and conformal methods with different nonconformity scores in section 3.1 . Other details remain the same as in Figure 1 .

\hat{C}_{\alpha}(X_{n+1})=\{y\in[K]:\hat{S}(X_{n+1},y)\leq\widehat{Q}^{y}_{1-\alpha}\}.

(6)

Algorithm 2 Set-valued ConformalHDC with label-conditional coverage

\displaystyle\widehat{C}_{\alpha}(X_{n+1})=\left\{\arg\min\nolimits_{y\in\widehat{C}_{\alpha}(X_{n+1})}\widehat{S}(X_{n+1},y)\right\}.

Algorithm 3 Point-valued CHDC

Figure 3: ConformalHDC outperforms benchmarks by providing smaller prediction sets, enhanced point-prediction accuracy, and superior OOD detection. Data generation process is detailed in Section A.4 with

\sigma

controlling the heteroscedasticity of the data. Nominal coverage level is

90\%

. Results are summarized over 100 repetitions.

	MNIST ( $\alpha=0.05$ )			Languages ( $\alpha=0.01$ )			ISOLET ( $\alpha=0.02$ )			Neural ( $\alpha=0.2$ )
Method	Cov.	Size	AUC	Cov.	Size	AUC	Cov.	Size	AUC	Cov.	Size	AUC
HDC	0.862	1.000	-	0.953	1.000	-	0.889	1.000	-	0.640	1.000	-
Inv. quantile	0.950	2.002	0.483	0.990	2.514	0.472	0.980	3.415	0.490	0.799	1.782	0.599
Penalized	0.950	4.218	0.655	0.990	16.392	0.294	0.980	21.344	0.536	0.796	2.901	0.016
Similarity	0.951	3.370	0.745	0.990	9.712	0.960	0.980	7.428	0.759	0.792	2.979	0.986
CHDC-ratio	0.950	1.770	0.873	0.990	3.291	0.982	0.979	4.412	0.759	0.796	1.643	0.600

Table 1: Performance comparison of ConformalHDC and benchmarks under real data applications. Results for benchmark datasets in Section 5.1 are averaged over 100 repetitions. See Table E.3 – Table E.5 for full results including standard errors. Results for the neural decoding experiment in section 5.2 are averaged over 500 repetitions. While results for one representative subject (Buchanan) are shown here, complete results for all five subjects are provided in Table E.6 .

Figure 4: Overview of the behavioral task and neural activity data processing. (a) Schematic of the sequence memory task in which each presentation of the sequence of non-spatial stimuli (odors ABCDE) is followed by a running period (Run). For each odor presentation, subjects (rats) must perform the correct response to receive a water reward. (b) Visualization of neural spiking activity aggregated from all five rats across different experimental states (odors A–D and running) and the subsequent data augmentation and binning process.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A.1 : Encoding of the spike activities. (a) The full encoding pipeline using FHRR. (b) A T-SNE visualization of the encoded hypervectors for different states using data from rat Superchris.

Algorithm	Calibration (One-time)	Inference ( $m$ points)	Total Cost
Set-valued marg. ( Algorithm 1 )	$\mathcal{O}(T+n_{\text{cal}}Kd)$	$\mathcal{O}(mKd)$	$\mathcal{O}(T+n_{\text{cal}}Kd+mKd)$
Set-valued cond. ( Algorithm 2 )	$\mathcal{O}(T+n_{\text{cal}}Kd)$	$\mathcal{O}(mKd)$	$\mathcal{O}(T+n_{\text{cal}}Kd+mKd)$
Point-valued ( Algorithm 3 )	$\mathcal{O}(T+n_{\text{cal}}Kd)$	$\mathcal{O}(mKd)$	$\mathcal{O}(T+n_{\text{cal}}Kd+mKd)$

Appendix

Table B.1 : Computational complexity of ConformalHDC algorithms.

T

is the training cost,

d

the hypervector dimension,

K

the number of classes,

n_{\text{cal}}

the calibration size, and

m

the number of test points.

		Set-Valued		Point	OOD
Sigma	Method	Coverage	Size	Accuracy	AUC
3	HDC	0.861 (0.001)	1.000 (0.000)	0.861 (0.001)	-
	Inv. quantile	0.901 (0.001)	1.448 (0.004)	0.862 (0.001)	0.391 (0.001)
	Penalized	0.899 (0.001)	1.246 (0.004)	0.876 (0.001)	0.884 (0.001)
	Similarity	0.900 (0.001)	1.444 (0.005)	0.875 (0.001)	0.997 (0.000)
	CHDC-ratio	0.900 (0.001)	1.103 (0.002)	0.875 (0.001)	0.986 (0.000)

Appendix

Table E.2 : Full results for synthetic experiment with alpha=

0.1

. In-distribution and out-of-distribution data are sampled according to the distributions described in Section A.4 . For all conformal methods, the in-distribution data is partitioned into training (

40\%

), calibration (

50\%

), and testing (

10\%

) sets. For the standard HDC classifier, the training and calibration folds are combined for model training, as it does not require a separate calibration step. Results are averaged over 100 repetitions. Values in parentheses report the standard errors.

	Set-Valued		Point	OOD
Method	Coverage	Size	Accuracy	AUC
HDC	0.862 (0.001)	1.000 (0.000)	0.862 (0.001)	-
Inv. quantile	0.950 (0.001)	2.002 (0.007)	0.862 (0.001)	0.483 (0.000)
Penalized	0.950 (0.001)	4.218 (0.007)	0.858 (0.001)	0.655 (0.001)
Similarity	0.951 (0.001)	3.370 (0.009)	0.863 (0.001)	0.745 (0.001)
CHDC-ratio	0.950 (0.001)	1.770 (0.005)	0.863 (0.001)	0.873 (0.001)

Appendix

Table E.3: Full results for MNIST experiment with alpha=

0.05

. Among 10 handwritten digits, last four digits, i.e.,

\{6,7,8,9\}

are treated as OOD classes. For all conformal methods, the in-distribution data is split into training (

80\%

), calibration (

15\%

), and testing (

5\%

) sets. Other details remain the same as in Table E.2 .

	Set-Valued		Point	OOD
Method	Coverage	Size	Accuracy	AUC
HDC	0.953 (0.0008)	1.000 (0.0000)	0.953 (0.0008)	-
Inv. quantile	0.990 (0.0004)	2.514 (0.0140)	0.953 (0.0008)	0.472 (0.0001)
Penalized	0.990 (0.0003)	16.392 (0.0203)	0.947 (0.0008)	0.294 (0.0019)
Similarity	0.990 (0.0003)	9.712 (0.0436)	0.952 (0.0008)	0.960 (0.0005)
CHDC-ratio	0.990 (0.0004)	3.291 (0.0113)	0.953 (0.0008)	0.982 (0.0003)

Appendix

Table E.4: Full results for Languages experiment with alpha=

0.01

. Among the 21 European languages, Indo-European languages are treated as in-distribution, while non-Indo-European languages, i.e., {Finnish, Estonian, Hungarian} are treated as OOD classes. For all conformal methods, the in-distribution data is partitioned into training (

75\%

), calibration (

22.5\%

), and testing (

2.5\%

) sets. Other details remain the same as in Table E.2 .

	Set-Valued		Point	OOD
Method	Coverage	Size	Accuracy	AUC
HDC	0.889 (0.002)	1.000 (0.000)	0.889 (0.002)	-
Inv. quantile	0.980 (0.001)	3.378 (0.027)	0.883 (0.002)	0.482 (0.000)
Penalized	0.980 (0.001)	21.344 (0.025)	0.872 (0.002)	0.536 (0.002)
Similarity	0.980 (0.001)	7.428 (0.052)	0.883 (0.002)	0.759 (0.002)
CHDC-ratio	0.979 (0.001)	4.429 (0.021)	0.882 (0.002)	0.747 (0.001)

Appendix

Table E.5: Full results for ISOLET experiment with alpha=

0.02

. Among the 26 English alphabet letters, the last four letters, i.e.,

\{W,X,Y,Z\}

are treated as OOD classes. For all conformal methods, the in-distribution data is split into training (

57\%

), calibration (

38\%

), and testing (

5\%

) sets. Other details remain the same as in Table E.2 .

		Set-Valued		Point	OOD
Rat	Method	Coverage	Size	Accuracy	AUC
Barat	HDC (train)	0.472 (0.004)	1.000 (0.000)	0.472 (0.004)	-
	HDC	0.492 (0.004)	1.000 (0.000)	0.492 (0.004)	-
	Inv. quantile	0.794 (0.004)	2.403 (0.008)	0.472 (0.004)	0.605 (0.000)
	Penalized	0.794 (0.004)	3.003 (0.016)	0.460 (0.004)	0.011 (0.001)
	Similarity	0.803 (0.004)	3.091 (0.017)	0.458 (0.004)	0.979 (0.001)

Appendix

Table E.6: Full results for odor decoding with alpha=

0.2

. Results aggregated over 500 independent repetitions. For all conformal methods, the odor data is split into training (

50\%

), calibration (

40\%

), and testing (

10\%

) sets. The standard HDC classifier utilizes the combined training and calibration folds, whereas HDC (train) uses the training fold only. Point-valued ConformalHDC achieves performance comparable to HDC (train), though it performs slightly lower than the full HDC model. This is due to data splitting constraints on the relatively small neural dataset (

\approx 600

samples per subject).

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