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

TL;DR

The 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, positioning the framework as a reliable, uncertainty-aware foundation for neuromorphic computing.

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 (5)

• 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 \ref{['sec:conformity-scores']}. Other details remain the same as in \ref{['fig:hdc-vs-discount']}.
• Figure 3: ConformalHDC outperforms benchmarks by providing smaller prediction sets, enhanced point-prediction accuracy, and superior OOD detection. Data generation process is detailed in \ref{['app:synthetic-3class']} with $\sigma$ controlling the heteroscedasticity of the data. Nominal coverage level is $90\%$. Results are summarized over 100 repetitions.
• 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.
• 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.

Theorems & Definitions (4)

• Theorem 1
• Theorem 2
• proof : Proof of \ref{['thm:marginal']}
• proof : Proof of \ref{['thm:conditional']}