HRIR-Former · Listening Demo

Our contributions

What HRIR-Former does

Direct time-domain reconstruction

HRIRs are reconstructed directly as time-domain waveforms.
Magnitude and phase are reconstructed together, with no minimum-phase assumption or separate timing model.

Arbitrary directions in 3D space

Query any direction in 3D space.
Grid-free, continuous reconstruction.
Supports datasets with different measurement configurations.
Enabled by sinusoidal geometric embeddings of the direction coordinates (Figure 4).

As few as 3 measured directions

Only 3 measured directions of a listener are needed to query HRIRs at any other direction.

A head surrounded by a sphere of candidate directions: a few measured positions in red and many unmeasured positions in white. — **Figure 1. HRIR spatial up-sampling.** Estimating HRIRs at unmeasured target directions (white) from a sparse set of measured directions (red).

Listening demo

Ground truth vs. HRIR-Former

In each example, a mono source circles the head of a subject from the SONICOM dataset [1] in the horizontal plane. HRIR-Former only sees M = 19 measured HRIRs (orange diamonds in the video) and reconstructs the other 774 directions.

Use headphonesUse headphones to better preserve binaural cues.

Switch while playingClick or tap a condition while the example plays. Or press 1 2 3; Space plays / pauses.

Nearly identical. The HRIR-Former rendering is almost indistinguishable from the ground-truth rendering: same source position, movement and timbre.
Sometimes even smoother. Measured HRIRs carry small, unavoidable errors, e.g. from slight head movements of the subject during the measurement. They show up as tiny discontinuities between neighbouring directions (see Figure 3). HRIR-Former does not reproduce them, so the moving source can sound smoother than with the measured HRIRs.
Close in the numbers, too. Each example lists the NMSE and cosine distance between the two renderings (details below).

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01Music

Keyboard activeSubject P0189M = 1930 s

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0:00 / 0:30

NMSE −15.86 dB CD 0.0123

02Pink noise

Keyboard activeSubject P0187M = 1930 s

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0:00 / 0:30

NMSE −12.42 dB CD 0.0284

03Speech[2]

Keyboard activeSubject P0188M = 1930 s

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0:00 / 0:30

NMSE −15.22 dB CD 0.0116

Conditions. Audio: 48 kHz AAC.

Objective metrics

Waveform differences in the listening demos above

NMSE = ‖ŷ − y‖² / ‖y‖² and cosine distance (CD) = 1 − cos∠(ŷ, y), where ŷ and y are the HRIR-Former and ground-truth renderings. Lower is better for both.

−12.4 to −15.9 dB NMSE

Cosine Similarity ≥ 0.97

		NMSE (dB) ↓			NMSE ↓			Cosine distance ↓
Example	Subject	Left	Right	Mean	Left	Right	Mean	Left	Right	Mean
Music	P0189	−15.456	−16.262	−15.859	0.0285	0.0236	0.0261	0.0127	0.0119	0.0123
Pink noise	P0187	−13.121	−11.724	−12.423	0.0487	0.0672	0.0580	0.0243	0.0325	0.0284
Speech	P0188	−16.145	−14.302	−15.224	0.0243	0.0371	0.0307	0.0114	0.0119	0.0116

M = 19 measured directions for all three subjects.

A closer look

Reconstructed HRIRs

Left-ear HRIR over 256 samples: the estimated HRIR (dotted) closely follows the ground-truth HRIR (solid). — **Figure 2.** Left-ear HRIR reconstruction for subject P0187 at (φ, θ, r) = (90°, 20°, 1.5 m) under M = 19: estimated HRIR (dashed) versus ground-truth HRIR (solid). Angular distance to the nearest measured direction: 35.2°. Both magnitude and phase (timing) are reconstructed directly in the time domain.

Stacked binaural HRIRs over 793 directions for ground truth (left) and estimation (right), with zoomed insets. The ground-truth insets show a small discontinuity; the estimate is smooth. — **Figure 3.** Stacked binaural HRIRs for subject P0187 under M = 19 over 793 directions (each column: one direction; left/right ears concatenated along time). Ground truth (left) and estimation (right). The zoomed insets show a small discontinuity between neighbouring directions in the measured HRIRs. The HRIR-Former estimate varies smoothly across directions, which is why its renderings can sound smoother than the ground truth. P0187 is also the subject of the pink-noise example.

Method

HRIR-Former pipeline

Pipeline diagram: measured HRIRs and direction embeddings go through an MLP, a Transformer encoder, ITD/ILD heads and a decoder, followed by reordering by direction and Conv1D temporal refinement. — **Figure 4.** Overview of the proposed HRIR-Former pipeline. Swipe the figure sideways, or tap a module to jump to it.

Overview: Input: M measured HRIRs and their directions → Output: HRIRs at N arbitrary target directions.

Abstract

Individualized head-related impulse responses (HRIRs) enable binaural rendering, but dense per-listener measurements are costly. We address HRIR spatial up-sampling from sparse per-listener measurements: given a few measured HRIRs for a listener, predict HRIRs at unmeasured target directions. Prior learning methods often work in the frequency domain, rely on minimum-phase assumptions or separate timing models, and use a fixed direction grid, which can degrade temporal fidelity and spatial continuity. We propose HRIR-Former, a time-domain, grid-free binaural Transformer for reconstructing HRIRs at arbitrary directions from sparse inputs. It uses sinusoidal spatial features, a Conv1D refinement module, and auxiliary interaural time difference (ITD) and interaural level difference (ILD) heads. On SONICOM, it improves normalized mean squared error (NMSE), cosine distance, and ITD/ILD errors over prior methods; ablations validate modules and show minimum-phase preprocessing is unnecessary.

Citation

BibTeX

@inproceedings{xu26c_interspeech,
  title     = {{HRIR-Former: Grid-Free Time-Domain Reconstruction of Head-Related Impulse Responses with a Spatially Encoded Transformer}},
  author    = {Shaoheng Xu and Chunyi Sun and Jihui Zhang and Amy Bastine and Prasanga N. Samarasinghe and Thushara D. Abhayapala and Hongdong Li},
  year      = {2026},
  booktitle = {{Interspeech 2026}},
  pages     = {690--695},
  doi       = {10.21437/Interspeech.2026-702},
  issn      = {2958-1796},
}

References

I. Engel, R. Daugintis, T. Vicente, A. O. T. Hogg, J. Pauwels, A. J. Tournier, and L. Picinali, “The SONICOM HRTF Dataset,” Journal of the Audio Engineering Society, vol. 71, no. 5, pp. 241–253, 2023. doi:10.17743/jaes.2022.0066
C. K. A. Reddy, E. Beyrami, J. Pool, R. Cutler, S. Srinivasan, and J. Gehrke, “A Scalable Noisy Speech Dataset and Online Subjective Test Framework,” in Proc. Interspeech, 2019, pp. 1816–1820. doi:10.21437/Interspeech.2019-3087 (MS-SNSD)