Hao Lu

Hao Lu, Richard J. Radke

Understanding the locations of occupants in a commercial built environment is critical for realizing energy savings by delivering lighting, heating, and cooling only where it is needed. The key to achieving this goal is being able to recognize zone occupancy in real time, without impeding occupants' activities or compromising privacy. While low-resolution, privacy-preserving time-of-flight (ToF) sensor networks have demonstrated good performance in zone counting, the performance depends on careful sensor placement. To address this issue, we propose an automatic sensor placement method that determines optimal sensor layouts for a given number of sensors, and can predict the counting accuracy of such a layout. In particular, given the geometric constraints of an office environment, we simulate a large number of occupant trajectories. We then formulate the sensor placement problem as an integer linear programming (ILP) problem and solve it with the branch and bound method. We demonstrate the effectiveness of the proposed method based on simulations of several different office environments.

Hao Lu, Onur C. Koyun, Yongxin Guo et al.

Vector Quantization (VQ) underpins many modern generative frameworks such as VQ-VAE, VQ-GAN, and latent diffusion models. Yet, it suffers from the persistent problem of codebook collapse, where a large fraction of code vectors remains unused during training. This work provides a new theoretical explanation by identifying the nonstationary nature of encoder updates as the fundamental cause of this phenomenon. We show that as the encoder drifts, unselected code vectors fail to receive updates and gradually become inactive. To address this, we propose two new methods: Non-Stationary Vector Quantization (NSVQ), which propagates encoder drift to non-selected codes through a kernel-based rule, and Transformer-based Vector Quantization (TransVQ), which employs a lightweight mapping to adaptively transform the entire codebook while preserving convergence to the k-means solution. Experiments on the CelebA-HQ dataset demonstrate that both methods achieve near-complete codebook utilization and superior reconstruction quality compared to baseline VQ variants, providing a principled and scalable foundation for future VQ-based generative models. The code is available at: https://github.com/CAIR- LAB- WFUSM/NSVQ-TransVQ.git

Hao Lu, Onur C. Koyun, Yongxin Guo et al.

Vector-quantized autoencoders deliver high-fidelity latents but suffer inherent flaws: the quantizer is non-differentiable, requires straight-through hacks, and is prone to collapse. We address these issues at the root by replacing VQ with a simple, principled, and fully differentiable alternative: an online PCA bottleneck trained via Oja's rule. The resulting model, PCA-VAE, learns an orthogonal, variance-ordered latent basis without codebooks, commitment losses, or lookup noise. Despite its simplicity, PCA-VAE exceeds VQ-GAN and SimVQ in reconstruction quality on CelebAHQ while using 10-100x fewer latent bits. It also produces naturally interpretable dimensions (e.g., pose, lighting, gender cues) without adversarial regularization or disentanglement objectives. These results suggest that PCA is a viable replacement for VQ: mathematically grounded, stable, bit-efficient, and semantically structured, offering a new direction for generative models beyond vector quantization.