Scalable video retrieval is increasingly challenging as datasets reach tens of millions of videos. Current text-to-video retrieval (T2VR) methods either compress videos into single dense vectors, losing segment-level detail, or expand them into multi-frame representations, incurring prohibitive storage and search costs. We propose a binary hyperdimensional representation that encodes each video into a compact 3,072-dimension hypervector, preserving semantic fidelity while reducing memory via bit-packing. To leverage the properties of hypervectors for sublinear search, we introduce Hypervector Retrieval (HVR), a frequency-aware inverted index that prioritizes rare informative positions and refines candidates using GPU-accelerated Hamming search. Experiments show that our approach matches or exceeds dense baselines for T2VR and surpasses state-of-the-art partially relevant video retrieval (PRVR) by over 5% Recall@ 10 on ActivityNet. At scale, HVR processes over 2,000 queries per second on 10M videos, maintains recall within 1% of exact search, and achieves 5.3× greater storage capacity than CLIP4Clip and over 2,116× over MS-SL.

Retrieval-Augmented Generation (RAG) systems typically rely on dense floating-point embeddings to retrieve relevant documents, but this approach incurs significant memory and compute costs at scale. We propose a Hyperdimensional Computing (HDC) framework that projects transformer token embeddings into high-dimensional binary hypervectors, which are aggregated into compact document representations. To support sublinear search, we introduce HD-NSW, a graph-based index inspired by navigable small-world networks. HD-NSW clusters similar hypervectors into bundled centroids and connects them with sparse Hammingdistance edges, enabling efficient, beam-guided traversal entirely in the binary domain. Across 15 BEIR benchmarks and synthetic Gaussian mixture corpora, HD-NSW achieves over 99% of dense retrieval quality, reduces memory usage by $8 \times$, and supports over 860 queries per second at 10 million documents while maintaining over 80% throughput at 40 million documents. At five million documents, HD-NSW achieves $7.68 \times$ higher throughput compared to state of the art approximate nearest neighbor methods. Beyond this point, competing baselines encounter memory exhaustion, while HD-NSW continues scaling and maintains high throughput at larger corpus sizes.