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HiHPQ: Hierarchical Hyperbolic Product Quantization for Unsupervised Image Retrieval
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Proposes HiHPQ, an unsupervised deep product quantization method that performs quantized contrastive learning and hierarchical semantics learning on a hyperbolic (Lorentz) product manifold, outperforming SPQ and MeCoQ on image retrieval benchmarks.
Problem
Unsupervised deep product quantization for image retrieval relies on view-augmentation contrastive objectives that ignore multi-level semantic similarity between images and operate in Euclidean space, which poorly fits hierarchical structure.
Approach
Represents the quantizer embeddings and codewords on a Lorentzian hyperbolic product manifold with a soft hyperbolic codebook attention, and injects hierarchical semantics obtained by bottom-up clustering as prototype-wise and instance-wise contrastive supervision.
Key results
- On CIFAR-10 (II) at 64 bits HiHPQ reaches 67.11 MAP vs 65.07 for MeCoQ.
- On CIFAR-10 (I) at 64 bits HiHPQ reaches 73.71 MAP vs 71.06 for MeCoQ.
- On NUS-WIDE at 32 bits HiHPQ reaches 82.05 MAP vs 81.59 for MeCoQ; on Flickr25K at 16 bits MeCoQ (81.31) slightly beats HiHPQ (80.74).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add hierarchical semantics supervision to view-augmented contrastive learning (ablation) | HiHPQ · CIFAR-10 (II) | MAP (%): 58.40 -> 63.31; 61.86 -> 65.81; 62.17 -> 67.11 | Helped |
| add instance-wise hierarchical contrastive learning in hyperbolic space (ablation) | HiHPQ · CIFAR-10 (II) | MAP (%): 61.80 -> 63.31; 63.84 -> 65.81; 63.98 -> 67.11 | Helped |
| add prototype-wise hierarchical contrastive learning in hyperbolic space (ablation) | HiHPQ · CIFAR-10 (II) | MAP (%): 62.65 -> 63.31; 65.54 -> 65.81; 66.85 -> 67.11 | Helped |
| use hyperbolic rather than Euclidean space with no hierarchical supervision (ablation) | Vanilla quantization · CIFAR-10 (II) | MAP (%): 59.26 -> 58.40; 62.52 -> 61.86; 62.72 -> 62.17 | Hurt |
| use hyperbolic rather than Euclidean space with instance-wise hierarchical learning (ablation) | Instance-wise variant · CIFAR-10 (II) | MAP (%): 61.56 -> 61.80; 64.70 -> 63.84; 65.40 -> 63.98 | Mixed |
| use hyperbolic rather than Euclidean space with prototype-wise hierarchical learning (ablation) | Prototype-wise variant · CIFAR-10 (II) | MAP (%): 60.84 -> 62.65; 64.36 -> 65.54; 65.10 -> 66.85 | Helped |
| use prototype-wise rather than instance-wise hierarchical contrastive loss (ablation) | Hyperbolic variant · CIFAR-10 (II) | MAP (%): 61.80 -> 62.65; 63.84 -> 65.54; 63.98 -> 66.85 | Helped |
| increase preset hierarchy from Vanilla-Hyperbolic to 200,100,50 (ablation) | Prototype-Hyperbolic · CIFAR-10 (I) 32bits | MAP (%): 66.87 -> 73.58 | Helped |
| use hierarchy 200,100 rather than no hierarchical supervision (ablation) | Prototype-Hyperbolic · CIFAR-10 (I) 32bits | MAP (%): 66.87 -> 72.97 | Helped |
| use hierarchy 50,20 rather than no hierarchical supervision (ablation) | Prototype-Hyperbolic · Flickr25K 32bits | MAP (%): 80.63 -> 82.63 | Helped |
| use a small contrastive-learning temperature (e.g., 0.2) (ablation) | HiHPQ · CIFAR-10 (II) | MAP (%) | Helped |
| increase initial curvature beyond the robust range (0.01, 2.0) (ablation) | HiHPQ · CIFAR-10 (II) | MAP (%) | Hurt |
Surprising findings
- Instance-wise hierarchical supervision gives larger gains in Euclidean space than in hyperbolic space, while prototype-wise supervision benefits most from hyperbolic geometry.
- Vanilla hyperbolic quantization does not necessarily outperform its Euclidean counterpart without hierarchical supervision (e.g., 58.40 vs 59.26 at 16 bits on CIFAR-10 II).
Limitations
- Hierarchical clustering is done in the Euclidean tangent space because direct clustering in hyperbolic space is challenging.
- Baselines SPQ and MeCoQ were re-run under the authors' own reduced setting (VGG16, 50 epochs, 10,500 NUS-WIDE training images), so numbers differ from originally reported results.
- MeCoQ is slightly better than HiHPQ at 16 bits on Flickr25K and CIFAR-10 (II) at 16 bits differences are small in some settings; hyperparameters (hierarchy sizes, curvature init) matter.
Experimental setup
Datasets: Flickr25K CIFAR-10 NUS-WIDE
Benchmarks: Flickr25K CIFAR-10 (I) CIFAR-10 (II) NUS-WIDE
Metrics: MAP@1000 MAP@5000
Baselines: LSH SH SpH ITQ DeepBit SGH HashGAN GreedyHash BinGAN BGAN SSDH DVB
Builds on: MeCoQ SPQ Riemannian SGD hyperbolic neural networks
Closest papers by meaning
- Weakly Supervised Deep Hyperspherical Quantization for Image Retrieval (AAAI 2021 · similarity 0.89)
- Similarity Preserving Deep Asymmetric Quantization for Image Retrieval (AAAI 2019 · similarity 0.88)
- Compositional Entailment Learning for Hyperbolic Vision-Language Models (ICLR 2025 · similarity 0.86)
- Learning Structured Representations with Hyperbolic Embeddings (NeurIPS 2024 · similarity 0.86)
- Accept the Modality Gap: An Exploration in the Hyperbolic Space (CVPR 2024 · similarity 0.85)
- Fully Hyperbolic Convolutional Neural Networks for Computer Vision (ICLR 2024 · similarity 0.85)
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