HyFL-CLIP: Hyperbolic Fine-Tuning of CLIP for Robust Long-Context Understanding

Conference: ECCV 2026
arXiv: 2607.00428
Project Page: https://janeyeon.github.io/hyflclip
Code: None
Area: Multimodal VLM
Keywords: Hyperbolic space fine-tuning, Long-context image-text alignment, CLIP fine-tuning, Hierarchical entailment relation, Cross-manifold distillation

TL;DR

HyFL-CLIP distills the Euclidean image-text alignment of pretrained CLIP into hyperbolic space (Lorentz model). By modeling the "global description - local component" hierarchical entailment relationship via Einstein midpoint aggregation, the model stably retrieves correct images even when long texts are perturbed (reordered, deleted, word-dropped), achieving up to a 19.5% improvement over the strongest baseline under word perturbations.

Background & Motivation

Background: CLIP has become the de facto standard for image-text alignment, but its training data is dominated by short captions, and its absolute position encoding only supports 77 tokens. To support long contexts, existing works (Long-CLIP, HiMo-CLIP, FineLIP, TULIP, Fix-CLIP, LongD-CLIP) widely adopt strategies of expanding position encodings through interpolation combined with coarse-to-fine feature alignment, achieving considerable performance in long-context image-text retrieval.

Limitations of Prior Work: The authors find that although the aforementioned methods perform well on normal long-text retrieval, they are extremely sensitive to semantic-preserving text perturbations. Merely shuffling sentence order, deleting the first sentence, randomly dropping half of the words, or replacing a few words causes a sharp decline in retrieval performance (e.g., HiMo-CLIP drops by 27.82% under random word dropping with \(o=0.5\), and by 83.58% under randomly selecting 2 sentences). This indicates that existing methods learn fragile point-to-point matching rather than a true understanding of semantic structures.

Key Challenge: The fundamental cause of this issue lies in the objective of Euclidean contrastive learning, which enforces strict one-to-one matching and lacks explicit modeling of the hierarchical part-whole or entailment relationships between a "global description" and its "constituent components". When certain sentences or words in the long text are removed or reordered, the global semantics remain unchanged, but the corresponding embedding points in the Euclidean space shift, leading to matching failures.

Goal: (1) Adapt the model to long-context scenarios while maintaining the pre-existing short image-text alignment capability of CLIP; (2) explicitly model the hierarchical entailment relationships between global descriptions and local components in long texts; (3) provide the model with a geometric tolerance margin against text perturbations, rather than relying on fragile point-to-point matching.

Key Insight: Hyperbolic space inherently possesses a negative curvature and a tree-like geometric structure, making it highly suitable for representing hierarchical containment relationships. In hyperbolic space, a geometric tolerance region can be defined using an entailment cone—as long as the sub-node embedding falls within the parent node's cone, it is semantically parsed as being contained. This "region containment" is much more forgiving than "point overlap" in Euclidean space, directly corresponding to the desired robustness. However, most existing hyperbolic VLMs are trained from scratch, failing to leverage the powerful pre-trained representations of CLIP. The key insight proposed by the authors is to avoid training from scratch, and instead "distill and transfer" the Euclidean representation of CLIP into hyperbolic space, reorganizing the semantic structure of long texts using entailment relationships in the hyperbolic space.

Core Idea: Transfer the Euclidean image-text alignment of CLIP to the Lorentz hyperbolic space via cross-manifold similarity distillation, and then explicitly model the part-whole hierarchical relationship of "token-level features \(\rightarrow\) global description \(\rightarrow\) image" using Einstein midpoint aggregation and a hierarchical entailment loss. This endows the model with geometric tolerance margins when facing text perturbations.

Method

Overall Architecture

Starting from a pre-trained Open-CLIP model, HyFL-CLIP aims to "transfer" its Euclidean image-text alignment capability into the Lorentz hyperbolic space. During this transfer process, hierarchical entailment modeling is introduced to establish stable geometric containment relationships between the global representation of long texts and their token-level components. The training of the entire framework involves four objectives: short-text-guided cross-manifold similarity distillation, hyperbolic geodesic contrastive loss, Einstein midpoint aggregation-based hierarchical entailment loss, and radius entropy regularization.

The input to the framework consists of triplets: image \(I\), short text \(T^s\) (corresponding to the same image), and long text \(T^l\) (corresponding to the same image). The image and texts are processed by the frozen Euclidean CLIP encoders to obtain Euclidean embeddings \(\tilde{\mathbf{v}}, \tilde{\mathbf{t}}^s, \tilde{\mathbf{t}}^l\), which are then projected into the hyperbolic space via the exponential map \(\exp_{\mathbf{o}}^{\kappa}\), yielding the corresponding hyperbolic embeddings \(\mathbf{v}, \mathbf{t}^s, \mathbf{t}^l \in \mathbb{L}^n\). During training, short-text pairs are used for cross-manifold distillation (maintaining the original short image-text alignment quality of CLIP), while long-text pairs are used for geodesic contrastive learning and hierarchical entailment modeling. The final output is a CLIP model that simultaneously performs short image-text matching and robust long-text understanding in hyperbolic space.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Input<br/>Image + Short Text + Long Text"] --> B["Frozen Euclidean CLIP Encoder<br/>Outputs Euclidean Embeddings"]
    B --> C["Exponential Map exp^κ_o<br/>Euclidean → Lorentz Hyperbolic Space"]
    C --> D["Cross-manifold Similarity Distillation<br/>KL Matching for Short Text Pairs"]
    C --> E["Hyperbolic Geodesic Contrastive Learning<br/>Long/Short Text ↔ Image"]
    C --> F["Einstein Midpoint Aggregation<br/>Token Features → Hierarchical Entailment"]
    D --> G["Weighted Sum of Total Loss"]
    E --> G
    F --> G
    G --> H["CLIP in Hyperbolic Space<br/>Robust Long-context Image-text Alignment"]

Key Designs

1. Short-text Guided Cross-manifold Similarity Distillation: "Transporting" the Euclidean Image-Text Similarity Geometry of CLIP into Hyperbolic Space

CLIP has already learned high-quality similarity structures on short image-text pairs. Directly discarding this knowledge and training from scratch in hyperbolic space would lose the pre-training advantages. The authors' approach is to use the frozen Euclidean CLIP (teacher) to compute the cosine similarity \(S^{\mathrm{E}}(\tilde{\mathbf{t}}_i^s, \tilde{\mathbf{v}}_j) = \frac{\langle\tilde{\mathbf{t}}_i^s, \tilde{\mathbf{v}}_j\rangle}{\|\tilde{\mathbf{t}}_i^s\| \|\tilde{\mathbf{v}}_j\|}\) between the short text \(\tilde{\mathbf{t}}_i^s\) and the image \(\tilde{\mathbf{v}}_j\), while simultaneously computing the negative geodesic distance \(S^{\mathrm{H}}(\mathbf{t}_i^s, \mathbf{v}_j) = -d_{\mathbb{L}}(\mathbf{t}_i^s, \mathbf{v}_j)\) in the hyperbolic space (student). These similarities are converted into probability distributions \(P^{\mathrm{E}}\) and \(P^{\mathrm{H}}\) via softmax with a temperature coefficient, and KL divergence is used to push the hyperbolic student to mimic the similarity distribution of the Euclidean teacher: \(\mathcal{L}_{\text{distill}} = \frac{1}{B}\sum_i \text{KL}(P^{\mathrm{E}}_{i\cdot} \| P^{\mathrm{H}}_{i\cdot})\).

The clever part of this design is that it is "cross-manifold"—the teacher and student do not reside in the same geometric space, yet matching via probability distributions bypasses the difficulty of directly aligning the two spaces. Ablation experiments demonstrate that removing this loss significantly degrades short-text retrieval (COCO/Flickr30k) performance, indicating that distillation indeed preserves CLIP's original short image-text alignment. Additionally, this loss only utilizes short-text pairs because CLIP's short-text alignment is the most reliable.

2. Einstein Midpoint Aggregation-based Hierarchical Entailment Loss: Replacing Point Overlap with Cone Containment for Perturbation Tolerance Margin

This is the most core design of the paper. Intuitively, a long description is composed of multiple semantic components (tokens, phrases, sentences), and the global semantics should act as the "parent node" of these components. The authors use the Einstein midpoint to aggregate token-level features into a summary representation \(\bar{\mathbf{t}}_i^{\ell}\), and then constrain the global text embedding \(\mathbf{t}_i^{\ell}\) to fall within the entailment cone centered at \(\bar{\mathbf{t}}_i^{\ell}\).

Specifically, for each token embedding \(\mathbf{t}_{i,k}^{\ell}\), its attention weight is first computed using its geodesic distance to the corresponding image embedding \(\mathbf{v}_i\): \(\alpha_{i,k} = \frac{\exp(-d_{\mathbb{L}}(\mathbf{t}_{i,k}^{\ell}, \mathbf{v}_i)/\tau_{\text{ent}})}{\sum_m \exp(-d_{\mathbb{L}}(\mathbf{t}_{i,m}^{\ell}, \mathbf{v}_i)/\tau_{\text{ent}})}\)—tokens more relevant to the image receive higher weights. Then, a weighted Einstein average of token embeddings is performed in the Klein model and mapped back to the Lorentz model to obtain the summary embedding \(\bar{\mathbf{t}}_i^{\ell}\). The half-aperture of the entailment cone is defined as \(\omega(\bar{\mathbf{t}}_i^{\ell}) = \arcsin\left(\frac{2K}{\sqrt{\kappa} \|\bar{\mathbf{t}}_i^{\ell}\|_{\mathbb{L}}}\right)\), where embeddings closer to the origin have wider cones (looser containment relationships), and embeddings farther from the origin have narrower cones (stricter containment relationships). The loss function penalizes the angle by which the global embedding exceeds the cone boundary: \(\mathcal{L}_{\text{ent}}^{\mathbf{t}^{\ell}} = \frac{1}{B}\sum_i \max(0, \phi(\bar{\mathbf{t}}_i^{\ell}, \mathbf{t}_i^{\ell}) - \eta \cdot \omega(\bar{\mathbf{t}}_i^{\ell}))\). The same operation is symmetrically executed on the image side.

Why does this design bring robustness? The key is that a "cone" is a region, not a single point. When text is perturbed (dropped words, reordered), the set of tokens changes, and the Einstein midpoint shifts. However, as long as the angle between the newly shifted midpoint and the global embedding \(\mathbf{t}_i^{\ell}\) remains within the half-aperture \(\omega\) of the cone, the matching relationship is preserved. This provides a geometric "tolerance margin" for semantic-preserving perturbations, whereas Euclidean contrastive learning requires exact point-to-point matching and lacks such a margin. Experiments validate this intuition: removing \(\mathcal{L}_{\text{ent}}\) significantly increases the performance drop under perturbations (from 32.38% to 35.64%).

3. Hyperbolic Geodesic Contrastive Loss: Simultaneously Optimizing Long and Short Image-Text Alignment on the Lorentz Manifold

After completing the Euclidean-to-hyperbolic distillation, the model still needs to be further optimized in the hyperbolic space using long texts. The authors employ a hyperbolic InfoNCE loss, replacing the Euclidean inner product with the negative geodesic distance: \(L_{\text{info}}(\mathbf{v}, \mathbf{t}; \tau_c) = -\sum_i \log \frac{\exp(-d_{\mathbb{L}}(\mathbf{v}_i, \mathbf{t}_i)/\tau_c)}{\sum_{k\neq i} \exp(-d_{\mathbb{L}}(\mathbf{v}_i, \mathbf{t}_k)/\tau_c)}\). This loss is applied bidirectionally to both long and short text-image pairs, culminating in the final form \(\mathcal{L}_{\text{itc}} = \mathcal{L}_{v\leftrightarrow t}^{\ell} + \lambda_1 \mathcal{L}_{v\leftrightarrow t}^{s}\), where \(\lambda_1 = 0.1\) controls the weight of the short-text loss. The necessity of this design lies in that while the distillation loss only ensures the correct relative ranking of the distribution, the contrastive loss directly pulls positive pairs closer and pushes negative pairs apart, establishing new decision boundaries within the hyperbolic space.

4. Radius Entropy Regularization: Preventing Hyperbolic Embeddings from Collapsing Near the Origin

A known issue in hyperbolic space is that embeddings can collapse into a small region near the origin, leading to low space utilization and excessively wide entailment cones that lose discriminative power. The authors introduce radius entropy regularization \(\mathcal{L}_{\text{reg}} = -H(\mathbf{p})\), where \(p_i = \frac{\exp(d_{\mathbb{L}}(\mathbf{t}_i^{\ell}, \mathbf{o}))}{\sum_j \exp(d_{\mathbb{L}}(\mathbf{t}_j^{\ell}, \mathbf{o}))}\) is the normalized hyperspherical radius distribution of samples within a batch. Maximizing this entropy encourages embeddings to be uniformly distributed across different radii, preventing them from grouping entirely at the origin. This is a lightweight but effective stability trick, derived from the concept of entropy regularization in semi-supervised learning.

Loss & Training

The total loss is a weighted sum of the four objectives: \(\mathcal{L} = \lambda_2 \mathcal{L}_{\text{distill}} + \mathcal{L}_{\text{itc}} + \lambda_3 \mathcal{L}_{\text{ent}} + \lambda_4 \mathcal{L}_{\text{reg}}\), where \(\lambda_2 = 0.05\), \(\lambda_3 = 0.1\), and \(\lambda_4 = 0.1\). Training is conducted on ShareGPT4V (1.2 million image-long caption pairs, averaging 143.6 words) for 2 epochs, with a batch size of 1024, using AdamW (lr=\(10^{-5}\), weight decay=\(2.5\times10^{-2}\)) and 4 A100 GPUs. The curvature \(\kappa\) is initialized at 1.0 and is learnable, converging to 0.9994 after training. Distillation temperatures are set to \(\tau_E = \tau_H = 0.005\), the contrastive temperature to \(\tau_c = 0.07\), and the entailment cone parameters to \(K=1, \eta=1.2\). For position encodings, the original encodings for the first 20 tokens are retained, while the remaining part is linearly interpolated to extend from 77 to 248 tokens. Hyperparameter sensitivity analysis indicates that performance remains stable across a wide range of values for all \(\lambda\) values.

Key Experimental Results

Main Results

Zero-Shot Long-Context Cross-Modal Retrieval (Table 1, Top-1 Accuracy %). HyFL-CLIP comprehensively outperforms all Euclidean baselines on both ViT-B/16 and ViT-L/14 architectures across four long-text datasets (DOCCI / DCI / Long-DCI / Urban-1k).

Model (ViT-L/14)	DOCCI I2T	DOCCI T2I	DCI I2T	DCI T2I	Long-DCI I2T	Long-DCI T2I	Urban-1k I2T	Urban-1k T2I
Long-CLIP	66.78	78.61	64.13	67.83	46.55	54.25	82.40	86.20
HiMo-CLIP	82.35	84.59	74.59	74.54	62.06	61.94	93.00	93.20
FineLIP	82.20	83.10	—	—	60.80	60.70	93.20	93.00
HyFL-CLIP	82.12	85.39	74.74	76.19	61.92	63.93	94.60	94.30

Long-Context Cross-Modal Retrieval Under Perturbations (Table 2, Average Top-1 Accuracy, with percentage change relative to original performance in parentheses). This is the key experiment of the paper, directly validating the core motivation.

Model	Word Drop p=0.5	Del First Sent	Order Shuffled	Sample 2 Sent	Sample 3 Sent
Long-CLIP	48.88 (↓35.81%)	55.41 (↓19.45%)	61.79 (↓3.46%)	26.50 (↓91.89%)	31.29 (↓79.89%)
HiMo-CLIP	58.75 (↓27.82%)	64.44 (↓17.42%)	72.94 (↓1.88%)	28.24 (↓83.58%)	34.84 (↓71.52%)
FineLIP	58.70 (↓26.59%)	64.18 (↓16.25%)	73.41 (↑1.17%)	27.20 (↓86.05%)	33.41 (↓74.32%)
HyFL-CLIP	70.20 (↓9.21%)	68.22 (↓12.69%)	76.16 (↑1.27%)	32.55 (↓75.36%)	39.05 (↓63.94%)

Under all five perturbation types, HyFL-CLIP achieves the highest absolute performance and the smallest relative decline. Notably, in the word drop scenario (\(p=0.5\)), HyFL-CLIP drops by only 9.21%, compared to a 27.82% drop for HiMo-CLIP. For order shuffling, HyFL-CLIP even slightly improves upon the original performance (+1.27%).

Zero-Shot Short-Context Cross-Modal Retrieval (Table 3). HyFL-CLIP's short-text retrieval performance on COCO and Flickr30k is comparable to or slightly better than Euclidean baselines, proving that distillation successfully preserves CLIP's original short image-text alignment.

Ablation Study

Configuration (ViT-L/14, 6-dataset average)	Avg Performance I2T+T2I	Description
Full model	69.8%	Full model
w/o \(\mathcal{L}_{\text{ent}}\)	69.3%	Removing hierarchical entailment loss slightly reduces long-text retrieval
w/o \(\mathcal{L}_{\text{ent}}\) + w/o \(\mathcal{L}_{\text{distill}}\)	68.3%	Simultaneously removing both core losses drastically reduces short-text retrieval

The contribution of the hierarchical entailment loss (\(\mathcal{L}_{\text{ent}}\)) is far more significant for perturbation robustness than for perturbation-free retrieval—removing \(\mathcal{L}_{\text{ent}}\) degrades the average performance under perturbation from 32.38% to 35.64%, validating the fault-tolerant role of the entailment cone mechanism. The contribution of the distillation loss (\(\mathcal{L}_{\text{distill}}\)) is primarily reflected in short-text retrieval—removing it significantly degrades COCO/Flickr30k performance, and embedding visualizations show that image clusters deviate from text clusters.

Key Findings

• Entailment loss is the primary source of robustness: Removing \(\mathcal{L}_{\text{ent}}\) leads to the largest degradation under perturbations, while removing \(\mathcal{L}_{\text{distill}}\) has a smaller impact on robustness. This aligns with the design intuition—the entailment cone provides a "region containment" margin, whereas distillation only ensures correct ranking.
• The sorting concentration of perturbed texts in hyperbolic space is far superior to that in Euclidean space: t-SNE/HoroPCA visualizations reveal that while perturbed text embeddings are sparsely distributed in Euclidean space, they are tightly clustered around the original text embeddings in hyperbolic space. Entailment-based ranking reduces the mean rank of perturbed texts from 184.94 (Euclidean distance) to 78.50 (entailment), and the rank variance from 42250 to 12666.
• Insensitivity to all hyperparameters: When \(\lambda_1\) through \(\lambda_4\) vary within the 0.01-0.20 range, performance fluctuations are minimal (<1%), indicating that the method does not require meticulous parameter tuning.
• Significantly outperforms baselines under hard-negative perturbations generated by LLMs: Replacing a single content word with LLaMA-30B on Urban-1k to generate hard negatives, HyFL-CLIP achieves a correct disambiguation rate of 62.07%, whereas Long-CLIP / HiMo-CLIP / FineLIP only achieve around 52-54% (close to random).
• High training efficiency: Training for only 2 epochs consumes a total of \(5.34 \times 10^{17}\) FLOPs, which is lower than HiMo-CLIP (\(1.96 \times 10^{18}\)) and FineLIP (\(1.19 \times 10^{18}\)).

Highlights & Insights

• "Replacing points with cones"—The design intuition of geometric tolerance margins is elegant: Euclidean contrastive learning requires \(\mathbf{t}_i\) to strictly align with an optimal direction, whereas the entailment cone dictates "it is correct as long as it is within the cone". This shift in perspective from "point matching" to "region containment" is the most beautiful insight of the paper, essentially relaxing single-point supervision into set supervision.
• Cross-manifold distillation is a general transfer paradigm: Without modifying the weights of the Euclidean CLIP, the model trains a hyperbolic student using the Euclidean CLIP's similarity distribution as a teacher signal. This non-intrusive approach of "extracting knowledge without altering the source model" can be extended to any scenario wishing to transfer Euclidean pre-trained models to hyperbolic, spherical, or other manifolds.
• Einstein midpoint aggregation + image-guided attention weights provide a concise "summarization" mechanism: Without requiring additional summarization networks or LLMs, taking a weighted Einstein average (with token-image similarity as weights) directly yields a semantically meaningful "parent node" representation that naturally lies on the hyperbolic manifold.
• Comprehensive experimental design for perturbation robustness: The paper includes syntactic-level perturbations like word dropping, sentence deletion, and shuffling, alongside semantic-level hard-negative perturbations generated by an LLM (replacing a single word to change semantics) and BLIP-VQA verification for semantic consistency. This multi-layered validation makes the robustness claims highly solid.

Limitations & Future Work

• Only validated on CLIP, neglecting other VLM architectures: The core of the method—cross-manifold distillation + hierarchical entailment—theoretically applies to any contrastive learning VLM (such as SigLIP, ALIGN), but the paper only conducts experiments using Open-CLIP (ViT-B/16 and ViT-L/14). Variations in encoder structures across different VLM architectures might affect distillation performance, requiring further investigation.
• The upper limit for long text length is still 248 tokens: Position encoding interpolation is essentially a "patch" rather than a fundamental solution, rendering the model inadequate for even longer, multi-paragraph, or multi-page documents. A potential avenue of improvement is combining recurrent or block-wise encoding strategies to enable the model to process texts of arbitrary lengths.
• Limited improvement in text-to-text intra-modality retrieval: Although it outperforms the baselines, the relative gain is not as pronounced as in cross-modal retrieval, indicating that hierarchical entailment modeling for abstracting intra-modality semantics still has room for improvement (as the current token aggregation method is relatively simple).
• Lack of deep discussion on the additional computational overhead of hyperbolic space: Although exponential/logarithmic mapping and Einstein midpoint calculations are computationally manageable in total FLOPs (training for 2 epochs is lower than HiMo-CLIP's 10 epochs), the inference latency and memory overhead increases are not reported in detail.
• Quality and bias of ShareGPT4V data remain unanalyzed: The training data is generated by GPT-4V, which may introduce hallucinations or stylistic biases. The impact of these factors on the quality of hyperbolic embeddings remains undiscussed.

Related Work & Insights

• vs Long-CLIP / HiMo-CLIP / FineLIP: These works support long contexts in Euclidean space through position encoding expansion and coarse-to-fine grain alignment. Their core paradigm remains one-to-one matching via Euclidean contrastive learning. HyFL-CLIP moves the entire problem to hyperbolic space and replaces point-to-point contrast with hierarchical entailment, fundamentally changing the geometric constraints of matching from exact match to region containment. This represents a paradigm shift rather than an incremental upgrade.
• vs MERU / HyCoCLIP / UNCHA (Hyperbolic VLMs): Existing hyperbolic VLMs are mostly trained from scratch on data scales vastly smaller than CLIP (approx. 20.5M vs 2.3B image-text pairs), which limits their performance ceilings. HyFL-CLIP's cross-manifold distillation approach allows leveraging the powerful pre-trained CLIP before doing domain adaptation in hyperbolic space. Fine-tuning these hyperbolic VLMs with the HyFL-CLIP framework significantly improves their performance, validating the generalizability of this "Euclidean pre-training + hyperbolic fine-tuning" paradigm.
• vs General similarity distillation (TinyCLIP, etc.): Traditional distillation operates within the same space (Euclidean to Euclidean). The challenge of cross-manifold distillation lies in the different distance metrics (cosine similarity vs geodesic distance), making direct embedding alignment impractical. Thus, the authors match the softmax probability distributions instead of the embeddings themselves. This "distribution-level, manifold-independent distillation" approach is highly instructive for other cross-geometry transfer tasks.

Rating

• Novelty: ⭐⭐⭐⭐⭐ First to fine-tune Euclidean CLIP to hyperbolic space for long-context understanding. The perspective of "cross-manifold distillation + hierarchical entailment tolerance" is highly novel, and not a simple combination of existing methods.
• Experimental Thoroughness: ⭐⭐⭐⭐⭐ Evaluated across four task scenarios, six perturbation types, two architectures, two types of ablations, VQA validation, and SDXL generation experiments, alongside comprehensive comparisons with 7+ concurrent baselines. The experiments are exceptionally solid.
• Writing Quality: ⭐⭐⭐⭐ The core motivation and mechanisms are clearly articulated, but some mathematical derivations skip steps (e.g., the Klein coordinate transform of the Einstein midpoint is not very friendly to readers unfamiliar with differential geometry).
• Value: ⭐⭐⭐⭐⭐ The problem addressed (long-text robustness) is a real-world pain point in deploying CLIP. The proposed "cone containment instead of point matching" logic could inspire future work to apply hyperbolic geometry in more scenarios.

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