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Disentangling Hallucinations: Orthogonal Semantic Projection for Robust Interpretability

This paper introduces a unified theoretical framework and a geometric intervention called Orthogonal Semantic Projection (OSP) to mathematically explain and mitigate semantic hallucinations in Vision-Language Model explanations by orthogonalizing query vectors against distractor concepts to ensure robust interpretability.

Original authors: Emirhan Bilgiç, Baptiste Caramiaux, Zhi Yan, Gianni Franchi

Published 2026-06-16

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CC BY 4.0

Original authors: Emirhan Bilgiç, Baptiste Caramiaux, Zhi Yan, Gianni Franchi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Problem: The "Confused Spotlight"

Imagine you have a smart camera system (a Vision-Language Model) that can look at a picture and tell you what's in it. To make sure we trust this camera, we use a special tool called XAI (Explainable AI). This tool acts like a flashlight or a heat map that shines on the parts of the image the camera is "looking at" to make its decision.

The Issue: Sometimes, this flashlight gets confused.
If you ask the camera, "Where is the cat?" and the photo actually contains a dog, the flashlight might still shine brightly on the dog. It's as if the flashlight thinks, "Well, dogs and cats are both fluffy animals with four legs, so I'll highlight the dog even though you asked for a cat."

The paper calls this "Semantic Hallucination." The explanation looks convincing, but it's lying. It's highlighting the wrong object because the concepts in the computer's brain are too "sticky" and mixed together.

The Cause: The "Crowded Room" of Ideas

Why does this happen? The paper argues that inside the computer's brain, all words and images live in a giant, high-dimensional room.

In this room, the concept of "cat" and the concept of "dog" aren't in separate, isolated corners.
Instead, they are standing close together, sharing some of the same space because they share traits (like "fur" or "paws").

When the computer tries to find the "cat," it grabs the whole cluster of "cat-ness." But because "dog" is standing right next to it and sharing some of that space, the computer accidentally grabs the "dog" part too. This is called Linear Semantic Leakage. The ideas are "leaking" into each other because they aren't perfectly separated.

The Solution: The "Noise-Canceling" Filter

The authors propose a new method called Orthogonal Semantic Projection (OSP). Think of this as a smart noise-canceling filter for the computer's thoughts.

Here is how it works, step-by-step:

The Dictionary of Distractions: Before the computer looks at the image, OSP creates a list of "distractors." If you are looking for a "cat," the system knows that "dog," "lion," and "tiger" are close relatives. It gathers the mathematical "signatures" of these distractors.
The Geometric Cleanup: OSP takes the computer's "cat" idea and mathematically pushes it away from the "dog," "lion," and "tiger" ideas.
- Analogy: Imagine you are trying to listen to a specific song (the "cat") in a crowded room where everyone is singing similar tunes. OSP is like putting on headphones that actively cancel out the voices of the people singing about dogs and lions.
The Pure Signal: What remains is a "purified" version of the "cat" idea. It has had all the shared traits with other animals stripped away. It is now orthogonal (at a perfect 90-degree angle) to the distractors.
The Result: When the computer uses this purified "cat" idea to shine its flashlight, it ignores the dog completely. The heat map now only lights up the actual cat, or nothing at all if there is no cat.

Why This Matters

The paper proves that this isn't just a trick for one specific type of camera; it works for many different AI models (like CLIP, SigLIP, and Stable Diffusion) and many different ways of creating heat maps.

It stops the lies: The computer stops highlighting objects that aren't there just because they look similar.
It keeps the truth: It doesn't make the computer worse at finding the right object; in fact, it often makes the "right" highlight even sharper.
It's a plug-and-play tool: You don't need to retrain the whole AI. You just add this "filter" step before the explanation is generated.

The Proof

The researchers tested this on thousands of images.

Quantitative Proof: They measured how often the AI correctly identified the right object and ignored the wrong ones. The "filter" (OSP) significantly improved these scores.
Human Proof: They showed heat maps to 200 real people. When the maps were generated with the old method, people were often confused or tricked by the wrong highlights. When they saw the maps generated with the new OSP method, people were much better at guessing what the AI was looking at and felt more confident in the answer.

Summary

In short, this paper introduces a way to clean up the AI's vocabulary before it tries to explain itself. By mathematically separating similar concepts (like cats and dogs) so they don't bleed into each other, the AI can finally point its flashlight at the exact thing you asked for, without accidentally lighting up the wrong object next to it.

Technical Summary: Disentangling Hallucinations via Orthogonal Semantic Projection

Problem Statement

As Vision-Language Models (VLMs) and multimodal diffusion models are deployed in safety-critical applications, the trustworthiness of their explanations becomes paramount. However, existing Explainable AI (XAI) methods for these models frequently suffer from semantic hallucination. In this phenomenon, attribution maps (saliency maps) highlight image regions corresponding to objects that are not present in the image when prompted with specific text descriptions. For instance, a model might highlight a dog when the prompt is "cat," or highlight a sheep when the prompt is "cat" and no sheep exists.

The paper argues that this issue is not merely a flaw in specific architectures but a fundamental consequence of Linear Semantic Leakage within high-dimensional embedding spaces. In models like CLIP and SigLIP, text and image embeddings reside in a shared space where semantically related but distinct concepts (e.g., "cat" and "dog") are not orthogonal. They share common directional components. When saliency methods compute attributions based on these non-orthogonal embeddings, the shared components cause the method to highlight irrelevant regions, leading to "ghost signals" or hallucinated explanations. The paper posits that the model may appear correct but is actually "right for the wrong reasons."

Methodology: Orthogonal Semantic Projection (OSP)

To address this, the authors propose Orthogonal Semantic Projection (OSP), a geometric intervention designed to disentangle unique semantic signals from shared concepts before computing saliency maps.

Theoretical Framework

The authors formalize the problem through the Linear Semantic Attribution (LSA) framework. They demonstrate that most multimodal saliency methods (including GradCAM, LeGrad, CheferCAM, and DAAM) can be expressed as linear (or locally linear) functions of the text embedding.

Lemma 1 (Linear Semantic Leakage): If the angle between the text embedding of the target class $A$ and a distractor class $B$ is non-zero (i.e., they are not orthogonal), the saliency map for $B$ will contain a component proportional to the true saliency map of $A$ . This "ghost signal" is directly controlled by the cosine similarity between the embeddings.

The OSP Algorithm

OSP utilizes Orthogonal Matching Pursuit (OMP) to perform a sparse decomposition of the text embedding. The process involves:

Dictionary Construction: A dictionary of semantics ( $\mathbf{D}$ ) is created, consisting of "distractor" concepts that are semantically or visually related to the target. The authors explore four strategies for this: ImageNet classes, ImageNet + WordNet relations, and dictionaries generated by LLMs (Gemini 3 Flash and GPT-OSS 120B).
Sparse Decomposition: The target text embedding ( $\mathbf{a}^{\text{txt}}_{\text{target}}$ ) is treated as a signal to be approximated by the dictionary atoms.
Residual Extraction: The algorithm iteratively selects atoms most correlated with the current residual and updates the active set. Crucially, the final residual ( $\mathbf{r}$ ) is strictly orthogonal to all selected distractor atoms.
Projection: The residual $\mathbf{r}$ represents the "unique semantic direction" of the target concept, stripped of shared components with distractors.
Application: This purified residual replaces the original text embedding in the saliency computation. For discriminative models, this is done directly on the query embedding. For diffusion models (like Stable Diffusion), OSP is applied to the key vectors in the cross-attention mechanism before the softmax operation.

The method is plug-and-play, requiring no retraining of the underlying VLM or diffusion model.

Key Contributions

Geometric Analysis of Hallucination: The paper provides a formal mathematical framework linking grounding failures to the non-orthogonality of semantic embedding directions. It characterizes hallucination as a function of linear semantic leakage and offers a geometric interpretation of how these errors propagate.
A Universal XAI Technique: OSP is presented as a generalized framework compatible with multiple architectures (CLIP, SigLIP, Diffusion models) and various saliency methods (GradCAM, LeGrad, CheferCAM, AttentionCAM, DAAM).
Extensive Validation: The method is evaluated across three foundational models, five XAI methods, and multiple datasets (ImageNet-Segmentation, MS COCO).
Human-Centric Evaluation: A user study involving 200 participants demonstrates that OSP improves human identification accuracy, confidence, and trust in model explanations.

Experimental Results

The authors evaluated OSP on the ImageNet-Segmentation and MS COCO datasets using metrics such as mean Intersection-over-Union (mIoU), mean Average Precision (mAP), and Area Under the ROC Curve (AUROC).

Hallucination Suppression: OSP consistently widens the gap between positive prompts (target present) and negative prompts (target absent). Specifically, it significantly improves AUROC, indicating better discrimination between present and absent concepts.
Localization Fidelity: The method improves or maintains localization performance (mIoU) for positive prompts while suppressing inaccurate heatmaps for negative prompts.
Robustness: The improvements hold across different dictionary construction strategies, including those generated by LLMs and those based on static datasets like ImageNet and WordNet.
Efficiency: The computational overhead of OSP is negligible (less than one second), making it practical for inference-time intervention.
User Study: Participants using OSP-enhanced heatmaps showed higher accuracy in identifying the model's focus, higher confidence in their answers, and greater trust in the explanations compared to baseline methods.

Significance and Claims

The paper claims that OSP represents a fundamentally new paradigm for interpretability. Unlike previous approaches that attempt to decompose image embeddings to find visual concepts, OSP mathematically decomposes the text embedding space to isolate pure semantic directions.

The authors assert that by addressing the root cause of hallucination—the non-orthogonality of embeddings in the representation space—they provide a theoretically sound and empirically validated solution. They emphasize that this geometric intervention makes attribution maps more reliable for end-users, translating theoretical grounding into measurable improvements in human interpretability. The work suggests that the geometric perspective opens promising directions for extending robust interpretability to larger-scale generative architectures and broader trustworthy AI applications.