Forte : Finding Outliers with Representation Typicality Estimation

Dear Reviewer,

Thank you for your positive evaluation of our paper. We are pleased you found the problem relevant, the method sound, and the experimental framework thorough. Your feedback is valuable, and we are eager to address your concerns.

Addressing Weaknesses:

1. Comparison with Current SOTA and DoSE:

   • Explicit Comparison with DoSE:

     • We acknowledge our comparison with DoSE could be more explicit. In the revised manuscript, we will enhance the Introduction and related work sections to clearly state how Forte builds upon and differs from DoSE.
     • Core Differences from DoSE:
       • Elimination of Generative Model Training:
         • DoSE requires training generative models (e.g., Glow, VAEs) on in-distribution data to estimate likelihoods, which is computationally intensive and impractical for large datasets, and access to a small sample of total in-distribution samples due to:
           1. Glow models rely on invertible architectures and exact log-likelihood evaluations, resulting in inefficient computation and high memory requirements.
           2. VAEs suffer from sample inefficiency on complex datasets, leading to poorly structured latent spaces and degraded performance.
         • Forte eliminates generative models, using pre-trained self-supervised models (e.g., CLIP, ViT-MSN, DINOv2) for feature extraction. This reduces computational overhead and simplifies implementation. A forward pass suffices, with no retraining or fine-tuning needed.
       • Addressing Likelihood Estimation Challenges:
         • Likelihood-based methods can be unreliable in high-dimensional spaces, where OOD samples may have higher likelihoods than in-distribution data (e.g., CIFAR-10 vs. SVHN). DoSE partially addresses this but has limitations.
         • Forte avoids likelihoods by operating in feature space and using per-point summary statistics to capture local data structures.
       • Introduction of Per-Point Metrics:
         • DoSE relies on global statistics, which may miss local nuances.
         • Forte uses per-point statistics—precision, recall, density, coverage—computed in feature space, enabling fine-grained OOD detection by accurately estimating the manifold.

   • Performance Improvements:

     • Empirical Results:
       • On CIFAR-10 (in-distribution) vs. CIFAR-100 (OOD), DoSE achieves an AUROC of 56.90%, while Forte achieves 97.63% ± 0.15% (Table 2).
       • Forte outperforms DoSE and all techniques benchmarked in the DoSE paper across tasks, including challenging scenarios with synthetic data and medical images.

2. Clear Statement about the Method and its Relation to DoSE:

   • Method Description in the Introduction:
     • We will, as mentioned above, revise the Introduction to clarify how Forte builds on DoSE's typicality concept while introducing significant improvements, such as eliminating generative models and using per-point metrics.
   • Guiding the Reader:
     • Early in the paper, we will provide an overview of Forte, highlighting its core components and differences from DoSE and other methods.

Additional Enhancements:

• Comparison with Other SOTA Methods:

  • We will expand the related work section to compare Forte with other SOTA OOD detection methods, highlighting how it addresses their limitations:
    • Versus ODIN (Liang et al., 2018): Requires temperature scaling, input perturbation, and extensive tuning, dependent on NN architecture. Forte surpasses ODIN without these dependencies.
    • Versus VIM (Wang et al., 2022): Relies on class labels and logit matching, limiting its unsupervised applicability. Forte excels without requiring labels or OOD exposure during training.
    • Versus NNGuide (Park et al., 2023): Depends on labeled data and complex training. Forte matches or exceeds performance without these complexities.
  • Our benchmarking considers these methods and others. Table 1 reports results against the best-performing methods for each task in the OpenOOD v1.5 leaderboard.

• Clarifications:

  • We will ensure the methodology section title explicitly states it describes Forte, guiding readers effectively.

Conclusion and Request for Consideration:

We appreciate your constructive feedback, which will improve the paper's clarity and impact. By addressing your concerns, emphasizing Forte's core differences from DoSE, and comparing it with other SOTA methods, we aim to provide a comprehensive presentation.

Given Forte’s significant advancements in performance, scalability, and practicality, we kindly ask you to consider our clarifications and enhancements in your evaluation and increase our score. Please let us know if further clarifications are needed.

Thank you again for your positive review and valuable suggestions.

Sincerely,
The Authors

Dear Reviewer,

Thank you for your thoughtful review and recognition of Forte's strengths, including its performance, flexibility, evaluation, and innovative metrics. We value your feedback and appreciate the opportunity to address your concerns.

Addressing Weaknesses:

1. Paper Structure:

   • Focus on Novel Contributions:
     We acknowledge that the Introduction focuses heavily on existing literature, which may detract from our novel contributions. In the revised version, we will streamline the background and emphasize Forte's unique aspects early, clearly distinguishing it from prior methods like DoSE.
     • Key Differences from Other Methods:
       • Unlike DoSE, which relies on training complex generative models (e.g., Glow, VAEs), Forte leverages pre-trained self-supervised models, reducing computational overhead and eliminating the need for training.
       • Forte introduces per-point summary statistics in feature space, enhancing OOD detection performance with fine-grained data assessments.
       • By avoiding reliance on likelihood estimations prone to failure (e.g., DoSE), Forte offers a more robust and scalable solution.

2. Complexity in Practical Implementation:

   • Computational Efficiency:
     • Forte's reliance on pre-trained models ensures efficient feature extraction via parallelizable forward passes. Non-parametric density estimators (e.g., OCSVM, KDE, GMM) are lightweight, with low training and inference times.
   • Simplification:
     • Forte does not require training deep neural networks, unlike methods requiring complex generative models or supervised classifiers. It adapts to data drift without retraining, operating in a zero-shot setting.
   • Flexibility:
     • Our ablation study (Table 3) shows strong performance using a single model like CLIP (99.13% AUROC). Resource-constrained settings can achieve competitive results without needing all three models, while the ensemble provides additional performance benefits.

3. Insight into Self-Supervised Model Choices:

   • Rationale for Selection:
     • CLIP, ViT-MSN, and DINOv2 were chosen for their complementary strengths:
       • CLIP captures semantic relationships through image-text alignment.
       • ViT-MSN emphasizes local structures via masked self-supervision.
       • DINOv2 learns hierarchical representations through knowledge distillation.
   • Enhancing Robustness:
     • Integrating these models allows Forte to capture diverse data features, improving robustness against challenging OOD cases, including synthetic samples from models like Stable Diffusion.
   • Empirical Support:
     • Ablation studies confirm that combining representations from diverse models outperforms any single model, highlighting their complementary contributions.

Addressing Questions:

1. Computational Demands and Real-Time Applicability:

   • Efficiency:
     • Feature extraction is efficient, with CLIP processing images at ~30 ms per image. Anomaly detection involves simple computations on low-dimensional metrics, enabling real-time application.
   • Adaptability:
     • For resource-constrained or real-time use cases, a subset of models or optimization can be employed without significant performance loss. Forte's lack of training requirements further enhances its practicality.

2. Effectiveness of Multiple Models from a Single Self-Supervised Approach:

   • Exploring Variations:
     • While multiple models from one self-supervised approach may offer some diversity, combining models with distinct training objectives (e.g., CLIP, ViT-MSN, DINOv2) provides broader feature coverage and enhances robustness.
   • Framework Flexibility:
     • Forte is adaptable, allowing users to select models based on specific requirements and constraints.

Conclusion and Request for Reconsideration:

We believe our planned revisions, emphasizing Forte's core differences from other methods—particularly those relying on generative models like DoSE—will enhance clarity and highlight its practicality and robustness. Forte avoids the computational challenges and limitations of such methods, offering an efficient, effective OOD detection solution.

We kindly request that you reconsider our paper, and give us a higher score in light of these clarifications and revisions. Your constructive feedback has been valuable in strengthening our work, and we are happy to address any additional questions.

Thank you again for your time and thoughtful review.

Sincerely,
The Authors

Thank you for your continued engagement and feedback. We would like to address your remaining concerns and continue our discussion.

Novelty: We respectfully maintain that the novelty of our work is irrefutable. While prior work on density of states estimation focused solely on generative models (Morningstar et al. 2021), and current OOD detection approaches using supervised/self-supervised models either use a single summary statistic as a score (e.g. Hendrycks et al. 2022) or train generative models for representation scoring (e.g. Cook et al. 2023), our work introduces a novel set of statistics never before considered in OOD detection. We must acknowledge that building on prior work is fundamental to scientific progress. Importantly, our contributions have improved DoSE-like OOD detector performance by 0.4 AUROC on challenging problems, while exceeding previous SOTA by 0.07 AUROC on near OOD (73% of possible improvement) and 0.04 on far OOD (98% of possible improvement) - demonstrating significant impact.

We have added Figures 15 & 16 in the appendix comparing our performance to established SOTA methods including OpenMax (CVPR '16), MSP (ICLR '17), Temp Scaling (ICML '17), MDS (NeurIPS '18), RMDS (arxiv '21), ReAct (Neurips '21), VIM (CVPR '22), KNN (ICML '22), SHE (ICLR '23), GEN (CVPR '23), and MLS (ICML '22). Table 1 already shows results against top-performing methods from the OpenOOD v1.5 leaderboard.

Insight into encoders: The results in Table 3 demonstrate that richer representations improve OOD detection, with CLIP > DINO v2 > MSN individually, and CLIP + DINO v2 > CLIP + MSN > DINO v2 + MSN for 2-model combinations. As you requested, we conducted additional experiments with DeIT (ViT-B and ViT-Ti) evaluating OOD detection performance from Table 2 settings. These results are now in the appendix. DeIT-B and DeIT-Ti achieved 0.87 and 0.82 AUROC respectively on CIFAR-10 vs CIFAR-100, confirming that more informative representations are crucial for performance. DeIT's training objective approximates supervision, resulting in less informative embeddings than DINO v2. Similarly, the tiny model's lower capacity leads to worse performance. We appreciate your encouragement to include this insight, as it helps understand which encoders are most valuable for practitioners. (Full results and analysis in Appendix D)

Please let us know if you have any remaining concerns or if any points require further clarification.

We would appreciate if you could consider revising our score upwards if all your concerns have been adequately addressed.

Dear Reviewer 2mpC,

We appreciate your continued engagement with our submission. After our previous responses and added experimental results, we wanted to follow up one final time to ensure we've fully addressed your core concerns:

1. Regarding novelty: Our work demonstrates substantial empirical improvements over existing methods, with gains of:

   • 0.4 AUROC on challenging problems

   • 73% of possible improvement on near OOD detection

   • 98% of possible improvement on far OOD detection

2. On SSL model insights: We've now provided comprehensive comparisons including:

   • Individual model performance rankings (CLIP > DINO v2 > MSN)

   • New DeIT variant experiments in Appendix D

   • Detailed analysis of representation quality impact on performance

Our additional benchmarking comparisons against established methods (OpenMax, MSP, ReAct, VIM, etc.) in Figures 15 & 16 further validates these contributions. We believe these additions directly address your concerns about both novelty and SSL model insights.

If you feel any aspects still require clarification or additional analysis, we would be grateful for your specific feedback. We remain committed to strengthening the paper further based on your expertise.

Thank you for your thorough review and consideration.

Best regards,

The Authors

4. Explicit Comparison with DoSE:

Concern: Is the method simply taking DoSE and running it on a new set of statistics? How does it differ from DoSE?

Response: While our method is inspired by the concept of typicality used in DoSE, Forte introduces significant novel contributions that differentiate it from DoSE. The differences are as follows:

Core Differences from DoSE:

• Elimination of Generative Model Training:

  • DoSE requires training generative models (e.g., Glow, VAEs) on in-distribution data to estimate likelihoods, which is computationally intensive and impractical for large datasets, and access to a small sample of total in-distribution samples due to: 1. Glow models rely on invertible architectures and exact log-likelihood evaluations, resulting in inefficient computation and high memory requirements. 2. VAEs suffer from sample inefficiency on complex datasets, leading to poorly structured latent spaces and degraded performance.

    • Forte eliminates generative models, using pre-trained self-supervised models (e.g., CLIP, ViT-MSN, DINOv2) for feature extraction. This reduces computational overhead and simplifies implementation. A forward pass suffices, with no retraining or fine-tuning needed.
    • Addressing Likelihood Estimation Challenges:
      • Likelihood-based methods can be unreliable in high-dimensional spaces, where OOD samples may have higher likelihoods than in-distribution data (e.g., CIFAR-10 vs. SVHN). DoSE partially addresses this but has limitations.
      • Forte avoids likelihoods by operating in feature space and using per-point summary statistics to capture local data structures.
    • Introduction of Per-Point Metrics:
      • DoSE relies on global statistics, which may miss local nuances.
      • Forte uses per-point statistics—precision, recall, density, coverage—computed in feature space, enabling fine-grained OOD detection by accurately estimating the manifold.

  • Performance Improvements:

    • Empirical Results:
      • On CIFAR-10 (in-distribution) vs. CIFAR-100 (OOD), DoSE achieves an AUROC of 56.90%, while Forte achieves 97.63% ± 0.15% (Table 2).
      • Forte outperforms DoSE and all techniques benchmarked in the DoSE paper across tasks, including challenging scenarios with synthetic data and medical images.

5. Consistency of Density Definition with Figure 1

Concern: Density definition is inconsistent with Figure 1. As defined, it is just a scaled "recall," which would make it useless to model.

Response: The density definition is consistent with Figure 1. Figure 1 was generated using the actual functions and code we use in our experiments, applied to simplified 2D data points for illustrative purposes using matplotlib. The density metric measures the average number of reference points within the neighborhood of each test point, normalized by the product of $k$ (the number of nearest neighbors) and the total number of reference points $m$. Mathematically, it is defined as:

$\mathrm{density_{pp}^{(i)}} = \frac{1}{k m} \sum_{j=1}^m **1**\left( x_j^g \in B\left( x_j^r, \mathrm{NND}_k(x_j^r) \right) \right).$

This metric provides an estimate of the local density around each test point, which is crucial for distinguishing between ID and OOD samples. It is not simply a scaled recall but captures different information.

6. Novelty of the Summary Statistics

Concern: The four metrics are not newly proposed in this paper.

Response: While the metrics of precision, recall, density, and coverage have been previously used in the context of evaluating generative models (e.g., in "Reliable Fidelity and Diversity Metrics for Generative Models" by Naeem et al., 2020), our contribution lies in adapting these metrics as per-point summary statistics for OOD detection.

In prior work, these metrics are computed as aggregate statistics over entire datasets, primarily to evaluate the performance of generative models in terms of fidelity and diversity. Our novel adaptation involves computing these metrics for individual data points in the feature space, which enables us to capture local anomalies and perform fine-grained OOD detection.

7. Use of Gaussian Mixture Models (GMMs)

Concern: Incorrect claims are made, e.g., GMM is not non-parametric.

Response: You are correct; Gaussian Mixture Models (GMMs) are parametric models. In our paper, we did not intend to misclassify GMMs as non-parametric. Our method employs GMMs without making strong assumptions about the underlying distribution because we perform hyperparameter tuning (e.g., varying the number of components) to best fit the data. While GMMs are parametric, our approach is flexible and does not assume a specific distribution a priori.

We will correct this in the manuscript to accurately describe GMMs as parametric models.

(continued further in next comments)

8. Additional Clarifications

Regarding Figure 1: The figure is generated using the actual functions and code employed in our experiments, applied to simplified data points for visualization done via matplotlib. It accurately represents the definitions provided for the per-point metrics.

Regarding Minor Typos and Formatting: We will carefully proofread the manuscript to correct any minor typos or formatting inconsistencies, such as the commas missing "in Figure 2 Figure 3 Figure 4," "near-ood" instead of "near-OOD," and "Table 1 & 2" instead of "Tables 1 & 2."

9. Pseudocode for OOD Detection Using Per-Point PRDC Metrics

Here is an informal pseudocode for your understanding, and can add a more formal version to the appendix. We are happy to make a partial anonymized release of the codebase for Forte, if required for additional clarity during the review process. Post-acceptance, the code will be made public and open source.

Inputs:

• Reference data features: $\{ x_j^r \}_{j=1}^m$
• Test data features: $\{ x_i^g \}_{i=1}^n$
• Number of nearest neighbors: $k$

Outputs:

• OOD detection performance metrics: AUROC, FPR@95

Algorithm Steps

1. Feature Extraction:

   • Use pre-trained models (e.g., CLIP, ViT-MSN, DINOv2) to extract features for both reference and test data.
     • Reference features: $\{ x_j^r \}$
     • Test features: $\{ x_i^g \}$

2. Compute Nearest Neighbor Distances:

   • For each reference feature $x_j^r$, compute $\mathrm{NND}_k(x_j^r)$: distance to its $k$-th nearest neighbor in $\{ x_j^r \}$.
   • For each test feature $x_i^g$, compute $\mathrm{NND}_k(x_i^g)$: distance to its $k$-th nearest neighbor in $\{ x_i^g \}$.

3. Compute Per-Point PRDC Metrics:

   • For each test feature $x_i^g$, compute per-point Precision, Recall, Density, and Coverage metrics relative to the reference data.
     • Note: Detailed computations are omitted for brevity. Please check section 3 for exact details.

4. Assemble Feature Vectors:

   • For each test feature $x_i^g$, create a feature vector $\phi^{(i)}$ consisting of its per-point PRDC metrics.

5. Prepare Training Data:

   • Split reference data features $\{ x_j^r \}$ into:
     • Training set: for model training.
     • Validation set: for model evaluation.

6. Compute Per-Point Metrics for Reference Data:

   • Repeat steps 2 and 3 for the reference training set to obtain per-point metrics $\{ \phi_{\text{ref}}^{(j)} \}$.

7. Train Anomaly Detection Models:

   • Use the reference per-point metrics $\{ \phi_{\text{ref}}^{(j)} \}$ to train unsupervised anomaly detection models:
     • One-Class SVM (OCSVM)
     • Kernel Density Estimation (KDE)
     • Gaussian Mixture Model (GMM)

8. Evaluate Models on Test Data:

   • For each test feature vector $\phi^{(i)}$:
     • Compute anomaly scores using the trained models.

9. Assign Ground Truth Labels:

   • In-distribution (ID) samples: label $y^{(i)} = 0$
   • Out-of-distribution (OOD) samples: label $y^{(i)} = 1$

10. Compute Evaluation Metrics:

    • Calculate performance metrics using the anomaly scores and ground truth labels:
      • AUROC: Area Under the Receiver Operating Characteristic Curve
      • FPR@95: False Positive Rate at 95% True Positive Rate

Notes:

• The per-point PRDC metrics capture local relationships between test samples and the reference data manifold.
• Anomaly detection models are trained solely on reference (in-distribution) data metrics to learn the typical data distribution.
• Evaluation metrics assess the models' ability to distinguish OOD samples based on the per-point metrics.

End of Pseudocode

Conclusion

We are committed to improving the clarity and quality of our paper. We believe that Forte offers significant advancements in OOD detection by introducing novel per-point metrics and eliminating the need for training generative models. Our method provides a scalable and effective solution applicable to various challenging scenarios, including synthetic data detection and medical imaging.

We hope that our extremely detailed responses address your concerns and clarify the contributions and novelty of our work. We kindly request that you consider our explanations in your evaluation to increase our ratings and are open to any further questions or suggestions you may have.

Thank you again for your valuable feedback.

Sincerely,

The Authors

Dear Reviewer GdRX,

We appreciate your thorough review of our paper and the valuable insights you've provided. We are glad that you found our proposed approach effective and that our experiments cover a wide range of scenarios. We would like to address your concerns and clarify some misunderstandings to improve the clarity and impact of our work.

1. LaTeX Formatting and Notation

Concern: The paper is extremely poorly written. None of the math LaTeX in Section 3.2 is well formatted. Subscripts and superscripts are wrong. Variables are used without definition, making it difficult to follow the mathematical descriptions.

Response: We apologize if the notation in Section 3.2 was unclear. We want to assure you that the LaTeX formatting and notation are correct. All variables are properly defined according to standard mathematical conventions followed in the literature, such as Naeem et al, 2020.

In Section 3.2, we introduce per-point metrics using the following notation:

• $**1**(\cdot)$: Indicator function.
• $S({x_j^r}{j=1}^m) = \bigcup{j=1}^m B(x_j^r, \mathrm{NND}_k(x_j^r))$ : The union of Euclidean balls centered at reference points $x_j^r$ with radius equal to their $k$-th nearest neighbor distance.
• $B(x, r)$: Euclidean ball centered at point $x$ with radius $r$.
• $\mathrm{NND}_k(x)$: Distance between point $x$ and its $k$-th nearest neighbor in the dataset.

We recognize that explicitly defining $\mathrm{NND}_k(x)$ and other variables could enhance clarity. We will add these definitions to ensure that all readers can follow the mathematical derivations seamlessly. For example, we will include a sentence like:

"Here, $\mathrm{NND}_k(x)$ denotes the Euclidean distance from point $x$ to its $k$-th nearest neighbor in the dataset."

2. Use of Summary Statistics

Concern: No description is given on how the four metrics (precision, recall, density, and coverage) are used. Are they used as the "summary statistics" that the proposed method models?

Response: Yes, the four per-point metrics are indeed used as the summary statistics in our method. We mention this in Section 3.2:

"We propose the following per-point summary statistics (precision, recall, density, and coverage) that effectively capture the 'probability distribution of the representations' using reference and unseen test samples in the feature space, enabling more nuanced anomaly detection."

These per-point metrics serve as summary statistics that capture local geometric properties of the data manifold in the feature space. They enable us to model the distribution of in-distribution (ID) data and identify out-of-distribution (OOD) samples effectively. We will emphasize this connection more clearly in the revised manuscript.

3. Definition and Clarity of "Forte" Method

Concern: The method, referred to as "Forte," is never truly defined or mentioned in the method section.

Response: We apologize for any confusion. The entire Section 3 is dedicated to detailing our proposed method, which we refer to as "Forte." We will make this explicit at the beginning of Section 3 by revising the section title and introduction as follows:

"3. Forte: A Framework for OOD Detection Using Per-Point Metrics

In this section, we introduce Forte, a novel framework that combines diverse representation learning techniques with per-point summary statistics and non-parametric density estimation models to detect out-of-distribution (OOD) and synthetic data."

This will ensure that readers understand that the subsequent subsections describe the components and methodology of Forte.

(Continued further in next comments)

1. It is a fact that the latex formatting is not correct. In fact your latex formatting here has the same mistake. Most underscores are missing! Instead of writing $\bigcup_{j=1}^m$ (\biccup_{j=1}^m), you wrote $\bigcup {j=1}^m$ (\biccup {j=1}^m).

   It is not unclear, but a mistake. I require an explanation on this because the mistakes are so obvious that it should be immediate to anyone who looked at the equations.

2. Thanks for the clarification. However, the sentence you quote appears to be from the introduction, rather than Sec 3.2. I believe that Section 3.2 and/or 3.3 should be changed to make this clearer.

3. Thanks for the clarifications. I agree that the change will improve readability.

4. Thanks for the explanation. It appears that indeed, while there are similarities (i.e., fitting a simple model over summary stats), there are also important differences.

5. From just looking at the definitions, it is obvious that the definition of density (Eqn 3) is a scaled version of recall (Eqn 2). One of your definition is wrong.

6. To avoid confusion, I suggest not saying that you proposed these metrics, but you novelly adopted them for anomaly detection.

7. Thank you for the clarification. The proposed change sounds good to me.

8. Thank you for the pseudocode. It confirms my speculation and I think would be a strong addition to the paper.

We are truly grateful for your detailed evaluation and positive feedback. We appreciate your recognition of our paper's clarity, implementability, and the comprehensive supporting materials we provided in the appendix. Your suggestion for conference highlighting is very much appreciated.