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REVIEW 4 major objections 5 minor 52 references

Pursuing Better Decision Boundaries for Long-Tailed Object Detection via Category Information Amount

T0 review · 4 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Category information amount — the volume of a category's embedding manifold — predicts detection difficulty better than instance count, and an angular-margin loss tuned by it reduces category bias in long-tailed and balanced object…

desk verdict A strong empirical long-tail detection paper whose 'information amount beats instance count' claim is undercut by a covariance shrinkage confound for rare classes. read the letter →

arxiv 2502.03852 v1 pith:YITPRE4Q submitted 2025-02-06 cs.CV cs.AI

Yanbiao Ma , Wei Dai , Jiayi Chen This is my paper · ORCID
classification cs.CVcs.AI
keywords categoryinformationamountlong-tailedobjectdetectionIGAMlossangularmarginperceptualmanifoldvolumedecisionspaceallocationbiascovariancedeterminant
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that a category's information amount, measured as the log determinant of the covariance of its classification embeddings, is a truer indicator of how hard the category is to detect than the number of training instances. Across LVIS, COCO-LT, and PASCAL VOC, this quantity shows a strong negative correlation with per-class accuracy, while instance count explains little of the variation on a balanced dataset. The paper then derives IGAM loss, a cosine-classifier loss whose angular margins are set by ratios of information amounts, so high-information categories receive larger decision regions and low-information categories smaller ones. The reported result is that IGAM raises rare-category average precision substantially on long-tailed benchmarks and also lifts the weakest categories on the balanced PASCAL VOC set. If the claim is right, decision-space allocation in object detection should follow measured intra-class complexity rather than frequency counts.

What carries the argument

The engine of the method is category information amount $I_i$, the log volume of the perceptual manifold that a category occupies, estimated as $I_i = \frac{1}{2}\log_2\det(\Sigma_i + I)$ from classification-module embeddings, after a nonlinear shrinkage step that stabilizes the covariance estimate in high dimensions. This single scalar carries the whole argument: it explains why balanced datasets still show bias, and it supplies the margin schedule. IGAM loss converts the information amount into a normalized score $I'_i$ and sets pairwise margins $m_{ij} = \max(0, \frac{1}{\pi}\log(I'_i/I'_j))$ in a cosine classifier, so the decision region of each category scales with its measured complexity. To keep the measurement current, the paper stores embeddings in a bounded queue and merges local covariance matrices into a global covariance at each epoch, making dynamic updates affordable.

What would settle it

Take one detector and compute category information amounts from a randomly initialized feature extractor and from the same extractor after full training, then compare how each set correlates with per-class accuracy. If the random-initialization correlation is near zero while the trained correlation is strongly negative, the measurement is tracking the model's learning state rather than an intrinsic property of the category; a synthetic dataset with controlled intra-class diversity could then settle whether margins actually track difficulty.

Watch

Extended reading notes

Core claim

The central claim is that category informativeness, defined as $I_i = \frac{1}{2}\log_2 \det(\Sigma_i + I)$ from the covariance of a category's classification embeddings after nonlinear shrinkage, tracks category learning difficulty in object detection. The paper reports correlations around $-0.66$ to $-0.70$ between this information amount and category average precision on long-tailed datasets, and a near-zero correlation between instance count and accuracy on the relatively balanced PASCAL VOC set. From that observation it constructs IGAM loss, which inserts an angular margin $m_{ij} = \max(0, \frac{1}{\pi}\log(I'_i/I'_j))$ into a cosine cross-entropy objective to enlarge the decision space of high-information categories. Experiments with Faster R-CNN, Cascade Mask R-CNN, and DETR show that the loss improves overall mAP and rare-category AP on LVIS v1.0 and COCO-LT, reduces the variance of class-wise AP, and improves the hardest categories on PASCAL VOC, which the paper takes as evidence that the mechanism is not simply frequency rebalancing.

Load-bearing premise

The claim depends on treating the spread of a category's learned embeddings as its true information content, rather than as a side effect of how well the model has learned that category; if the spread mostly reflects poor current performance, the correlation with accuracy is partly circular.

Editorial extensions

If this is right

  • On LVIS v1.0, replacing cross-entropy with IGAM raises mAP by 5.2–7.5 points and rare-class AP by about 15–20 points across Faster R-CNN, Cascade Mask R-CNN, and DETR with ResNet-50, ResNet-101, and Swin-T backbones.
  • On COCO-LT, IGAM improves the rarest AP group by 2.3–3.0 points over the second-best method while keeping the frequent group's AP close to the cross-entropy baseline.
  • On PASCAL VOC, despite near-balanced instance counts, IGAM lifts overall mAP by about one point and delivers its biggest gains on the five hardest categories, including bottle and potted plant.
  • IGAM lowers model bias, measured as the variance of class-wise AP, by roughly half relative to Seesaw on LVIS v1.0.
  • Because IGAM changes only the classification loss, it can be applied to any detector that uses cosine-based classification on pooled embeddings, without extra modules or test-time changes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An implication left implicit: because information amount is computed from the model's own embeddings, it could be re-estimated on a labeled validation set and used at deployment time to predict which categories a detector will struggle with, independent of the training set's frequency counts.
  • A testable extension: if the negative correlation is driven partly by label noise and intra-class heterogeneity rather than by intrinsic geometry, the same $I_i$ could double as a data-quality score, pointing to categories that need cleaning or extra collection.
  • An alternative implementation worth probing: replacing the fixed log-ratio margin $m_{ij}$ with a learned monotonic map from information amount to margin would show whether the gain comes from the proportionality principle or from the specific normalization.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper introduces a per-category 'information amount' (IA), defined as half the log-determinant of (the Ledoit-Péché-shrunk covariance matrix of a category's classification embeddings plus identity), and argues that IA reflects category learning difficulty more accurately than instance count. Based on observed negative correlations between IA and class-wise average precision, the authors propose IGAM Loss, which adds an angular margin derived from IA ratios to a cosine-normalized softmax classifier. Experiments on LVIS v1.0, COCO-LT, and Pascal VOC across several detectors and backbones show substantial improvements, particularly on rare categories, and the authors report reduced variance of class-wise AP.

Significance. If the central claim were established—that category information amount is a better guide than instance count for allocating decision space—the paper would provide a conceptually new tool for diagnosing and mitigating category bias in object detection, with potential extension to balanced datasets. The experimental scope is broad (three datasets, four detection frameworks, multiple backbones) and the gains on rare classes are large, which makes the approach practically interesting. The paper also ships a reproducible low-storage update strategy for dynamic IA computation. However, the conceptual contribution is currently under-supported: the missing comparison to the plain cosine loss, the endogeneity of IA with respect to the trained model, and the shrinkage-floor behavior for small-sample classes all leave the specific role of IA uncertain.

major comments (4)
  1. [Section 3.2, Eq. (6)] The margin is defined as m_ij = max(0, (1/π) log(I'_i/I'_j)), which is always nonnegative. The text immediately after the equation states that if I_i < I_j, then m_ij is negative and the decision space for class i is compressed. This is not what the formula implements: when the positive class i has a smaller IA than a negative class j, the margin is zero, so the decision space of the low-IA class is not actively compressed. Only categories with larger IA than their competitors receive an expansion. The paper's stated mechanism of dynamically adjusting decision spaces in both directions is therefore not realized by the loss, and the authors should either correct the text or modify the margin formula, and report which version was used in the experiments.
  2. [Section 4.3, Tables 3–5] The baseline compared against IGAM is the unnormalized cross-entropy loss (Eq. 3), not the cosine-normalized loss of Eq. (5). Because IGAM includes angular normalization, the observed gains could stem entirely from that standard technique, independent of the information-amount-based margin. To support the paper's central claim that IA, rather than angular normalization, drives the improvement, the authors should add an ablation comparing IGAM to the plain cosine loss of Eq. (5), and ideally also to a version with margins based on instance count or on random margins.
  3. [Section 3.1, Listing 1 and Eq. (2)] The Ledoit-Péché shrinkage in Listing 1 replaces every eigenvalue of the sample covariance below lambda_minus = (1 - sqrt(p/m))^2 with lambda_minus. For classes with m < p—which includes essentially all LVIS rare classes (1–10 instances) and many COCO-LT tail classes—the covariance matrix is rank-deficient, and after flooring, the determinant is approximately (1 + lambda_minus)^p. The IA then equals approximately 0.5 p log2(1 + lambda_minus), a deterministic monotonically decreasing function of m. Hence, the reported negative correlation between IA and AP may simply be a nonlinear re-encoding of instance count. The paper compares IA only against the raw instance count, not against a monotone transform such as -log m, so the claim that IA 'more accurately reflects learning difficulty' is not established. A partial-correlation analysis controlling for m, or an evaluation on classes with matched instance counts, is needed.
  4. [Section 3.3 and Section 4] IA is computed from the embeddings of the model being trained and is updated during training. Since the loss reshapes those embeddings, IA is endogenous: it may reflect the model's current proficiency at a category rather than an intrinsic property of the category. This creates a feedback loop (embeddings affect margins, margins affect embeddings) that is not analyzed. A control experiment that computes IA from a fixed pretrained encoder, or from a separate model, and uses those values to set margins without updating, would clarify whether the margin mechanism relies on a stable external property or on the model's own failure signal.
minor comments (5)
  1. [Section 4.2] The sentence 'We did not use any test-time augmentations.' appears twice in the implementation details; please remove the duplicate.
  2. [Section 3.3.2, Eq. (10)] The formula for the storage-space ratio R as printed is dimensionally inconsistent. The correct expression should be R = (d + C * (floor(N/d) + 1) * p) / N, which matches the numerical examples given (e.g., saving approximately 56.44% memory for Pascal VOC). Please correct the displayed equation.
  3. [Table 1 and Figure 2] The tables and figures report Pearson correlations between IA and AP, and between instance count and AP, but do not provide confidence intervals or significance tests. Given the small number of categories in some settings (e.g., 20 on Pascal VOC), reporting uncertainty would make the claimed advantage of IA over instance count more convincing.
  4. [Section 3.2] The definition of normalized information amount I'_i = exp(I_i/(Ibar*sqrt(C))) / sum_j exp(I_j/(Ibar*sqrt(C))) * C + 1 is introduced without explaining the role of the '+1' term; please clarify why this offset is needed and how it affects the margin range.
  5. [Section 1 and Section 2.2] The claim that this is 'the first to directly report on widespread bias present in object detection models' is overstated given the long-tailed detection literature; please soften to 'the first to directly investigate the role of intra-class feature diversity as a cause of such bias in detection' or similar.

Circularity Check

2 steps flagged · score 5.0 of 10

In the long-tail regime the information-amount estimator is, by construction, a deterministic transform of instance count: the eigenvalue floor of Listing 1/Eq. (1) makes I_i approx 0.5 p log2(1+(1-sqrt(p/m))^2) for LVIS rare/common and COCO-LT tail classes (m<p), so the Table 1 correlations and Eq.

  1. renaming known result [Section 3.1, Eq. (1)-(2) and Listing 1; applied in Table 1 and Section 3.2, Eq. (6)]
    "lambda_i = max(lambda_i, lambda_-), with lambda_- = (1 - sqrt(p/m))^2 as the nonlinearly transformed minimum eigenvalue. Finally, the information amount of category i is formally defined as: I_i = 1/2 log2 det(Sigma(X_i) + I), (2)."

    For a category with m <= p instances (all LVIS rare classes with 1-10 instances and most common classes, at the paper's own p=128 storage example), the centered covariance has rank at most m-1, so at least p-m+1 sample eigenvalues are exactly zero. Listing 1's 'd = np.maximum(eigvals, lambda_minus)' replaces every such eigenvalue with lambda_- = (1-sqrt(p/m))^2, so I_i ~ 0.5 p log2(1+lambda_-), a deterministic, monotonically decreasing function of m alone. The negative IA-AP correlations in Table 1 (-0.68, -0.66, -0.70) and the margins m_ij = max(0, (1/pi) log(I'_i/I'_j)) in Eq. (6) therefore re-encode the known instance-count-performance relationship through a nonlinear transform.

  2. other [Section 3.2, Eq. (6), with Section 3.3 dynamic update and Eq. (2)]
    "In practical training, we face an engineering challenge: the information amount of categories changes as the model parameters evolve, necessitating dynamic updates. ... we propose using each category's information amount to dynamically adjust the decision boundaries, allowing categories with larger information amounts to have larger decision spaces."

    The margin m_ij in Eq. (6) is a function of I_i from Eq. (2), which is computed from the classification embeddings of the very model being trained by that loss; the loss then reshapes those embeddings, changing I_i, which changes the margins again. Section 3.3 makes this loop an explicit design feature (embeddings stored in a queue and refreshed each epoch). The difficulty signal is therefore not an independent property of the category but a function of the model's own state, and observed embedding spread partly measures how poorly a class is currently learned. This makes the Table 1 negative IA-AP correlation partly self-referential (both quantities are read off the same model) and makes the margin allocation partly chase the model's own failure signal.

full rationale

The paper's central claim is that category information amount (Eq. 2) reflects intrinsic learning difficulty better than instance count, and that margins set by its ratios (Eq. 6) improve long-tailed detection. The honest finding is partial circularity, not full. On one side, the shrinkage floor in Listing 1/Eq. (1) makes the estimate degenerate: for the m < p categories that dominate LVIS (rare 1-10, common 11-100) and COCO-LT (groups with <20 and 20-400 instances, at p=128 used in Section 3.3.2), essentially all eigenvalues are floored at lambda_- = (1-sqrt(p/m))^2 and I_i ~ 0.5 p log2(1+lambda_-) is a deterministic function of m. The reported correlations (Table 1) and margins (Eq. 6) therefore partly rename instance count under a nonlinear map, and the comparison against raw count (not -log m or another monotone baseline) does not establish a genuinely new signal in the tail. This is concrete and exhibit-able, and it directly affects the motivating observation. On the other side, the Pascal VOC experiments supply independent content: per-class counts there are far above p, the floor is negligible, IA still correlates with AP (Figure 2), and IGAM improves balanced-dataset classes; this part is self-contained measurement, not a by-construction identity. The self-referential training loop (margins reshape the embeddings that define I_i) is real but is not an equation-level equivalence of prediction and input, and the authors' self-citations (Ma et al. 2023a and related) are peer-reviewed, externally falsifiable support supplemented by fresh experiments here, so they do not by themselves raise the score. Net: the long-tail 'better than instance count' claim is substantially degraded by construction, while the balanced-dataset evidence remains independent - a 5 on the 0-10 scale.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the model-dependent definition of information amount, on a standard covariance estimation technique, and on a normalization choice imported from the authors' earlier work. The only parameter fitted to the outcome data is the scale s; the other constants are hand-set. No new physical entities are introduced.

free parameters (2)
  • s (angular margin scale) = 30 (tuned on LVIS v1.0, Table 2)
    Scales the cosine logits in IGAM Loss; chosen by grid search on the LVIS validation set and used for all other datasets. The performance is sensitive to s (mAP ranges 16.8 to 26.8 for s=10..50), so this is a fitted hyperparameter central to the reported results.
  • Margin formula constants (1/pi, sqrt(C)) = 1/pi and sqrt(C), chosen by hand
    The angular margin m_ij = max(0, (1/pi) log(I'_i/I'_j)) and the normalization I'_i = e^{I_i/(Ibar*sqrt(C))}/sum * C + 1 contain constants set without ablation or theoretical derivation; they determine margin magnitudes but are not tuned per dataset.
assumptions (4)
  • domain assumption Feature slow drift: embeddings of a sample change slowly during training, so previously stored embeddings approximate current ones.
    Invoked in Section 3.3.1 to justify updating the information amount only once per epoch using a queue of embeddings from earlier in the epoch. If drift is not slow, the information amount used in the loss is stale.
  • domain assumption The embeddings of a category lie near a low-dimensional perceptual manifold, so the volume of the manifold can be estimated by the determinant of the embedding covariance matrix.
    Section 3.1 builds the definition of I_i on this hypothesis, citing Cohen et al. (2020). If the manifold hypothesis fails, the determinant is not a meaningful volume.
  • standard math The Ledoit-Peche nonlinear shrinkage with lambda_minus = (1 - sqrt(p/m))^2 correctly estimates the covariance in the high-dimensional embedding space.
    Section 3.1 uses this shrinkage to stabilize the determinant estimate. It is a standard statistical technique, but its applicability to these embeddings is assumed.
  • ad hoc to paper The normalization I'_i = e^{I_i/(Ibar*sqrt(C))}/sum * C + 1, adopted from Ma et al. (2023a), scales information amounts appropriately for margin computation.
    This exact normalization is carried over from the authors' prior work without a derivation specific to detection; it is a design choice that affects the margins.

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Cite this review

Pith. "Pith review of Pursuing Better Decision Boundaries for Long-Tailed Object Detection via Category Information Amount." pith.science (2026). https://pith.science/paper/YITPRE4Q

@misc{pith2026250203852,
  author       = {Pith},
  title        = {Pith review of: Pursuing Better Decision Boundaries for Long-Tailed Object Detection via Category Information Amount},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YITPRE4Q}},
  note         = {Machine review of arXiv:2502.03852}
}
read the original abstract

In object detection, the instance count is typically used to define whether a dataset exhibits a long-tail distribution, implicitly assuming that models will underperform on categories with fewer instances. This assumption has led to extensive research on category bias in datasets with imbalanced instance counts. However, models still exhibit category bias even in datasets where instance counts are relatively balanced, clearly indicating that instance count alone cannot explain this phenomenon. In this work, we first introduce the concept and measurement of category information amount. We observe a significant negative correlation between category information amount and accuracy, suggesting that category information amount more accurately reflects the learning difficulty of a category. Based on this observation, we propose Information Amount-Guided Angular Margin (IGAM) Loss. The core idea of IGAM is to dynamically adjust the decision space of each category based on its information amount, thereby reducing category bias in long-tail datasets. IGAM Loss not only performs well on long-tailed benchmark datasets such as LVIS v1.0 and COCO-LT but also shows significant improvement for underrepresented categories in the non-long-tailed dataset Pascal VOC. Comprehensive experiments demonstrate the potential of category information amount as a tool and the generality of our proposed method.

Figures

Figures reproduced from arXiv: 2502.03852 by the authors.

Figure 1
Figure 1. The left vertical axis repre￾sents the number of instances per class. The right vertical axis represents the per￾formance of Faster R-CNN trained with cross-entropy loss using R-50-FPN as the backbone across all classes, trained on the Pascal VOC. The model was trained using the settings described in Section 4.2. The red text box displays the Pearson correlation coefficient between class per￾formance and the number … view at source ↗
Figure 2
Figure 2. Pearson correlation coefficients between category information amount and category average precision and between category instance count and category av￾erage precision, under two backbone net￾works and three loss function settings. Consider the following scenario: if a head category has very little category information amount, the model can more easily learn and abstract the patterns of that cate￾gory Cui et al. (20… view at source ↗
Figure 3
Figure 3. The function of the storage space ratio R as it varies with the queue length d on the Pascal VOC and MS COCO datasets. When R < 1, the new strategy saves more stor￾age space. To visually compare the storage space requirements of the new and original strategies, we take the Pascal VOC and MS COCO datasets as examples and plot the function graph of the storage space ratio R as it varies with the queue length d in [PI… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Model bias from models trained with different methods on LVIS v1.0. To more clearly demonstrate the effectiveness of our method in mitigating model bias, we use the variance of class-wise average precision (AP) as a measure of model bias. The comparison results on LVIS…

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    @esa (Ref

    \@ifxundefined[1] #1\@undefined \@firstoftwo \@secondoftwo \@ifnum[1] #1 \@firstoftwo \@secondoftwo \@ifx[1] #1 \@firstoftwo \@secondoftwo [2] @ #1 \@temptokena #2 #1 @ \@temptokena \@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should ...

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    \@lbibitem[] @bibitem@first@sw\@secondoftwo \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 @tmp #1 NAT@b@open@#2 NAT@b@shut@#2 \@ifnum @merge>\@ne @bibitem@firs...

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    a henb \

    @open @close @open @close and [1] URL: #1 \@ifundefined chapter * \@mkboth \@ifxundefined @sectionbib * \@mkboth * \@mkboth\@gobbletwo \@ifclassloaded amsart * \@ifclassloaded amsbook * \@ifxundefined @heading @heading NAT@ctr thebibliography [1] @ \@biblabel @NAT@ctr \@bibset...

    2023 arXiv

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.