---
kind: concept
slug: long-tailed-recognition
title: Long-tailed recognition
summary: >-
  Raising accuracy on rare classes when a few classes dominate training. Covers Copy-Paste with two-stage class-balanced retraining, equalization loss v2 for end-to-end detection, weight balancing and distribution alignment for classifiers, rare-predicate methods for scene graphs, and rarer-word web data. Numbers are author-reported; compare within one recipe.
tags: [long-tail, instance-segmentation, object-detection, image-classification, data-augmentation, semantic-segmentation, scene-graph, vision-language, calibration]
papers: ["2012.07177", "2011.12954", "2104.01111", "2012.08548", "2203.14197", "2102.08981", "2103.16370", "2003.12962"]
related: [data-augmentation, instance-segmentation, semantic-segmentation, object-detection, class-balanced-loss, calibration, scene-graph-generation, focal-loss, vision-language-pretraining, image-captioning, dataset-curation]
status: draft
updated_at: 2026-11-01
---

## Overview

Many real datasets are long-tailed: a few classes have many training instances
and many classes have only a handful. Plain training then favours the frequent
classes. On LVIS, single-stage Eff-B7 FPN (640) reaches 9.7 AP_r on rare classes
against 35.1 AP_f on frequent ones [arxiv:2012.07177 tab. 8]. Detection and
segmentation results are reported per group as AP_r, AP_c and AP_f. Classifiers
are reported per split as Many, Medium and Few accuracy [arxiv:2203.14197 tab. 1].

Eight cards cover eight settings. On LVIS instance segmentation, the rare-class
gains come from a second training stage and from Copy-Paste augmentation
[arxiv:2012.07177 §4.7] [arxiv:2012.07177 §3]. On LVIS detection with a sigmoid
classifier, the EQL v2 authors reweight the classification loss inside a single
end-to-end stage [arxiv:2012.08548 §3.2]. On image classification, weight
balancing retrains only the last layer after a normal training stage
[arxiv:2203.14197 §3.3]. Distribution Alignment instead learns a per-class
scale and offset on the frozen classifier scores, which lifts ResNet-50
ImageNet-LT accuracy from 41.6% to 51.3% [arxiv:2103.16370 tab. 1]. On
off-road LiDAR and image segmentation, the authors
attribute weak results mainly to class imbalance and unclear boundaries
[arxiv:2011.12954 §V-B], and for the point-cloud model they report a
label-distribution sampling gain [arxiv:2011.12954 §V-C]. The scene graph
survey notes that frequent predicates dominate plain recall, and recommends mean
recall per predicate [arxiv:2104.01111 §6.2]. GPS-Net instead softens a
predicate frequency prior and gates it per pair, and reweights a focal-style
loss by each object's share of triplets [arxiv:2003.12962 §3.2] [arxiv:2003.12962 §3.3].
In web image-caption pre-training, a looser filter
keeps more rare words, and the authors report the gain after fine-tuning
[arxiv:2102.08981 §1] [arxiv:2102.08981 tab. 3].

Measure the rare-class number next to the overall one. Scene graph recall can
look high while mean recall is low [arxiv:2104.01111 §6.2]. Each paper uses its
own benchmark and backbone. EQL v2 reports LVIS v1.0 with Mask R-CNN R-50 at 1x
[arxiv:2012.08548 tab. 1], and Copy-Paste reports LVIS v1.0 with Eff-B7 FPN at
640 [arxiv:2012.07177 tab. 8]. Compare numbers only within one paper's table.
In the EQL v2 card, rows marked as copied are taken from other papers
[arxiv:2012.08548 tab. 4]. The RELLIS-3D authors' imbalance explanation is not
tested by an ablation [arxiv:2011.12954 §V-B].

## Variants

### Two-stage classifier retraining with class-balanced loss

Stage 1 trains the ordinary single-stage model. Stage 2 fine-tunes only the
final classification layer of Mask R-CNN, using the classification loss alone
and a 3x schedule [arxiv:2012.07177 §4.7]. Each class gets a weight from its
instance count $n_c$ [arxiv:2012.07177 §4.7, footnote]:

$$ w_c = \frac{1-\beta}{1-\beta^{n_c}}, \quad \beta = 0.999 $$

The weights are divided by their mean and clipped to $[0.01, 5]$
[arxiv:2012.07177 §4.7, footnote]. On Eff-B7 FPN (640), the two-stage model
reaches 25.0 AP_r, against 9.7 for the single-stage baseline [arxiv:2012.07177
tab. 8] [arxiv:2012.07177 tab. 9]. Card: [Simple Copy-Paste](/papers/2012.07177).

### Repeat Factor Sampling

The paper uses Repeat Factor Sampling (RFS), with threshold $t = 0.001$, as a
second rare-class method [arxiv:2012.07177 §4.7]. In the single-stage setting
it lifts AP_r from 9.7 to 15.4 [arxiv:2012.07177 tab. 8]. In the two-stage
setting it lowers AP_r from 25.0 to 21.8 [arxiv:2012.07177 tab. 9]. The card
does not describe the sampling mechanism, so read the paper's §4.7 before
implementing it. Card: [Simple Copy-Paste](/papers/2012.07177).

### Copy-Paste augmentation

Copy-Paste builds each training example from two images, pastes a random subset
of instance masks from one onto the other, and updates the occluded masks and
boxes [arxiv:2012.07177 §3]. It needs instance masks, not only boxes
[arxiv:2012.07177 §3]. The paper presents it as general augmentation for
instance segmentation; the rare-class gain is a measured result, not the stated
goal [arxiv:2012.07177 §1]. On LVIS it raises AP_r for every two-stage model in
the paper's comparison, by +2.7 to +6.1 [arxiv:2012.07177 tab. 7]. On Eff-B7 FPN
(640) it raises AP_r from 9.7 to 12.8 single-stage [arxiv:2012.07177 tab. 8]
and from 25.0 to 27.3 two-stage [arxiv:2012.07177 tab. 9]. Card: [Simple
Copy-Paste](/papers/2012.07177).

### Equalization loss v2 in end-to-end detection

EQL v2 changes the classification loss of a sigmoid detector and does not
resample the data. Each class keeps a running ratio of accumulated positive to
negative gradient magnitude. A sigmoid of that ratio sets the weight of
negatives, and positives get a larger weight as negatives are suppressed
[arxiv:2012.08548 §3.2] [arxiv:2012.08548 eq. 5] [arxiv:2012.08548 eq. 6]. The
paper sets α = 4, γ = 12 and μ = 0.8 [arxiv:2012.08548 §4.2]. Training is
end-to-end with a random sampler and no second stage [arxiv:2012.08548 tab. 1].
On LVIS v1.0 with Mask R-CNN R-50 at 1x, the reported figures are 23.7 AP and
14.9 AP_r. The same table gives 18.6 and 2.1 for EQL, and 16.1 and 0.0 for
softmax [arxiv:2012.08548 tab. 1]. The best decoupled row, BAGS with 12 plus 12
epochs, reaches 23.1 AP and 13.1 AP_r [arxiv:2012.08548 tab. 1]. The ablation
adds the parts one at a time: an extra category-agnostic objectness output gives
18.1 AP, the negative term 19.7 and the positive term 23.7 [arxiv:2012.08548
tab. 2]. The paper reports a 2C-softmax classifier as comparable, at 23.7 AP and
14.9 AP_r [arxiv:2012.08548 tab. 9]. On Open Images with a ResNet-50 detector,
the LVIS hyperparameters give 52.6 mAP@0.5 against 43.1 for Faster R-CNN
[arxiv:2012.08548 tab. 10]. Card: [Equalization Loss v2](/papers/2012.08548).

### Weight balancing in image classification

Weight balancing changes no loss in the feature stage. Stage 1 trains the
backbone with cross-entropy and tuned weight decay. Stage 2 freezes the
features and retrains the classifier with a class-balanced loss, weight decay
and MaxNorm [arxiv:2203.14197 §3.3]. The paper tunes the stage-2 weight decay
and the MaxNorm threshold with Bayesian optimisation [arxiv:2203.14197 §3.3]. On
CIFAR100-LT with imbalance factor 100, the ablation gives 38.38% for plain
cross-entropy, 46.08% for tuned weight decay alone and 53.35% for the full
recipe [arxiv:2203.14197 tab. 1]. On ImageNet-LT and iNaturalist2018, the same
recipe reaches 53.9% and 70.2% all-class accuracy, against 38.0% and 46.1% for
the naive baseline [arxiv:2203.14197 tab. 3]. Post-hoc L2 normalisation helped
on CIFAR100-LT, from 46.08% to 49.60% with weight decay [arxiv:2203.14197
tab. 1]. On iNaturalist it dropped to 51.3% from 65.4% with weight decay
[arxiv:2203.14197 tab. 3]. Card: [Long-Tailed Recognition via Weight
Balancing](/papers/2203.14197).

### Distribution alignment of a frozen classifier

Stage 1 trains the backbone and the original classifier head on the
imbalanced data. Stage 2 freezes both and trains only a few new parameters
[arxiv:2103.16370 §3.2] [app. A.2]. Each class gets a learned scale alpha and
offset beta on its original score. A per-example confidence, a learned layer
followed by a non-linearity (a sigmoid in the paper's example), blends the
transformed score with the original one [arxiv:2103.16370 §3.2.1] [eq. 4]
[eq. 5]. Stage 2 minimises a cross-entropy whose class weights are inverse
frequency raised to a power rho. Rho = 0 gives instance balance and rho = 1
gives class balance [arxiv:2103.16370 §3.2.2] [eq. 11]. On ImageNet-LT with
ResNet-50, the paper reports 51.3% top-1 average with a dot-product head and
52.9% with a cosine head, against 41.6% for the joint baseline [arxiv:2103.16370
tab. 1]. Its ablation gives 50.1 with the re-weighting and a learned scale, 49.9
with the re-weighting and a learned offset, and 51.3 with both [arxiv:2103.16370
tab. 5]. The same formula is applied per pixel for ADE20K and per box for LVIS
[arxiv:2103.16370 §3.1] [app. C.2]. Card: [Distribution
Alignment](/papers/2103.16370).

### Label-distribution sampling in 3D segmentation

On RELLIS-3D, the KPConv point-cloud model uses label-distribution sampling. The
authors report that it adds 0.6 mIoU [arxiv:2011.12954 §V-C]. The paper's
description is brief, and the card does not verify the implementation. Card:
[RELLIS-3D Dataset](/papers/2011.12954). The same card's per-class table
lists 0.00 IoU for KPConv on mud, puddle and rubble [arxiv:2011.12954 tab. 2].

### Rare predicates in scene graph generation

The survey groups the approaches to long-tailed predicates into zero-, one- and
few-shot learning, causal debiasing, and an energy-based loss over joint object
and relation likelihood [arxiv:2104.01111 §4]. It also names language, statistical
and knowledge-graph priors, which it suggests help rare relations most
[arxiv:2104.01111 §3]. Mean recall per predicate, mR@100 under the PredCls
setting, is 8.0 for IMP, 22.0 for ResCAGCN with PUM and 29.97 for VCTree-TDE
with the energy-based loss [arxiv:2104.01111 tab. 2]. These values come from
different papers and were not re-run by the survey, so they are not a controlled
ranking. The survey says the energy-based loss gives the best mR@K among the
methods it investigated [arxiv:2104.01111 §6.2]. Card: [A Comprehensive Survey
of Scene Graphs](/papers/2104.01111).

### Gated frequency prior and node-priority loss in one-stage scene graphs

GPS-Net keeps a one-stage Faster R-CNN based generator and adds two
long-tail parts. The first is a predicate prior: the frequency of each
subject-object class pair, softened by a log-softmax [arxiv:2003.12962 eq. 9].
A sigmoid gate computed from each pair's union feature rescales the prior
before it is added to the classifier logits [arxiv:2003.12962 §3.3]
[arxiv:2003.12962 eq. 10]. The second is a node-priority loss. Each object's
priority is its share of ground-truth triplets. That share sets a focusing
parameter, capped at 2, in a focal-style term [arxiv:2003.12962 §3.2]
[arxiv:2003.12962 eq. 6-8]. The paper's best exponent is mu = 4
[arxiv:2003.12962 §4.4]. On Visual Genome, the card's mR@100 table gives
22.8 for GPS-Net under PredCls, against 19.4 for VCTree-HL and 15.3 for
MOTIFS. All three rows use the Neural Motifs detector and metric
[arxiv:2003.12962 tab. 2]. The ablation adds recall gains for each part on its
own: the adaptive reasoning module alone reaches 68.5 PredCls R@100 against 67.3 for the
baseline, and the node-priority loss alone 67.7 [arxiv:2003.12962 tab. 5].
Recall is not mean recall, so these two results are not directly comparable.
Card: [GPS-Net: Graph Property Sensing Network for Scene Graph
Generation](/papers/2003.12962).

### Rare-concept coverage in web pre-training data

This variant changes the data, not the training loss. CC12M keeps about four
times as many image-caption pairs as CC3M by relaxing the CC3M filters. The
authors argue that the strict filters drop long-tail concepts [arxiv:2102.08981
§1] [arxiv:2102.08981 §2.2]. Rare words occur more often: "mangosteen" goes
from 0 to 212 occurrences and "quiche" from 50 to 1109, counted in CC3M and
then CC12M [arxiv:2102.08981 §2.3]. The captions are less precise, at 76.6%
against 90.3% for CC3M on a 100-example check by two annotators
[arxiv:2102.08981 §2.3]. A captioner pre-trained on CC12M and fine-tuned on COCO
reaches 87.4 overall CIDEr on nocaps val, against 54.7 with no pre-training
[arxiv:2102.08981 tab. 3]. Its out-of-domain CIDEr is 91.3, against 65.3 for
CC3M with fine-tuning [arxiv:2102.08981 tab. 3]. Without fine-tuning, CC12M is
weaker than CC3M overall on nocaps, 27.1 against 29.7, but it leads on
out-of-domain objects, 41.6 against 37.3 [arxiv:2102.08981 tab. 3]. Card:
[Conceptual 12M](/papers/2102.08981).

## When to use which

| Situation | Use | Why |
|---|---|---|
| Instance masks, two-stage pipeline, rare-class AP is the target | Two-stage classifier retraining with class-balanced loss, plus Copy-Paste | 27.3 AP_r with Copy-Paste is the highest rare-class value among the Eff-B7 FPN (640) rows of [arxiv:2012.07177 tab. 8] and [arxiv:2012.07177 tab. 9]. RFS lowered AP_r in this setting [arxiv:2012.07177 tab. 9] |
| Single-stage training only | Copy-Paste, plus RFS | RFS with Copy-Paste reaches 18.4 AP_r against 12.8 for Copy-Paste alone [arxiv:2012.07177 tab. 8] |
| Two-stage recipe | Do not add RFS on top | RFS lowered AP_r from 25.0 to 21.8 [arxiv:2012.07177 tab. 9] |
| Detector with sigmoid classifiers, one training run, no second stage | EQL v2 | 23.7 AP and 14.9 AP_r with 12 epochs, against 23.1 AP for the best decoupled row [arxiv:2012.08548 tab. 1]. The method assumes a sigmoid classifier per category and a Mask R-CNN style detector [arxiv:2012.08548 §4.2] |
| Detector with a softmax head | Not the described method | The paper's 2C-softmax variant is reported as comparable [arxiv:2012.08548 tab. 9] |
| Classification with a trained backbone, rare classes matter | Weight balancing | 53.35% against 38.38% for plain cross-entropy on CIFAR100-LT with imbalance factor 100 [arxiv:2203.14197 tab. 1]. Needs a stage-1 model, since stage 2 retrains only the classifier [arxiv:2203.14197 §3.3] |
| Classification, large datasets, and an ensemble or self-supervised model is affordable | Weight balancing is the single-model option | The paper's ImageNet-LT table lists RIDE at 56.1 and SSD at 56.0, above 53.9 for weight balancing [arxiv:2203.14197 tab. 3]. The paper says these methods trail the ensemble and self-supervised ones on large datasets [arxiv:2203.14197 §4.3] |
| Classification, post-hoc L2 normalisation as the only extra step | Check per dataset | It helped on CIFAR100-LT, but dropped iNaturalist accuracy from 65.4% to 51.3% with weight decay [arxiv:2203.14197 tab. 3] |
| Classification with a trained backbone, a few extra parameters, and per-class control of rare-class scores | Distribution alignment, dot-product head with rho 1.2 | 51.3% against 41.6% for the joint baseline on ImageNet-LT with ResNet-50 [arxiv:2103.16370 tab. 1]. Adds two parameters per class and a confidence layer [arxiv:2103.16370 eq. 4]. The paper says it has fewer free parameters than cRT but gives no count [arxiv:2103.16370 §3.2.1] |
| Classification, reproduction from released code | Check first | The release has only the dot-product ImageNet-LT config. The cosine config (rho 1.5) is absent [code: classification/imagenetlt/resnext50/] [arxiv:2103.16370 Paper vs code] |
| Detection or segmentation with rare classes, resampling hard to apply | Distribution alignment, with the paper's rho (0.3 for ADE20K, 0.8 for LVIS) | ADE20K FCN ResNet-50 mIoU 38.1 to 40.1 [arxiv:2103.16370 tab. 6]. LVIS v0.5 Mask R-CNN ResNet-50 box AP 20.8 to 23.9 with ImageNet pre-training [arxiv:2103.16370 tab. 8]. The release uses different values in places; see Contradictions |
| Only bounding boxes, no masks | Not covered by these cards | Copy-Paste needs masks to cut out objects and update occlusions [arxiv:2012.07177 §3] |
| Off-road or LiDAR semantic segmentation with rare classes | Label-distribution sampling for the point-cloud model | Reported gain of 0.6 mIoU [arxiv:2011.12954 §V-C]. Imbalance is the authors' stated cause, not an isolated result [arxiv:2011.12954 §V-B] |
| Scene graph generation, rare predicates matter | Energy-based loss, if the survey's table is the guide | Best mR@K among the methods the survey investigated [arxiv:2104.01111 §6.2]. Compare only within one graph constraint and protocol [arxiv:2104.01111 §6.2] |
| One-stage scene graph generator with a frequency prior, recall per predicate matters, and you can rebuild the released detector | GPS-Net's gated prior and node-priority loss | 22.8 mR@100 under PredCls against 19.4 for VCTree-HL, in the card's table [arxiv:2003.12962 tab. 2]. The gate is not in the released detector, which adds the prior without it [code: gpsnet-detectron/lib/modeling_rel/model_builder_rel_gpsnet.py#L563-L570]. The loss file in `lib/` does not run as shipped [code: lib/nps_loss.py#L1-L2] |
| Captioning or vision-language pre-training, rare object names matter, and a fine-tuning stage is affordable | Relaxed-filter web data (CC12M) | Out-of-domain CIDEr 91.3 against 65.3 for CC3M after fine-tuning [arxiv:2102.08981 tab. 3]. Zero-shot, CC12M is weaker overall than CC3M [arxiv:2102.08981 tab. 3]. The pairs were extracted in May 2020, so a present-day download is a different set [arxiv:2102.08981 §2.3] |
| Scarce labelled data in general, not a long tail | Copy-Paste | With 10% of COCO, Copy-Paste adds 6.9 box AP over SSJ [arxiv:2012.07177 §4.3]. This is data efficiency, not a long-tail result |

The gain from Copy-Paste on AP_r is smaller with the two-stage recipe (+2.3)
than with the single-stage one (+3.1) on Eff-B7 FPN (640) [arxiv:2012.07177
tab. 8] [arxiv:2012.07177 tab. 9].

## Implementation sketch

Five recipes, one block each, since they share no common core. Shapes and
units are noted at the end of each line.

The two-stage LVIS recipe from the paper, with Copy-Paste as an optional
augmentation in stage 1. RFS is not part of this recipe.

```pseudocode
# Stage 1: train the single-stage model, Copy-Paste optional,
# 180k steps at batch 256 [arxiv:2012.07177 §4.7]
model = train_maskrcnn(lvis_train, augment=copy_paste)

# Stage 2: freeze everything except the final classifier layer
# [arxiv:2012.07177 §4.7]
freeze_all_except(model.classifier)

# Class-balanced weight per class from its instance count n_c,
# beta = 0.999; divide by mean, clip to [0.01, 5]
# [arxiv:2012.07177 §4.7, footnote]
beta = 0.999
w = (1 - beta) / (1 - beta ** n)  # n: [num_classes]
w = clip(w / w.mean(), 0.01, 5)

# Classification loss only, weighted by w, 3x schedule
# [arxiv:2012.07177 §4.7]
train(model, loss=weighted_cls_loss(w), schedule="3x")
```

The EQL v2 loss for one batch of RoIs. The per-class accumulators run over all
iterations and are never reset [arxiv:2012.08548 eq. 9].

```pseudocode
# EQL v2 loss for one batch with a sigmoid head [arxiv:2012.08548 §3.2]
# State per class j: pos_sum[j], neg_sum[j], accumulated over iterations
def eql_v2_loss(logits, labels):
    # One-hot over C classes plus background; background is not reweighted
    # [arxiv:2012.08548 §4.2]
    y = one_hot(labels, C + 1)                     # (n, C + 1)
    # Ratio of accumulated positive to negative magnitude
    # [arxiv:2012.08548 eq. 9]
    g = pos_sum / (neg_sum + 1e-10)                # (C,)
    # Negative weight r = sigmoid(gamma * (g - mu)) [arxiv:2012.08548 eq. 6]
    r = concat(sigmoid(gamma * (g - mu)), ones(1)) # (C + 1,)
    # Positive weight q = 1 + alpha * (1 - r) [arxiv:2012.08548 eq. 5]
    q = 1 + alpha * (1 - r)                        # (C + 1,)
    w = q * y + r * (1 - y)                        # (n, C + 1)
    loss = sum(bce_with_logits(logits, y) * w) / n
    # Add reweighted gradient magnitudes to the accumulators
    # [arxiv:2012.08548 eq. 7] [arxiv:2012.08548 eq. 8]
    grad = abs(sigmoid(logits) - y) * w
    pos_sum += sum(grad * y, axis=0)[:C]
    neg_sum += sum(grad * (1 - y), axis=0)[:C]
    return loss
```

Stage 2 of weight balancing, as the paper describes it. The paper applies
MaxNorm after each batch update; the release differs (see Contradictions).

```pseudocode
# Stage 2: retrain the classifier on frozen features  [arxiv:2203.14197 §3.3]
# Input: stage-1 backbone, class counts n_c, weight decay lam, radius delta
def retrain_classifier(backbone, fc, train_set, n_c, lam, delta):
    # Class-balanced weights; beta is not stated in the paper
    # [arxiv:2203.14197 §3.3]
    w = class_balanced_weights(n_c, beta)          # (K,)
    # Weight decay on the classifier [arxiv:2203.14197 §3.1]
    opt = sgd(fc.parameters(), weight_decay=lam)
    for images, labels in train_set:
        with no_grad():
            feats = backbone(images)               # frozen features
        loss = class_balanced_loss(fc(feats), labels, w)
        opt.zero_grad(); loss.backward(); opt.step()
        # MaxNorm: rescale any class row whose norm exceeds delta
        # [arxiv:2203.14197 eq. 4] [arxiv:2203.14197 eq. 5]
        fc.weight.data = project_rows(fc.weight.data, delta)
    return fc
```

Distribution alignment, stage 2, as the paper's equations describe it. The
initial values of alpha and beta are from the appendix.

```pseudocode
# Stage 2: calibrate frozen scores  [arxiv:2103.16370 §3.2.1] [eq. 4-5]
# Input:  features x (B, d), scores z (B, K) from the frozen head
# Learned: alpha (K,) = 1, beta (K,) = 0 [app. A.2], confidence layer g
def calibrated_scores(x, z, alpha, beta, g):
    # Per-class scale and offset on the original score  [eq. 4]
    s = alpha * z + beta                              # (B, K)
    # Per-example confidence in (0, 1) [§3.2.1]
    sigma = sigmoid(g(x))                             # (B, 1)
    # Blend the transformed and the original score  [eq. 5]
    return sigma * s + (1 - sigma) * z                # (B, K)

# Class weights: inverse frequency to the power rho, summing to one
# [arxiv:2103.16370 eq. 11]
w = (1.0 / n) ** rho                                  # n: (K,) class counts
w = w / w.sum()                                       # (K,)

# Loss: weighted negative log-likelihood, batch mean  [eq. 9]
def alignment_loss(z_hat, y):
    logp = log_softmax(z_hat)                         # (B, K)
    return mean(-w[y] * logp[arange(len(y)), y])      # scalar
```

Node-priority focal term of GPS-Net, as the paper's equations describe it.
The paper does not say whether the focusing weight gets a gradient; the
released detector detaches it [code: gpsnet-detectron/lib/modeling_rel/refine_obj_feats.py#L41].

```pseudocode
# Node-priority focal term  [arxiv:2003.12962 §3.2] [eq. 6-8]
# Input: logits (N, O), gt_classes (N,), t (N,) triplets per node
def nps_loss(logits, gt_classes, t, total, mu=4):
    # Priority: share of ground-truth triplets with this node  [eq. 6]
    theta = t / total                                     # (N,)
    # Focusing parameter, capped at 2  [eq. 7]
    gamma = minimum(2, -((1 - theta) ** mu) * log(theta)) # (N,)
    p = softmax(logits)[arange(N), gt_classes]            # (N,)
    # Focal-style term  [eq. 8]; the reduction is not stated
    return mean(-((1 - p) ** gamma) * log(p))             # scalar
```

## Contradictions

- **Repeat Factor Sampling.** It raises single-stage AP_r by +5.7 (9.7 to 15.4)
  [arxiv:2012.07177 tab. 8] and lowers two-stage AP_r by 3.2 (25.0 to 21.8)
  [arxiv:2012.07177 tab. 9]. The paper states that RFS helps single-stage and
  hurts two-stage training [arxiv:2012.07177 §4.7]. The card gives no reason
  for the reversal.
- **Headline gains differ by setting, not by result.** The "+6.1 mask AP_r"
  headline is a two-stage model [arxiv:2012.07177 tab. 7]. Single-stage RFS
  with Copy-Paste gives +8.7 AP_r over the baseline [arxiv:2012.07177 tab. 8].
  Compare numbers only within the same training recipe.
- **EQL v2 headline gain.** The paper's abstract says "about 4 points" over EQL
  overall. Its Table 1 and §4.4 give +5.1 AP [arxiv:2012.08548 tab. 1]
  [arxiv:2012.08548 §4.4]. The card notes the abstract's rare-class figure is
  measured against softmax, not EQL.
- **Weight balancing, paper against release.** The paper reports 46.08% for
  weight decay alone and 53.35% for the full recipe [arxiv:2203.14197 tab. 1].
  The released logs record 47.18% for weight decay alone [code:
  exp/demo_1/with_WD_model_note_bestModel.log]. For the full recipe they record
  51.98% best-epoch accuracy [code: exp/demo_2/MaxNorm_WD_note_bestModel.log]
  and 51.83% at the final epoch [code: exp/demo_2/MaxNorm_WD_train.log]. The
  release selects the best epoch on the
  test loader [code: utils/trainval.py#L152], while the paper tunes on a
  validation set [arxiv:2203.14197 §4.1].
- **Weight balancing, paper against paper.** Table 2 gives 38.32% for
  cross-entropy on CIFAR100-LT with imbalance factor 100 [arxiv:2203.14197
  tab. 2], and Table 1 gives 38.38% for the same setting [arxiv:2203.14197
  tab. 1]. Its "+" labels mean different things in different places: "+ L2norm"
  and "+ τ-norm" in Table 2 match the post-hoc numbers in Table 1, which use no
  class-balanced loss [arxiv:2203.14197 tab. 2] [arxiv:2203.14197 tab. 1].
- **Weight balancing, MaxNorm details.** The paper applies MaxNorm after each
  batch [arxiv:2203.14197 §3.1]. The release applies it once per epoch
  [code: utils/trainval.py#L140-L142] and sets the radius from the initial row
  norms [code: utils/regularizers.py#L27]. The paper does not state δ.
- **DisAlign, paper against its release.** The paper states rho 0.3 for
  segmentation [arxiv:2103.16370 app. B.2]; the ADE20K config uses 0.2
  [code: semantic_seg/configs/ade20k_fcn_disalign/disalign_fcn_r50-d8_512x512_160k_ade20k.py#L22-L23].
  Stage 2 is 8k iterations in the paper [app. B.2] and 4000 in the config
  [code: semantic_seg/configs/ade20k_fcn_disalign/disalign_fcn_r50-d8_512x512_160k_ade20k.py#L12].
  For LVIS, the paper gives 9k iterations at LR 0.02 [app. C.2]; the config
  runs 4500 with the LR step at 4000 [code: instance_seg/lvis0.5/mask_rcnn/res50/mask_rcnn.res50.fpn.lvis.multiscale.cos_norm.disalign.1x/config.py#L31-L32].
- **DisAlign, loss scale and weights.** The paper's weights sum to one and
  its loss is a batch mean [arxiv:2103.16370 eq. 9] [eq. 11]. The LVIS code
  rescales the foreground weights to sum to the number of foreground classes
  [code: instance_seg/lvis0.5/mask_rcnn/res50/mask_rcnn.res50.fpn.lvis.multiscale.cos_norm.disalign.1x/roi_heads/fast_rcnn.py#L51-L58]
  and takes a weighted mean [code: instance_seg/lvis0.5/mask_rcnn/res50/mask_rcnn.res50.fpn.lvis.multiscale.cos_norm.disalign.1x/roi_heads/fast_rcnn.py#L73-L76].
  The segmentation weights are rescaled the same way [code: semantic_seg/disalign/models/losses/grw_cross_entropy_loss.py#L34-L35].
  The step size changes with the reduction, so copy the code's choice or
  retune the learning rate.
- **DisAlign, ImageNet-LT baselines.** The paper gives 52.6 for the
  ResNeXt-50 DisAlign row and 44.4 for its baseline [arxiv:2103.16370 tab. 1].
  The repository README lists 52.438 and 46.918 for the same rows
  [code: classification/README.md]. The repository does not say how its
  baseline was trained.
- **DisAlign, ResNet-152 ablation.** The text gives 54.9 for ResNet-152
  [arxiv:2103.16370 §4.1]. The appendix table gives 54.8 for the cosine variant
  and 53.7 for the dot-product variant [arxiv:2103.16370 app. A].
- **GPS-Net, paper against code.** The paper's best exponent is mu = 4
  [arxiv:2003.12962 §4.4]; both code paths use 5 [code: lib/nps_loss.py#L23]
  [code: gpsnet-detectron/lib/modeling_rel/model_builder_rel_gpsnet.py#L93].
  The paper priority is the triplet share [arxiv:2003.12962 eq. 6]. The `lib/`
  loss counts distinct related neighbours and uses 2θ [code:
  lib/nps_loss.py#L9-L23], and the detector counts proposal overlaps
  [code: gpsnet-detectron/lib/modeling_rel/model_builder_rel_gpsnet.py#L87-L93].
  The gated prior of eq. 10 is not in the detector [code:
  gpsnet-detectron/lib/modeling_rel/model_builder_rel_gpsnet.py#L563-L570]. The
  ablation numbers in the card therefore do not test the paper's definitions.
- **Scene graph mean recall, GPS-Net against the survey.** The survey lists
  29.97 mR@100 under PredCls for VCTree-TDE [arxiv:2104.01111 tab. 2]. GPS-Net's
  table lists 19.4 for VCTree-HL and 22.8 for GPS-Net under the Neural Motifs
  protocol [arxiv:2003.12962 tab. 2]. These come from different papers and
  protocols, so they are not a ranking.
- **Cross-card comparisons.** EQL v2 reports LVIS v1.0 with Mask R-CNN R-50 at
  1x [arxiv:2012.08548 tab. 1] and LVIS v0.5 with several detectors
  [arxiv:2012.08548 tab. 4]. The Copy-Paste card reports LVIS v1.0 with Eff-B7
  FPN at 640 [arxiv:2012.07177 tab. 8]. Their AP_r values are not a ranking.

## Papers

- [Simple Copy-Paste](/papers/2012.07177): Copy-Paste augmentation, the LVIS
  two-stage class-balanced recipe, Repeat Factor Sampling and the rare-class
  results.
- [Equalization Loss v2](/papers/2012.08548): a per-class gradient-ratio
  reweighting of a sigmoid detector's classification loss, trained end-to-end on
  LVIS and Open Images.
- [Long-Tailed Recognition via Weight Balancing](/papers/2203.14197): a two-stage
  classifier recipe with weight decay, MaxNorm and class-balanced loss, on
  CIFAR100-LT, ImageNet-LT and iNaturalist2018.
- [RELLIS-3D Dataset](/papers/2011.12954): an off-road segmentation benchmark
  whose authors attribute weak rare-class results to imbalance, with a reported
  label-distribution sampling gain for the point-cloud model.
- [A Comprehensive Survey of Scene Graphs](/papers/2104.01111): a survey of
  rare-predicate methods for scene graphs, and of mean recall as the metric.
- [Conceptual 12M](/papers/2102.08981): relaxed-filter web image-caption data
  with more rare words, and its nocaps results after fine-tuning.
- [Distribution Alignment](/papers/2103.16370): a two-stage recalibration of a
  frozen classifier with per-class scale and offset and a per-example gate,
  with results on classification, segmentation and LVIS.
- [GPS-Net: Graph Property Sensing Network for Scene Graph Generation](/papers/2003.12962):
  a one-stage scene graph generator with a gated predicate frequency prior and
  a node-priority focal loss, with mean recall per predicate on Visual Genome.