Image Retrieval & Metric Learning

Learning Objectives

• Explain triplet, contrastive, and proxy-based metric learning losses and pick the right one for a given dataset
• Implement L2-normalisation and cosine similarity correctly and audit the difference between "same item" and "same class" retrieval
• Build a FAISS index, query it by text and by image, and report recall@K for a held-out query set
• Use DINOv2, CLIP, and SigLIP as off-the-shelf embedding backbones and know when each wins

The Problem

Retrieval is everywhere in production vision: duplicate detection, reverse image search, visual search ("find similar products"), face re-identification, person re-ID for surveillance, instance-level matching for e-commerce. The product question is always the same: "given this query image, rank my catalogue."

Two design decisions shape the whole system. The embedding — what model produces the vectors. The index — how to find nearest neighbours at scale. Both are commodity in 2026 (DINOv2 for the embedding, FAISS for the index), which raises the bar: the hard part is defining what counts as similar for your application, then shaping the embedding space so the distances match.

That shaping is metric learning. It is a small but high-leverage discipline.

The Concept

Retrieval at a glance

The four loss families

For most production use cases, start with a pretrained backbone and only add a metric-learning fine-tune if the off-the-shelf embeddings underperform on your test set.

Triplet loss formally

L = \max\left(0, \lVert f(a) - f(p) \rVert^2 - \lVert f(a) - f(n) \rVert^2 + \text{margin}\right)

Pull anchor a close to positive p, push it away from negative n, with a margin that ensures a gap. The three-image structure generalises to any similarity ordering.

Mining matters: easy triplets (n already far from a) contribute zero loss; only hard triplets teach the network. Semi-hard mining (n further than p but within margin) is the 2016 FaceNet recipe and still dominates.

Cosine similarity vs L2

Two metrics, two conventions:

• Cosine: angle between vectors. Requires L2-normalised embeddings.
• L2: Euclidean distance. Works on raw or normalised embeddings, but is usually paired with L2-normalised + squared L2.

For most modern nets the two are equivalent: ||a - b||^2 = 2 - 2 cos(a, b) when ||a|| = ||b|| = 1. Pick the convention that matches your embedding training; mixing them silently changes what "nearest" means.

Recall@K

The standard retrieval metric:

recall@K = fraction of queries where at least one correct match is in the top K results

Report recall@1, @5, @10 side by side. A recall@10 above 0.95 with recall@1 below 0.5 means the embedding space has the right structure but the ranking is noisy — try longer fine-tunes or a re-ranking step.

For duplicate detection, precision@K matters more because every false positive is a user-visible mistake. For visual search, recall@K is the product signal.

FAISS in one paragraph

Facebook AI Similarity Search. The de-facto library for nearest-neighbour search. Three index choices:

• IndexFlatIP / IndexFlatL2 — brute force, exact, no training. Use up to ~1M vectors.
• IndexIVFFlat — partition into K cells, search only the closest few cells. Approximate, fast, needs training data.
• IndexHNSW — graph-based, fastest for many queries, large index size.

For 100k vectors you probably want IndexFlatIP on cosine similarity. For 10M you want IndexIVFFlat. For 100M+ combined with product quantisation (IndexIVFPQ).

Instance-level vs category-level retrieval

Two very different problems with the same name:

• Category-level — "find cats in my catalogue." Class-conditional similarity; off-the-shelf CLIP / DINOv2 embeddings work well.
• Instance-level — "find this exact product in my catalogue." Needs fine-grained discrimination between visually similar objects of the same class; off-the-shelf embeddings under-perform; fine-tuning with metric learning matters.

Always ask which one you are solving before picking a model.

metric-embedding

Build It

Step 1: Triplet loss

import torch
import torch.nn.functional as F

def triplet_loss(anchor, positive, negative, margin=0.2):
    d_ap = F.pairwise_distance(anchor, positive, p=2)
    d_an = F.pairwise_distance(anchor, negative, p=2)
    return F.relu(d_ap - d_an + margin).mean()

One line. Works on L2-normalised or raw embeddings.

Step 2: Semi-hard mining

Given a batch of embeddings and labels, find the hardest semi-hard negative for each anchor.

def semi_hard_negatives(emb, labels, margin=0.2):
    dist = torch.cdist(emb, emb)
    same_class = labels[:, None] == labels[None, :]
    diff_class = ~same_class
    N = emb.size(0)

    positives = dist.clone()
    positives[~same_class] = float("-inf")
    positives.fill_diagonal_(float("-inf"))
    pos_idx = positives.argmax(dim=1)

    semi_hard = dist.clone()
    semi_hard[same_class] = float("inf")
    d_ap = dist[torch.arange(N), pos_idx].unsqueeze(1)
    semi_hard[dist <= d_ap] = float("inf")
    neg_idx = semi_hard.argmin(dim=1)

    fallback_mask = semi_hard[torch.arange(N), neg_idx] == float("inf")
    if fallback_mask.any():
        hardest = dist.clone()
        hardest[same_class] = float("inf")
        neg_idx = torch.where(fallback_mask, hardest.argmin(dim=1), neg_idx)
    return pos_idx, neg_idx

Each anchor gets the hardest positive in-class and a semi-hard negative that is further than the positive but within margin.

Step 3: Recall@K

def recall_at_k(query_emb, gallery_emb, query_labels, gallery_labels, k=1):
    sim = query_emb @ gallery_emb.T
    _, top_k = sim.topk(k, dim=-1)
    matches = (gallery_labels[top_k] == query_labels[:, None]).any(dim=-1)
    return matches.float().mean().item()

Top-k by inner product on L2-normalised embeddings equals top-k by cosine. Report the mean proportion of queries with at least one correct neighbour.

Step 4: Putting it together

import torch
import torch.nn as nn
from torch.optim import Adam

class Encoder(nn.Module):
    def __init__(self, in_dim=128, emb_dim=64):
        super().__init__()
        self.net = nn.Sequential(
            nn.Linear(in_dim, 128), nn.ReLU(),
            nn.Linear(128, emb_dim),
        )

    def forward(self, x):
        return F.normalize(self.net(x), dim=-1)

torch.manual_seed(0)
num_classes = 6
protos = F.normalize(torch.randn(num_classes, 128), dim=-1)

def sample_batch(bs=32):
    labels = torch.randint(0, num_classes, (bs,))
    x = protos[labels] + 0.15 * torch.randn(bs, 128)
    return x, labels

enc = Encoder()
opt = Adam(enc.parameters(), lr=3e-3)

for step in range(200):
    x, y = sample_batch(32)
    emb = enc(x)
    pos_idx, neg_idx = semi_hard_negatives(emb, y)
    loss = triplet_loss(emb, emb[pos_idx], emb[neg_idx])
    opt.zero_grad(); loss.backward(); opt.step()

After a few hundred steps the embedding clusters form one cluster per class.

Use It

Production stacks in 2026:

• DINOv2 + FAISS — general-purpose visual retrieval. Works off-the-shelf.
• CLIP + FAISS — when queries are text.
• Fine-tuned DINOv2 + FAISS — instance-level retrieval, face re-ID, fashion, e-commerce.
• Milvus / Weaviate / Qdrant — managed vector DB wrappers around FAISS or HNSW.

For SOTA instance retrieval, the recipe is: DINOv2 backbone, add an embedding head, fine-tune with a triplet or InfoNCE loss on instance-labelled pairs, index in FAISS.

Ship It

This lesson produces:

• outputs/prompt-retrieval-loss-picker.md — a prompt that picks triplet / InfoNCE / ProxyNCA for a given retrieval problem.
• outputs/skill-recall-at-k-runner.md — a skill that writes a clean evaluation harness for recall@K with train/val/gallery splits and proper data contract.

Exercises

1. (Easy) Run the toy example above. Plot the embeddings with PCA before and after training to see the six clusters form.
2. (Medium) Add a ProxyNCA loss implementation: one learned "proxy" per class, standard cross-entropy on cosine similarity. Compare convergence speed vs triplet loss on the toy data.
3. (Hard) Take 1,000 ImageNet validation images, embed with DINOv2 via HuggingFace, build a FAISS flat index, and report recall@{1, 5, 10} against the same images as queries (should be 1.0) and against a held-out split with ImageNet labels as ground truth.

Key Terms

Further Reading

• FaceNet: A Unified Embedding for Face Recognition (Schroff et al., 2015) — the triplet loss / semi-hard mining paper
• In Defense of the Triplet Loss for Person Re-Identification (Hermans et al., 2017) — practical guide to triplet fine-tuning
• FAISS documentation — every index, every trade-off
• SMoT: Metric Learning Taxonomy (Kim et al., 2021) — survey of modern losses and their connections