Variance & Greediness: A comparative study of metric-learning losses

Metric learning is central to retrieval, yet its effects on embedding geometry and optimization dynamics are not well understood. We introduce a diagnostic framework, VARIANCE (intra-/inter-class variance) and GREEDINESS (active ratio and gradient norms), to compare seven representative losses, i.e., Contrastive, Triplet, N-pair, InfoNCE, ArcFace, SCL, and CCL, across five image-retrieval datasets. Our analysis reveals that Triplet and SCL preserve higher within-class variance and clearer inter-class margins, leading to stronger top-1 retrieval in fine-grained settings. In contrast, Contrastive and InfoNCE compact embeddings are achieved quickly through many small updates, accelerating convergence but potentially oversimplifying class structures. N-pair achieves a large mean separation but with uneven spacing. These insights reveal a form of efficiency-granularity trade-off and provide practical guidance: prefer Triplet/SCL when diversity preservation and hard-sample discrimination are critical, and Contrastive/InfoNCE when faster embedding compaction is desired.

Learning Audio-Visual Embeddings with Inferred Latent Interaction Graphs

Learning robust audio-visual embeddings requires bringing genuinely related audio and visual signals together while filtering out incidental co-occurrences - background noise, unrelated elements, or unannotated events. Most contrastive and triplet-loss methods use sparse annotated labels per clip and treat any co-occurrence as semantic similarity. For example, a video labeled "train" might also contain motorcycle audio and visual, because "motorcycle" is not the chosen annotation; standard methods treat these co-occurrences as negatives to true motorcycle anchors elsewhere, creating false negatives and missing true cross-modal dependencies. We propose a framework that leverages soft-label predictions and inferred latent interactions to address these issues: (1) Audio-Visual Semantic Alignment Loss (AV-SAL) trains a teacher network to produce aligned soft-label distributions across modalities, assigning nonzero probability to co-occurring but unannotated events and enriching the supervision signal. (2) Inferred Latent Interaction Graph (ILI) applies the GRaSP algorithm to teacher soft labels to infer a sparse, directed dependency graph among classes. This graph highlights directional dependencies (e.g., "Train (visual)" -> "Motorcycle (audio)") that expose likely semantic or conditional relationships between classes; these are interpreted as estimated dependency patterns. (3) Latent Interaction Regularizer (LIR): A student network is trained with both metric loss and a regularizer guided by the ILI graph, pulling together embeddings of dependency-linked but unlabeled pairs in proportion to their soft-label probabilities. Experiments on AVE and VEGAS benchmarks show consistent improvements in mean average precision (mAP), demonstrating that integrating inferred latent interactions into embedding learning enhances robustness and semantic coherence.