Contrastive Learning Assumptions

• Contrastive learning assumptions are foundational rules that define how positive and negative pairs are constructed to capture semantic similarity.
• They incorporate criteria on similarity metrics, margin constraints, and fairness adaptations for managing protected attributes and domain-specific challenges.
• Recent advances relax static assumptions through data-dependent, adaptive frameworks that enhance both performance and bias mitigation.

Contrastive learning assumptions define the foundation on which self-supervised, semi-supervised, and fair representation learning procedures operate. These assumptions specify the procedures for constructing positive and negative pairs, the statistical independence or relatedness between samples, the role of similarity metrics and margin constraints, and, crucially, how domain- or fairness-specific information is encoded or disregarded. Modern research has revealed both the power and the limitations of these assumptions, motivating the development of methods that can relax, adapt, or even learn them automatically.

1. Canonical Contrastive Learning Assumptions

Standard contrastive frameworks such as InfoNCE and SimCLR are predicated on precise sampling and independence assumptions:

• Pair Construction: Each anchor sample $x_i$ is paired with at least one positive (commonly an independent augmentation or semantically equivalent sample) and is contrasted against negatives drawn i.i.d. from the marginal data distribution (Nielsen et al., 22 Nov 2024).
• Distributional Independence: Standard noise-contrastive estimation (NCE) posits that positive pairs $(x_i, y_+)$ have high mutual information, while negatives $(x_i, y_-)$ are independent; this underlies the interpretation of the InfoNCE denominator as a noise distribution (Denize et al., 2021).
• Similarity Metric and Temperature: The similarity function (cosine or dot-product, rescaled by temperature $\tau$) is implicitly assumed to align with the semantic similarity targeted by downstream tasks, although this alignment need not hold in practice (Nielsen et al., 22 Nov 2024).
• Margin or Thresholds: Some losses (e.g., margin-based variants) assume a fixed margin $m$ exists such that positive similarities exceed negatives by at least $m$ (Nielsen et al., 22 Nov 2024).
• Objective Form: The generic InfoNCE objective is

$$L_{\text{contrast}} = -\sum_{(i,j)\in P}\log\frac{\exp(s(x_i,x_j)/\tau)}{\sum_{k\in N(i)}\exp(s(x_i,x_k)/\tau)}$$

with $P$ and $N(i)$ denoting positive and negative sets, $s(\cdot,\cdot)$ the similarity, and $\tau$ the temperature (Nielsen et al., 22 Nov 2024).

These assumptions are tractable in large, balanced datasets of natural images but become problematic when the pair construction procedure fails to align with semantic classes, when negatives are not i.i.d., or when class imbalance and domain-specific dependencies exist (Kokilepersaud et al., 2022).

2. Fairness and Protected-Attribute Assumptions

Fair contrastive learning surfaces additional, often rigid, assumptions:

• Binary Grouping: Initial methods enforced the binary nature of the protected attribute $Z$ (e.g., gender, race), with explicit pairing rules such as only contrasting across group boundaries or enforcing group-wise balance (Nielsen et al., 22 Nov 2024).
• Kernel/Clustering for High-Cardinality $Z$: For non-binary, high-cardinality, or continuous protected attributes, approaches employed predefined kernels $K_Z(z_i, z_j)$ (e.g., cosine kernel or clustering), with the assumption that $K_Z$ faithfully captures bias-causing similarities. The required matrix inversion is computationally intensive ($O(b^3)$ for batch size $b$) (Nielsen et al., 22 Nov 2024).
• Limitations: These predefined, non-learned assumptions frequently fail on continuous or high-dimensional $Z$ due to insufficient or misweighted negatives, harming both bias mitigation and downstream performance (Nielsen et al., 22 Nov 2024).

A notable advancement is the attention-based FARE and SparseFARE frameworks (Nielsen et al., 22 Nov 2024), which learn to assign data-dependent weights to negative samples, dynamically downweighting bias-causing samples in the contrastive loss. This approach eliminates the need for predefined kernel structure or binarization, generalizing to arbitrary protected-attribute structures.

Empirical Benchmarks:

Model	Downstream Accuracy (%)	Bias Removal MSE (higher = fairer)
InfoNCE	84.1 ± 1.8	48.8 ± 4.5
Fair-InfoNCE	85.9 ± 0.4	64.9 ± 5.1
CCLK (cosine kernel)	86.4 ± 0.9	64.7 ± 3.9
FARE	85.7 ± 0.9	68.4 ± 4.3
SparseFARE	86.4 ± 1.3	74.0 ± 3.8

On the ColorMNIST benchmark, SparseFARE achieves the strongest bias removal and maintains state-of-the-art accuracy, empirically validating the removal of hand-crafted contrastive assumptions (Nielsen et al., 22 Nov 2024).

3. Softening and Generalizing Pairwise Assumptions

Recent work has questioned the hard binary partitioning into positives and negatives:

• Class Semantics in Negatives: Many instances, while formally negative under standard protocols, are semantically similar (e.g., two images of cats) and should not be treated as pure noise. Hard-negative treatment can disrupt natural semantic clusters (Denize et al., 2021).
• Soft Similarity Targets: Similarity Contrastive Estimation (SCE) discards the hard partition in favor of assigning a continuous similarity target to every pair in a batch, interpolating between instance discrimination (hard positives/negatives) and relational similarity (soft). This allows transfer between fine-grained and coarse-grained tasks, reducing class collision and preserving semantic structure (Denize et al., 2021).

SCE’s loss (for a batch of N)

$$L_{\text{SCE}} = -\frac{1}{N}\sum_{i=1}^N\sum_{k=1}^N w_{ik}^2\log p_{ik}^1$$

where $w_{ik}^2$ is a soft target (mixing hard identity with batch similarity), enables learning representations that are both discriminative and semantically aligned.

4. Domain, Data, and Inductive Bias Assumptions

Several studies have analyzed the domain-specific validity of standard contrastive assumptions:

• Seismic and Volumetric Data: In domains such as seismic interpretation, spatial correlation means that nearby samples are functionally positives, and random augmentations may violate key semantic invariances. Customized positive definitions—e.g., “volume partition pseudo-labels”—outperform natural image assumptions (Kokilepersaud et al., 2022).
• Inductive Biases and Function Class: Analyses that ignore the inductive bias of the learned function class (e.g., linear vs. deep neural networks) produce vacuous guarantees if augmentations are disjoint or lack sufficient overlap. Good generalization requires that the feature map be expressive and consistent with semantic structure; otherwise contrastive minimization alone can produce degenerate or collapsed solutions (Saunshi et al., 2022).
• Multi-modal and Graph Domains: In CLIP-like multi-modal settings, the assumption that positive pairs (e.g., image–caption) align across domains with sufficient cross-modal variance and negatives are appropriately distributed is critical for balanced representations. The two-phase dynamic (alignment followed by balancing with well-calibrated negatives) is essential to avoid feature-space collapse, especially in anisotropic or heterophilic domains (Ren et al., 2023, Xiao et al., 2023).

5. Statistical and Computational Assumptions in Learning and Generalization

Key statistical assumptions underlie theoretical guarantees:

• Infinite Negatives (Asymptotic Regime): Classical analyses assume the number of negatives per anchor tends to infinity, enabling clean alignment–uniformity objective splitting and tight error bounds (Kim et al., 6 Aug 2025). In practice, actual batch sizes and memory constraints violate this regime, leading to

$$|\mathcal{L}_{\text{SupCon}}(f;\tau,M)-\log M - \lim_{M\to\infty}[\cdot]| \le \frac{1}{M}e^{2/\tau} + O(M^{-1/2})$$

where $M$ is the number of negatives (Kim et al., 6 Aug 2025).

• Finite Sample Corrections: In federated, online, or resource-constrained settings, alignment and uniformity must be decoupled in the contrastive loss to allow explicit, data-dependent calibration. For example, DCFL directly separates attractive (alignment) and repulsive (uniformity) terms, avoiding the pathologies of the log-sum-exp coupling when negative sets are limited or poorly representative (Kim et al., 6 Aug 2025).
• PAC and Rademacher-Bounded Guarantees: Efficient PAC-learnability and generalization error quantification further require that the metric, margin, and complexity of the hypothesis class allow convex relaxations (e.g., via SDP for the $\ell_2$ metric), and that large-margin conditions hold (Shen, 21 Feb 2025, Elst et al., 4 Dec 2024).

6. Assumption Relaxation and Adaptive Contrastive Priors

Recent frameworks offer mechanisms for adapting to unknown or data-driven assumption regimes:

• Data-Dependent Learning Paradigms: Instead of committing to a fixed radius, kernel, or margin, modern methodologies learn the best abstraction from data, e.g., by optimizing over collections of hypothesis subsets parameterized by an automatically-chosen “radius” or contextual similarity score (Pour et al., 13 Nov 2025).
• Attention-Based and Dynamic Reweighting: The FARE family of attention-based methods dynamically reweights contrastive negatives to suppress bias without explicit binarization or clustering, demonstrating empirical and computational superiority over fixed-rule schemes (Nielsen et al., 22 Nov 2024).
• Multi-head and Factorized Invariances: Architectures that factorize invariant and variant subspaces (e.g., multi-head networks, “leave-one-out” heads) allow representations to both discard and preserve distinct augmentation-induced factors, increasing adaptability and robustness to changing downstream task requirements (Xiao et al., 2020).

7. Practical and Theoretical Limitations

The utility of contrastive learning is ultimately bounded by the match between its assumptions and the actual data/task regime:

• Representational Collapse: Absence of suitable negative balancing or excessive invariance demands can result in degenerate “collapsed” features (rank deficiency, class merging) (Ren et al., 2023, Saunshi et al., 2022).
• Pathological Generative Processes: If the generator is non-invertible, if the conditional distributions for positives are not compatible with the chosen similarity metric, or if the marginal distribution is not less concentrated than the positive-conditional, theoretical identifiability and reconstruction results break down (Zimmermann et al., 2021, Matthes et al., 2023).
• Domain Mismatch and Generalization Failure: Application to graph or multi-modal data requires explicit replacement or augmentation of the pair construction heuristic, as prefabricated schemes often fail when social, structural, or semantic assumptions are violated (Xiao et al., 2023, Kokilepersaud et al., 2022).
• Empirical Verification and Data-Driven Adaptation: In the absence of prior knowledge (e.g., optimal kernel radius), data-driven approaches that automatically adapt to empirical context—such as data-dependent hypothesis class collections—achieve state-adaptive generalization with optimal trade-off between complexity and empirical fit (Pour et al., 13 Nov 2025).

In summary, the dominant paradigm in contrastive learning is moving from static, universal pairwise and metric assumptions toward adaptive, data-dependent, and often learnable frameworks that better align with the complex dependence structures intrinsic to modern datasets and fairness requirements. This trajectory is motivated and justified by empirical and theoretical advancements that expose the limitations of traditional assumptions and demonstrate the efficacy of dynamic alternatives (Nielsen et al., 22 Nov 2024, Denize et al., 2021, Saunshi et al., 2022, Kim et al., 6 Aug 2025).