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Generalization Analysis for Deep Contrastive Representation Learning

AAAI 2025 · Learning theory and algorithms › Kernels and regression theory · approach: Empirical generalization measures · 1 citations (OpenAlex)

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Gives covering-number and parameter-counting generalization bounds for unsupervised contrastive risk with deep ReLU-style networks, largely independent of the number of negatives k (up to logs), using spectral-norm bounds and loss augmentation.

Problem

Generalization of deep contrastive representation learning (DCRL): existing bounds either scale with sqrt(k) negatives or, for the log-k case, suffer exponential/product-of-Frobenius-norm dependence on network depth via peeling.

Approach

Build auxiliary datasets of all individual samples in the tuples and apply covering-number arguments (L_inf,2 covers) to bound Rademacher complexity, giving spectral-type complexity with logarithmic k-dependence; loss augmentation with soft indicators on hidden activation norms further reduces norm and depth dependence; a parameter-counting bound is also derived.

Key results

• Covering-number bounds have logarithmic dependence on the number of negatives k, avoiding the sqrt(k) factor of prior Rademacher-based bounds.
• Basic bound features a square of the product of spectral norms; loss augmentation reduces this to a single product of spectral norms, and a further augmentation replaces it with layer-wise empirical quantities.
• Experiments on MNIST show the proposed bounds are tighter than competing bounds, especially for larger widths and depths.

Measured effects reported in the paper

Surprising findings

• The basic covering-number bound has a square of the spectral-norm product, which is worse than the single product in standard neural network bounds.

Limitations

• The basic bound squares the spectral-norm product, so depth dependence is still exponential without augmentation.
• Parameter-counting bound scales with total number of neurons and can be large for massive architectures.
• Analysis assumes i.i.d. tuples; reusable fixed pools of labeled examples violate this assumption.

Experimental setup

Datasets: MNIST

Benchmarks: MNIST (comparison of bound values vs depth and width)

Metrics: generalization bound magnitude (ignoring constants and logs)

Baselines: Peeling-based DCRL bound (Wang et al.) Lipschitz-based sqrt(k) contrastive bound Log-k contrastive bound with Frobenius norms

Builds on: Arora et al. contrastive learning framework (unsupervised risk) Bartlett spectrally-normalized margin bounds Golowich et al. covering-number bounds for neural networks Wei et al. multi-class loss augmentation

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