Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
SimCLR reports an empirical projection-head effect
Example
In SimCLR's ImageNet experiments, a projection head is a map applied to the encoder representation to produce ; linear evaluation trains a linear classifier on a fixed representation. The authors report a comparison among an identity head, a linear projection head, and a nonlinear projection head with one additional hidden layer and ReLU. In their Figure 8, the nonlinear head's pre-projection representation scores about three percentage points above the linear-head condition and more than ten points above the no-head condition; they also report that scores more than ten points above the projected representation . Their default setup uses a ResNet-50 encoder, a two-layer MLP projection head to a 128-dimensional latent space, NT-Xent (normalized temperature-scaled cross-entropy), batch size 4096 and 100 training epochs. These are reported empirical results under the paper's evaluation protocol, not a theorem that projection heads universally improve representations.
Example references
Latent-class contrastive representation learning: supplies the representation-learning context only; the reported benchmark is empirical.
Chen et al., Section 4 default setup and Section 4.2, Figure 8: reports the encoder/head configuration and linear-evaluation comparisons.
Chen et al., Supplementary Appendix B.4: provides additional projection-head analysis.
Facts & Assumptions
Given: The published SimCLR paper and its ImageNet projection-head experiments.
The default configuration in Section 4 uses a ResNet-50 base encoder, a two-layer MLP projection head to dimension 128, NT-Xent, batch size 4096 and 100 epochs. Chen et al., Section 4, default setting
Figure 8 reports linear evaluation for identity, linear and nonlinear projection heads; its text reports roughly a three-point gain over a linear projection, more than ten points over no projection, and more than ten points for pre-projection over . Chen et al., Section 4.2 and Figure 8
Proof
Given: The complete relevant passages of the SimCLR paper inspected in [F1] and [F2].
The setup in [F1] identifies the encoder, projection head, latent dimension, loss, batch size and training duration for the reported default experiment.
The linear-evaluation comparisons in [F2] state the reported relative performance of the three head choices and of versus . The Example reports those empirical comparisons with their stated experimental scope and makes no universal claim.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
12 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Ting Chen et al., A Simple Framework for Contrastive Learning of Visual Representations, default setting in Section 4 and Section 4.2, Figure 8 (standard reference, not scraped)
- Ting Chen et al., A Simple Framework for Contrastive Learning of Visual Representations, Supplementary Appendix B.4 (standard reference, not scraped)