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When is Transfer Learning Possible?
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Presents a causal SCM-based framework for transfer learning that propagates parameter constraints through the graph to decide when transfer is feasible, and uses it to challenge sparse-mechanism-shift and layer-freezing beliefs.
Problem
When can knowledge learned in previous environments be transferred to speed up learning in new environments, across supervised, RL, and imitation learning settings?
Approach
Model the world as an SCM whose atomic parameters are constrained; environments are conditional interventions choosing parameters from these constrained sets. A top-down computation-tree procedure propagates atomic constraints to the target conditional's parameters, yielding a meta-algorithm for which parameters to transfer (e.g., freezing a linear coefficient rather than a whole layer).
Key results
- On Complex Colored MNIST, transferring only the first layer's linear coefficient performs best among compared transfer strategies, outperforming freezing the entire first layer and training from scratch.
- In the Colored MNIST construction the number of parameters to learn drops from 47040+20+40 to 20+40 with transfer (assuming np=20).
- Sparse changes across environments are shown to be neither necessary nor sufficient for transfer feasibility in the chain example.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Freeze only the first layer’s linear coefficient learned in Env. 1, rather than the entire first layer (ablation) | Two-layer Complex Colored MNIST model · Complex Colored MNIST, Env. 2 | accuracy | Helped |
| Freeze the entire first layer instead of only its linear coefficient (ablation) | Two-layer Complex Colored MNIST model · Complex Colored MNIST, Env. 2 | accuracy | Hurt |
| Use a randomly chosen first-layer linear coefficient rather than one learned in Env. 1 (ablation) | Two-layer Complex Colored MNIST model · Complex Colored MNIST, Env. 2 | accuracy | Hurt |
| Transfer the model trained in Env. 1 without adapting it | Complex Colored MNIST model · Complex Colored MNIST, Env. 2 zero-shot | accuracy | Hurt |
Surprising findings
- Sparse mechanism shifts are neither necessary nor sufficient for transfer feasibility.
- Freezing an entire layer of a neural network can cause poor transfer, while freezing a more refined subset of its parameters succeeds.
Limitations
- Assumes realizability and unique descriptions (Assumption 3.4) for main results; general case left to future work.
- Constraint learning method is simple and not state-of-the-art; the complexity measure is parameter count, not a practical measure of computation.
- Colored MNIST transfer requires strong assumptions (exponential family, linear region assumption) that may not hold in practice.
Experimental setup
Datasets: Colored MNIST (modified, Arjovsky et al. 2020)
Benchmarks: Complex Colored MNIST
Metrics: accuracy zero-shot accuracy sample efficiency
Baselines: learning from scratch without transfer freezing the entire first layer random transfer of first-layer coefficient
Builds on: Buesing et al. 2019 (SCM for RL) Independent Causal Mechanisms principle Sparse Mechanism Shift hypothesis Barreto et al. 2017 (successor features) Rolnick & Kording 2020 (ReLU network identification)
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