Statistical Gains from Looped Estimation under Parameter Budgets
Memory constraints in artificial intelligence motivate accurate function approximation with fewer parameters. We study looping, which repeatedly composes one update function with shared parameters; each output becomes the next input. A looped Transformer, for example, reuses one block, whereas its conventional untied counterpart uses separately parameterized blocks. We compare their parameter requirements for a given worst-case approximation accuracy, or equivalently, their approximation accuracy under a common budget limiting distinct trainable coefficients. We then ask whether this representational parsimony improves statistical accuracy. For general likelihood models, we establish an u...
| Authors | Xinyu Tian, Xiaotong Shen |
|---|---|
| Primary category | stat.ML |
| Published | 22 September 2026 |
| Last updated at source | 27 September 2026 |
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