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Yes, actually, they do. See the heading Blessings of scale in [0] [0]: https://gwern.net/scaling-hypothesis https://gwern.net/scaling-hypothesis:

• GaggiX 3y ago
  I have trained models on performing additions on numbers with fixed number of digits, just to prove to a friend that a neural network can learn to do addition, I hide in the dataset many combinations of numbers but the model was still able to sum them correctly, therefore it learned to perform addition on numbers with fixed number of digits. So no it's not memorizing, it's something that I have tested myself.
  • jjtheblunt 3y ago
    Interesting. Thanks for the comment. What if you ask it to add numbers with more digits?
    • GaggiX 3y ago
      The model is trained with a fixed number of tokens, I don't remember if the models I trained have sinusoidal embeddings or learnable positional embeddings, in the latter there would be no embedding to encode the position, in the former I think it would cause problems with the sinusoidal embedding layer as the sine and cosine would wrap around.
  • Der_Einzige 3y ago
    Fine-tuning the model to force it to understand the insane tokenization its forced to use for its vocabulary and perform accurate addition sounds great until you start trying very large numbers or messing with whatever decoding settings you're using (and let me guess, it was beam search). Or, you can simply ask it to use a tool, like a calculator for you. This is more reliable than fine-tuning a current technique BPE tokenized model ever will be.
    • GaggiX 3y ago
      I trained my models from scratch, the tokenization is extremely simple and designed just for this task, decoder-only models can learn to do sums of arbitrarily large numbers if the model is large enough (they are computationally bounded). The decoding method used was greedy or simple sampling.
• jjtheblunt 3y ago
  super cool and interesting link. thanks.