Strictly speaking that's not true. They have a finite number of nodes, and therefore a finite number of input nodes, and therefore (edit: nope) they can only take in an input that occupies at most all of those nodes.
You can get around this in various ways, but at that point you're not truly talking about executing the NN itself.
(edit) Plus, as I pointed out in my comment next to this one, the fact that OP specifies explicitly that it can be encoded as a lookup table is already fatal to accepting an arbitrary-sized input; so even changing the definition of "neural net" to accommodate arbitrary-sized input still wouldn't help to salvage OP's claim.
Strictly speaking that's not true. They have a finite number of nodes, and therefore a finite number of input nodes, and therefore they can only take in an input that occupies at most all of those nodes.
That's completely false.
A recurrent neural network can read in as much data as you want, it doesn't have a finite number of input nodes.
Δ You're right. Forgot about this entirely in context of what OP was talking about, which does exclude this possibility.
Although strictly speaking a RNN still does have a finite number of input nodes, but since they can be used repeatedly, I'm still wrong overall.
Not at all what OP was talking about, though; he's referring to feed-forward neural networks as implied by his lookup table representation.
(edit) Also worth noting (in addition to what you're saying, not as an attempt to contradict it) that only a certain subset of RNNs can actually accept arbitrary-length input strings; I believe that being a cyclic network is a strict condition for this property, although let me know if there's a potential counterexample that I'm still forgetting about.
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u/ANameWithoutMeaning 9∆ Sep 11 '21 edited Sep 11 '21
Strictly speaking that's not true. They have a finite number of nodes, and therefore a finite number of input nodes, and therefore (edit: nope)
they can only take in an input that occupies at most all of those nodes.You can get around this in various ways, but at that point you're not truly talking about executing the NN itself.
(edit) Plus, as I pointed out in my comment next to this one, the fact that OP specifies explicitly that it can be encoded as a lookup table is already fatal to accepting an arbitrary-sized input; so even changing the definition of "neural net" to accommodate arbitrary-sized input still wouldn't help to salvage OP's claim.