Word embeddings are flat and do not capture hierarchies. number space vs word space, for example, the similarity between '8' and 'eight' should be captured. Intrinstic and extrinsic properties of words are still cannot be captured by word-embeddings alone. Sure we can use character embedding and mix/concat them with word-embeddings, but that doesn't seem to improve the performance by far.
Meaning of a word is influenced by a lot of factors which can be
categorised into at least three.
Syntax - character order,
Semantics - what are the words that are seen together,
Pragmatics - we don't know how to handle this so far, because it depends
upon lot of things like history, culture, contemporary styles of use and
so on.
The neural network, all it does it mapping between two higher-dimensional spaces deterministically. To explain what I mean, I will use the OpAmp vs Microcontroller analogy. In an OpAmp circuitry, the output is completly based on the input and the relationship causal. Very similar to mechanical devices, it just the medium is different, electrons in circuitry. There is no arbitraryness . But I can, make a microcontroller to light up an LED regardless of what is on the input side.
I intentionally chose not use the phrase, 'program the microcontroller'. Programs is set of rules operating over data structured in, well... a structure. No shortcuts. But that is also a curse. Take NLP for example, we cannot completely specify language in a set of rules. Although link-grammar, dependency-grammar, and recent construction-grammars have evolved to more powerful and expressive, NLP is still an unsolved problem.
Neural networks tend to perform well on a subset of language defined-by/confined-to a text-corpus, because it tries to figure out the rules by themselves. But that is not an easy job. It is like watching a suspense-thriller. The story is intentionally crafted to make us infer/predict something to be true, say the movie, Mulholland Drive is about, Diane Selwyn is trying to help Camilla Rhodes figure who was she before the car accident, only to break that prediction, like revealing that all the damn is a dream, and make us feel like cheated and astonished at the same time, so that we are kept invested in the story. The movie is actually more complex and there can be more than one interpretation other than the one I chose to present here, exactly like there are many ways to interpret a sentence.
It is safe to say the that kind of reactions are the after-effects of the order in which the events in the story are presented to us. That is exactly the reason why beural networks perform well on one dataset and not on another and at times not even on the same dataset if the order of the samples are shuffled. The reason why our prediction of the hero or the anti-hero fails miserably is, we are trying to capture meaningful structures of the story from and confined to the events presented, i.e from the incomplete information.
We are connecting dots which may or may not be actually connected in the story, and we won't know it until we are provided with the full information. Similarly the neural networks creates shortcuts and believes that is the actual structure of the content in NLP case the syntax, semantics and even pragmatics of the language. And believe the datasets we currently have cannot capture all of three of them, in their entirety. So what the neural networks ends up learning are mere shortcuts, unless we provide them all sorts of combinations of meaning sentences.
For example to establish the similarity between word 'eight' and number '8' we need to provide the neural network enough examples where 'eight' and '8' exemplify similar meanings. In context of word-embeddings, duplicating samples with 'eight' replaced with '8' and vice-versa should capture that similarity, but how to make the neural network understand that '1' and '8' are from number spaces and 'one' and 'eight' are from word spaces? I don't know the answer to that. (May be multimodal learning might help?)