Use of "the same"

Solution 1:

Strictly speaking, it's ambiguous because it can be interpreted in different ways:

I see in the same way through your glasses as I do through mine.

Here, it's an adverb that describes the method of your seeing. "I have 20/20 vision when using your glasses too."

I see [it] / [the same (thing)] through your glasses as I do through mine.

Here, depending on how you interpret it, it's being used as a pronoun to refer to something previously mentioned (assuming there is context for it), or it's being used as an adjective to refer to something identical that has been elided from the sentence.

So, it depends on the sense that you are trying to convey. Without any further context, it's impossible to determine if it's meant to be an adverb, pronoun, or even adjective.

As an adjective:

I see the same meteor through your glasses as I do through mine.

And if it were used in the context of a dialogue, it would be considered a pronoun:

"Here, try my glasses. Do you still see a meteor?"
"I see the same through your glasses."

In this exchange, the more common pronoun-based response would be:

I still see it (through your glasses).

Note, however, that it's more likely to be an adverb than anything else because most people would not drop the noun from the sentence in this case.

From Oxford Dictionaries:

ADJECTIVE

1 Identical; not different.
‘she was saying the same thing over and over’
‘I have never made the same mistake since’
‘I'm the same age as you are’
‘the very same people who practised all the rules are now the most sceptical’
[with clause] ‘he put on the same costume that he had worn in Ottawa’
‘she was still the same old Beth’

1.1 Not having changed; unchanged.
‘he's worked at the same place for quite a few years’

1.2 Used to emphasize that one is referring to a particular, unique person or thing.
‘people will always notice if you wear the same shirt two days running’
‘they drank out of the same glass’

1.3 this/that same Referring to a person or thing just mentioned.
‘that same year I went to Boston’

2 Of an identical type; exactly similar.
‘they all wore the same clothes’

PRONOUN

1 (the same) The same thing as something previously mentioned.
‘I'll resign and encourage everyone else to do the same’

1.1 People or things that are identical or share the same characteristics.
‘there are several brands and they're not all the same’

2 (chiefly in formal or legal use) the person or thing just mentioned.
‘put the tailboard up and secure same with a length of wire’

ADVERB

Similarly; in the same way.
‘treating women the same as men’
‘he gave me five dollars, same as usual’

I find some of the definitions of its adjective sense to blur with some of the definitions of its pronoun sense. But however it's viewed, there still is a way of interpreting the sentence in which same is not used as an adverb.