# performing function (maxcol) across the column

I'm currently going through this paper:
Bidirectional Attention Flow for Machine Comprehension, Seo, Minjoon, et al. (2016)

They perform a $$max_{col}$$ function over a matrix $$S \in \mathbb R^{TxJ}$$:

We obtain the attention weights on the context words by $$b = softmax(max_{col}(S)) ∈ \mathbb R^{T}$$ , where the maximum function ($$max_{col}$$) is performed across the column.

Intuitively I would understand "where maximum function is performed across the column" as I taking the maximum from each of the $$J$$ columns and getting as a result a vector from $$\mathbb R^{J}$$ (one value for each column), not $$\mathbb R^{T}$$.

Even though it makes sense having a vector from $$\mathbb R^{T}$$ in the further course of the paper, the quoted passage really is counterintuitive for me.
(Naively I would rather call it $$max_{row}$$ what they are doing, am I wrong?)

To make things more confusing when looking after an explanation I found this paper with a similar procedure, but just the opposite outcome:
A Question-Focused Multi-Factor Attention Network for Question Answering, Kundu, S., & Ng, H. T. (2018)

There they have a matrix $$A \in \mathbb R^{TxU}$$:

We apply a $$maxcol$$ operation on $$A$$ which forms a row vector whose elements are the maximum of the corresponding columns of $$A$$. We define $$k \in \mathbb R^{U}$$ as the normalized max-attentional weights:

$$k = softmax(maxcol(A))$$

So my questions are:

• Am I misunderstanding "$$max_{col}$$ performed across the column"? What is normally meant by that statement?
• Is there some mistake in one of the papers? To me it seems that both papers using just the same function and getting converse results.