mitzvah of hakhel

Ramban writes that the children who the Torah says should be brought to hakhel, "u'bneihem asher lo yad'u yishm'u v'lamdu," must be children of the age of chinuch, otherwise how could they learn anything by coming -- what kind of "lamdu" could there be for children too young to understand anything.  However, continues Ramban, it does not appear from the gemara that this is the case, as the gemara quotes R' Elazer ben Azarya as saying that the children are brought "litein schar l'mivi'eihem," only to give their parents more reward for shlepping them. The Minchas Chinuch goes so far as to suggest that even newborns should be brought, as there is no shiur given for the definition of "taf."

The question of what age child should be brought may hinge on what the purpose of the mitzvah of hakhel is. "L'ma'an yishm'u u'lma'an yilmidu v'yar'u es Hashem Elokeichem" (31:12): Is the mitzvah of hakhel one of limud, and yiras shamayin is a byproduct, or is the mitzvah to inculcate yiras shamayim, and the limud is just a means to set the stage and create the experience that engenders yirah?

Ramban clearly views the mitzvah as one of limud. Therefore, only children who are old enough to learn and understand need to be brought. Contrast that with the language of the Rambam (Chagigah 3:6):

 אפילו חכמים גדולים שיודעים כל התורה כולה, חייבין לשמוע בכוונה גדולה יתרה.  ומי שאינו יכול לשמוע--מכוון ליבו לקריאה זו, שלא קבעה הכתוב אלא לחזק דת האמת; ויראה עצמו כאילו עתה נצטווה בה, ומפי הגבורה שומעה--שהמלך שליח הוא, להשמיע דברי ה-ל

According to the Rambam, even chachamim who are already versed in the pesukim must participate in hakhel, and even those who cannot hear must try to be attentive to the kriah. In other words, even when there is no limud involved, the mitzvah still applies.  The purpose of the kri'ah is not learning, but rather the  because the purpose is "l'chazek das ha'emes" -- the inculcate yiras shamayim.
   
The tension between the two elements of the mitzvah can be seen in the pesukim themselves. The parsha first tells us "mikeitz sheva shanim... tikra es haTorah ha'zos" -- read from the Torah. But then the parsha continues "hakhel es ha'am..." -- the miztvah is for the nation to gather together. Sadya Gaon in fact counts these as two seperate mitzvos: one to read the Torah, one to gather together. The majority of monei ha'mitzvos, however, count them as one mitzvah.  The question is which element is the engine and which is the caboose -- is the ultimate goal limud haTorah, and that's what the nation gathers for, or is the experience of coming together, children included, and end in itself, and the Torah reading is just a means to get us together. 

(A bit of derush: Shouldn't the order of the pesukim be reversed?  First the people have to gather -- "hakhel es ha'am" -- and only then is the Torah read -- "tikra es haTorah ha'zos."  Why does the parsha put it the other way around?  Maor vaShemesh explains that the "Torah ha'zos" that is read to the people, the Torah that they are supposed to learn and take with them, is "hakhel is ha'am" -- we have to come together as a people, men, women, and children included.)
   
See Shu"T Binyan Av vol 2 re: the parallel between the idea of bringing even little children to hear megilas esther and the mitzvah of hakhel.