It does not seem to be explicitly mentioned in the methods of the paper (available at https://arxiv.org/pdf/1409.4842.pdf).
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As you correctly note the batch-size specification is not available in the original publication. That said, it is probably 128 based on circumstantial evidence.
Circumstantial evidence: Caffe replicates GoogLeNet here using a batch-size of 128 where it is explicitly mentioned that: "This model is a replication of the model described in the GoogleNet publication. We would like to thank Christian Szegedy (the first author of the GoogLeNet paper) for all his help in the replication of GoogleNet model." In addition a batch-size of 128 is used by NVidia to run standard speed benchmarks here when using GoogLeNet.
(This not a definite answer so please feel to post another answer if you have a more authoritative source. Personally, 128 seems somewhat too big... I would suspect 10 would be more appropriate for a competition but there even less evidence for size 10 online...)
answered Feb 12, 2018 at 23:31
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$\begingroup$ That's very interesting, thanks. When using NVidia's DIGITS for quick prototyping, there's a fill in box where one can change the batch size -- if left blank it will be the network "default". But that default size is nowhere t be found... in my case, due to memory limitations I use 4. $\endgroup$– pecorinoCommented Feb 13, 2018 at 4:00