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Object recognition is challenging because the same object can produce vastly different images, mixing signals related to its identity with signals due to its image attributes, such as size, position, rotation, etc. Previous studies have shown that both signals are present in high-level visual areas, but precisely how they are combined has remained unclear. One possibility is that neurons might encode identity and attribute signals multiplicatively so that each can be efficiently decoded without interference from the other. Here, we show that, in high-level visual cortex, responses of single neurons can be explained better as a product rather than a sum of tuning for object identity and tuning for image attributes. This subtle effect in single neurons produced substantially better population decoding of object identity and image attributes in the neural population as a whole. This property was absent both in low-level vision …