"Ex" governs the ablative case
One of the talks at the Emerging Technology Conference here in San Diego that I'm going to miss because I'm coming home tomorrow is called "Deus Ex Automata". I found this title jarring because it reflects a misinterpretation of what's going on in the phrase "deus ex machina" (or, if you prefer, an overgeneralization of the apparent pattern in that phrase). The presenter seems to have thought that you can form a Latin phrase of the form "deus ex _____a" with any noun if you just know a Latin noun that ends in "a" (or, to overgeneralize even more incorrectly, perhaps the presenter thought that you could plug any noun in the blank spot after "deus ex _____").
This is not true. The preposition "ex" governs the ablative case, which is a fancy way of saying that noun forms change after the word "ex" to show that they are the particular things out of which something is coming, and so on. For example, the Nicene Creed (in the Western churches' versions) claims that the Holy Spirit "ex patre filioque procedit" (proceeds from the father and from the son), language which has been a point of theological controversy between Eastern and Western Christianity for hundreds of years. But the basic (nominative) forms of those nouns are "pater" and "filius"; they got modified into "patre" and "filio" because they came after "ex".
In a similar vein, if we wanted to translate Mao's claim about the origins of political power into Latin, we might say something like "tota potestas rei publicae ex armis oritur" (I'm not going to try to figure out a more precise way to refer to the "barrel of a gun" at the moment without access to some more skillful neolatinists or their dictionaries). But of course the basic form of the word for weapons is "arma". Now the fact that the first word of Vergil's Aeneid is also "arma" shows a coincidence, because Vergil's "arma" is in the accusative case because it is the direct object of "cano" (I sing [about]). It just so happens that "arma" is a word that doesn't visibly change when you change it from the nominative to the accusative. That's not true of the second word of the Aeneid, "virumque" (whose basic form is "vir" and which did indeed get changed as a result of being the object of "cano").
Similarly, "machina" is a noun which doesn't visibly change when you put it in the ablative case after "ex", unlike, say, "pater", "filius", or "arma". At least, it doesn't change if you're using a writing system that doesn't mark vowel quantity, since strictly speaking the final "a" was originally short and becomes long in the ablative, sometimes written as "māchinā" (thus "deus ex māchinā").
"Automata" can't possibly be in this category, because it's not in the first declension (where all nouns that don't change from the nominative to the ablative are) because it's plural, and the first declension doesn't have any plurals that end in "-a".
If we believe Lewis and Short and Wikipedia, "automaton" in Latin is a Greek loanword that must fall into the second declension neuter paradigm, which means that its nominative plural is "automata" but its ablative plural is "automatis". Then the only correct way to say "god from automata" in Latin is "deus ex automatis" (or "deus ex automatīs" if you mark vowel quantity).
Since the Emerging Tech page about that talk doesn't provide any contact information for the speaker and since I'm on my way home, I have no idea to whom to complain about this problem. A few years ago I had a similar quarrel with "magnum opii" as a purported plural of "magnum opus" in a Microsoft ad; this shows three different kinds of confusion about Latin plurals. The correct plural is "magna opera". I'm sorry to see that many other people writing on the web have used "magnum opii" or the more plausible but still wrong "magnum opi". But Microsoft should have been able to pay someone enough to achieve a correct plural!
If you happen to want to see the original Greek word in use in a Greek text, Eva Brann has pointed out that Hephaistos in Iliad 18 is busy making αυτοματοι, which she translates as "robots" (!). From the context, it appears that that's exactly what he's making.
