What evidence is there for inventions by slaves or former slaves in Ancient Rome?

What are these 'possible inventions' [of slaves, freedman ]?

I am tempted to reply almost all of them?

There are countless inventions, only the smallest part of all those inventions is really attributable to any name in particular. Even if there are names attached to an invention or innovation, that sometimes gives us not much information on the status of the individual.

The Greeks and Romans associated inventions with individuals: although these associations may have been accurate or inaccurate, real or imaginary, the habit reveals clearly that inventors could be celebrated in their lifetimes and even immortalized in literature. Daedalus and flight is perhaps the most famous association; while the most surprising is perhaps the mathematician Archytas’ invention of the baby’s rattle. Pliny’s Natural History contains hundreds of putative inventors’ and discoverers’ names, most of them otherwise unknown. Some famous Greeks wrote books about inventions, e.g. Theophrastus and Strato (consecutive leaders of the Lyceum after Aristotle); no such book has survived the past 2,000+ years unfortunately.

While that is an argument of absence, a more convincing argument is that like Tiro there were a great number of slaves that became famous enough to have books written about them:

Hermippus of Berytus (Beirut), who was born into slavery in the time of Hadrian, wrote a multiple-volume book entitled Slaves who were Famous in the Cultural Domain. The loss of these works is a real handicap to modern study of this topic. However, the very existence of these stories shows that the Greeks and Romans perceived ideas, tools, and techniques as inventions not givens, and they knowingly changed, improved, and supplemented the technical base over time.

What really counts as an invention or just an innovation? While that might be difficult to define for us when looking at the ancient world it is much easier to look at a certain socio-economic structure and the prevailing incentives:

In the ancient world, slaves who were skilled artisans or service providers were usually paid for their skills and products. Most people in this sector were paid piece rate, per unit that they made or performed. For example, stonemasons working on the Erechtheion frieze were paid per figure, those fluting the columns, per foot. As a rule of thumb, the more products or services the person sold, the more money she or he made. Slaves could raise the money needed to buy their freedom through saving the residual income from their earnings. Purely on an abstract, theoretical level, we can appreciate that the ancient, independently living slave had good reason to be industrious and to want to increase his or her output in terms of quantity or quality, since every obol earned was an obol closer to freedom. Indeed, the prospect of freedom may have been a more powerful motivator than any felt by a free worker. The prospect of freedom at a price would have provided a powerful motivator for those in the manufacturing sector to improve their productivity and/or the quality of their product. Consequently, we may speculate that slaves were responsible for at least some of the many inventions and technical developments of classical antiquity.
I believe that the key parameters that shaped the relationship between slaves and technologies were:
(1) the skill or care level of the work being performed
(2) the motivation provided to the workers
(3) the technical education of the workers
(4) the material or cash capital investment required by an innovation
(5) the physical and socio-economic benefits of an innovation
(6) the physical and socio-economic risks of an innovation
(7) the physical mobility of skilled workers and transaction costs.

_{Enrico Dal Lago & Constantina Katsari (Eds): "Slave Systems. Ancient and Modern", Cambridge University Press: Cambridge, New York, 2008, p137.}

Slaves and freedmen were skilled and hands on experienced enough and often highly motivated "to invent". They did for sure. They often became famous for what they accomplished and almost as often these innovations were so small in scale that a step in development would only become apparent in hindsight. We just lost too much information on most of the specifics; compare:

This article is built around a single source, which is an inventive fiction, a pack of lies, an anonymous accretive novella, composed and revised, as I suspect, over centuries, as a vehicle for comedy and manners. It is the biography of a slave, the only full-length biography of a slave surviving from classical antiquity; a text which as far as I know has never yet been used as the basis of historical reconstruction, probably because it is so obviously fiction.
_{Keith Hopkins: "Novel Evidence for Roman Slavery", Past & Present No. 138 (Feb., 1993), pp. 3-27.}

As unsatisfactory as this is, a reason for this state of knowledge available for us is the difficult transmission of information across time. But it is not only that much of this is lost, as it appears that even more of it was never recorded in the first place:

The authors of ancient texts are, with insignificant exceptions, men—and upper-class men at that—whose principal concerns are agriculture (as absentee landlords rather than farmers, of course), the military, and politics. Their interest in and knowledge of the lives and efforts of women, commoners, and slaves is very limited. Thus there are many aspects of our study for which we have little written evidence: ceramic production and textiles are two good examples. And even when our authors do tackle technical subjects that interest them, they sometimes show a surprising ignorance of their own machines and processes. Still, they are often our only source of comprehensive information about certain technologies.
_{John W. Humphrey: "Ancient Technology", Greenwood Guides to Historic Events of the Ancient World, Greenwood Press: Westport, London, 2006, p13.}

But to add at least one inventor, who was a slave and named, of quite early origin and quite some importance in the history of culture, and not Tiro, I will nominate Aesop, inventor of the fable:

Scattered details of Aesop's life can be found in ancient sources, including Aristotle, Herodotus, and Plutarch. An ancient literary work called The Aesop Romance tells an episodic, probably highly fictional version of his life, including the traditional description of him as a strikingly ugly slave (δοῦλος) who by his cleverness acquires freedom and becomes an adviser to kings and city-states.[…]
From Aristotle[5] and Herodotus we learn that Aesop was a slave in Samos and that his masters were first a man named Xanthus and then a man named Iadmon; that he must eventually have been freed, because he argued as an advocate for a wealthy Samian; and that he met his end in the city of Delphi. Plutarch tells us that Aesop had come to Delphi on a diplomatic mission from King Croesus of Lydia, that he insulted the Delphians, was sentenced to death on a trumped-up charge of temple theft, and was thrown from a cliff (after which the Delphians suffered pestilence and famine). Before this fatal episode, Aesop met with Periander of Corinth, where Plutarch has him dining with the Seven Sages of Greece, sitting beside his friend Solon, whom he had met in Sardis. (Leslie Kurke suggests that Aesop himself "was a popular contender for inclusion" in the list of Seven Sages.)
_{Wikipedia: Aesop}