Keenan Down

You know you’re a PhD student when your lunch consists of free samples at Borough Market

Does eating half a kilo of pasta count as an altered state of consciousness

I’m always a bit confused about why we often think of time as more relevant to consciousness than space somehow. I reckon spatial complexity is just as important as time complexity

I’m increasingly convinced that we might need some kind of semi-physical substrate for getting around the hard problem. I’d reckon that’s information, but I’m biased

This year's Mathematical Consciousness Science conference, Models of Consciousness 6 (#MoC6) will take place in Sapporo, Japan.

👉 You're cordially invited to join us!

Kudos to this year's main organizer, Robert Prentner!
amcs-community.org/events/moc6-... #consci

Algebraic Representations of Entropy and Fixed-Sign Information Quantities Many information-theoretic quantities have corresponding representations in terms of sets. Many of these information quantities do not have a fixed sign—for example, the co-information can be both pos...

Or if you want to see how you can apply this to study synergy in a brand new way, check out the sequel (recently featured on the banner of the journal Entropy!)

"Algebraic representations of entropy and fixed-sign information quantities"
👇
www.mdpi.com/1099-4300/27...

A Logarithmic Decomposition and a Signed Measure Space for Entropy The Shannon entropy of a random variable X has much behaviour analogous to a signed measure. Previous work has explored this connection by defining a signed measure on abstract sets, which are taken t...

For more information on this approach (which we call "Logarithmic Decomposition"), check out the paper where we introduce it, currently in review!

"A logarithmic decomposition and a signed measure space for entropy"
👇
arxiv.org/abs/2409.03732

When breaking down the dyadic and triadic systems, you can see a structural difference in their co-infos!

In particular, the atomic sets "generated" by shared pairwise distinctions give you 1 bit in the triadic and 0 bits in the dyadic!

And all this using completely classical Shannon entropy!

To solve this we made "sets of information" more concrete than ever before.

Each "atom" corresponds to a particular kind of information about different outcomes.

Each atom has a *fixed sign* (contrast with the co-info situation where it can be either), and adding them together gives quantities.

Telling the two apart is a challenging problem and is usually done non-classically (using partial information decomposition (PID)).

Both have zero co-info I(X;Y;Z).

The dyadic system has no interactions shared between all three, while the shared bit in the triadic cancels out its XOR to give zero.

The dyadic and triadic systems are two distinct probability distributions on three variables which look the same when considering Shannon entropy measures!

(Pictures from James and Crutchfield 2017)

The three variables have two bits.
~ means the bits are perfectly coupled;
(+) is an XOR gate.

With more than three variables, the co-information can be positive *or negative* (striking fear into the hearts of the measure theorists).

Because of that, the I-measure (so named by Yeung in 1991) is a *signed* measure.

The XOR gate X, Y, Z = XOR(X,Y) has I(X;Y;Z) = -1, for example!

Many Shannon measures look a bit like they ought to have representations as "sets of information" (and they do!)

The mutual information sits in the middle of an I-diagram on 2 variables, and the same quantity is called co-information (or interaction information) for 3 or more variables.

Recently myself and Pedro Mediano showed that you can use classical information theory to distinguish between the triadic and dyadic probability distributions.

Some people thought this was impossible so here's how we did it!

Here's the paper!
👇

arxiv.org/abs/2409.03732

Algebraic Representations of Entropy and Fixed-Sign Information Quantities Many information-theoretic quantities have corresponding representations in terms of sets. Many of these information quantities do not have a fixed sign—for example, the co-information can be both pos...

Happy to announce this work on the structure of entropy published in the journal Entropy!
🎉

In it we give a fun algebraic way of representing information quantities and show the XOR gate is unique in its pure-synergy behaviour!
🧠

Read it here:
👇
www.mdpi.com/1099-4300/27...

Keenan smiling on a Sheffield tram holding a bronze medal that says ‘British Ice Skating’ on it

Keenan posing while entering the ice, wearing a waistcoat and grinning

Despite ice being slippery I got bronze🥉at the British Adult Nationals last night (pre bronze young adult men’s free)!

Amazing skating from George 🥇, Ashe 🥈 and Ross! Well deserved wins and a surprisingly intense category!

#TeamCambridge

Finally migrated from the bad place - are there any psych*delic neuroscience starter packs to follow here?

We have x4 Postdoc positions @ Cambridge, @ the fantastic MRC Cognition & Brain Sciences Unit, working on exciting comp neuro, imaging and NeuroAI projects…

w/ @duncanastle.bsky.social, Petra Vertes + others!

Link here: jobs.cam.ac.uk/job/43796/

If you have any questions, hmu! (Do plz share!)

Two starter packs for Consciousness Science!

(A) go.bsky.app/CgkfpXZ

(B) go.bsky.app/T8z9NP4