Félix de Chaumont Quitry retweetledi
Félix de Chaumont Quitry
176 posts
Félix de Chaumont Quitry
@FelixCQ
Research engineer @GoogleDeepMind. Large language models for audio generation.
Zurich, Switzerland Katılım Mayıs 2010
375 Takip Edilen113 Takipçiler
@jamestanton If p is <= 50%, we end up with yesterday's puzzle, and if p is > 50%, it's impossible. So the answer is just half of yesterday's answer: ln(2) - 1/2
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Values p, q each chosen from [0, 100] at random (uniform distribution).
Hold up a stick, cut off p% of its length from the left end. Hold up the right piece,cut of q% of its length from its right end.
Try to make a triangle with the three pieces you have.
Chances possible?
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@jamestanton The variation here is trickier than I thought! I'm getting ln(4) - 1, so approximately 38.6% chance
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A Slight Variation on a Classic:
A stick is broken at random into two pieces, and then the longest piece is again broken into two pieces. (Each break point is chosen from a uniform distribution).
What are the chances that the three pieces can be used to make a triangle?
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@steph_bernard69 @jamestanton I thought this was the answer initially but all vertical slices in your diagram should have the same probability (even though they have different lengths), so using the area like this doesn't work, I believe
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@anishgiri In group theory, a transposition is a permutation of size 2
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@jamestanton Not as clever as the other answers, but simply inverting the system of 3 equations yields all three coefficients, and these are quite pretty as they involve elementary symmetric function
Q(x) = (a+b+c) x^2 - (ab+bc+ca) x + abc
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Three points (a,a^3), (b,b^3), (c,c^3) on the graph of y = x^3. Where does the quadratic that passes through those points cross the y-axis?
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@jamestanton I misread the question again. I don't think we can say much about _where_ the third cross is happening. Also it may cross three more times, so we can't really talk about "the" third crossing point.
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@jamestanton After dividing by (x-a) and (x-b) we'll be left with a polynomial of degree 3, which should have at least one real root. So the line should cross a third time, at least
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In my atrocious handwriting, here's an argument showing where a line crosses the curve y = x^3 a third time.
Can anything reasonable be said about the same setup for y = x^5? If a line crosses its graph at (a,a^5) and (b,b^5), where does it cross a third time?
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@jamestanton With integer coefficients, the value of P(x) % 3 is the same as P(x % 3) % 3, so yes
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A polynomial P has integer coefficients.
If P(-1), P(0), and P(1) are each multiples of three, must P(9437) also be a multiple of three?
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@jamestanton Actually sorry, the coefficients will not be integers in the general case, I think
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@jamestanton The Lagrange interpolation polynomial would work, but I don't know if the expression simplifies nicely
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The polynomial P(x) = a + b - x has
P(a) =b and P(b) = a.
Find a polynomial with integer coefficients along with three distinct integers a, b, c such that P(a) = b, P(b) = c, and P(c) = a.
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Félix de Chaumont Quitry retweetledi
🚨 New paper: Introducing MIND (Monge Inception Distance)
Everyone agrees that FID is broken, requires too many samples, slowing down evals.
MIND requires 10x fewer samples, is more robust, faster to compute.
Our new drop-in replacement for evaluating generative models. 🧵👇
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@fofrAI Do you know if this model would be able to hold a phoneme sound like "m" or "s" for 5 seconds, like you would if you were demonstrating the sounds to a kid?
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btw, I used this little vibe-coded app I made on AI Studio to turn the audio into video:
audio-as.video
fofr@fofrAI
[excitedly] I've been having fun with Gemini 3.1 Flash TTS, the audio tags are really flexible, you can do so much with them. [like dracula] I can't believe things like that just work.
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Félix de Chaumont Quitry retweetledi
Our most expressive and steerable TTS model yet! Designed to give builders granular control over AI-generated speech, Gemini 3.1 Flash TTS is really fun to play with! Available in preview today - for devs via the Gemini API & @GoogleAIStudio + for enterprises on Vertex AI
Logan Kilpatrick@OfficialLoganK
Introducing Gemini 3.1 Flash TTS 🗣️, our latest text to speech model with scene direction, speaker level specificity, audio tags, more natural + expressive voices, and support for 70 different languages. Available via our new audio playground in AI Studio and in the Gemini API!
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Félix de Chaumont Quitry retweetledi
Gemini 3.1 Flash TTS is our most controllable text-to-speech model yet.
With new Audio Tags, you can easily direct vocal style, delivery, and pace through text commands. 🧵
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@jamestanton Based on the size of the last group, one can derive
u_n = sum_{k=1}^{n} k * u_{n-k}
which can be rearranged into
u_n = 3 * u_{n-1} - u_{n-2}
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21 happens to be a Hemachandra/Fibonacci number.
Coincidence?
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@jamestanton There are three ways to continue the sequence: single green, single pink, linked green. But one can't continue with a linked green if the previous color was pink (which has to be a single pink). So we get again alternating Fibonacci numbers:
u_n = 3 * u_{n-1} - u_{n-2}
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Today's Puzzle:
Place N dots in a row.
Touching dots must be green. Single dots can be pink or green.
Is the count of possibilities always a Hemachandra/Fibonacci number?
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@jamestanton u_0 = 1
u_1 = 3
u_n = 3 * u_{n-1} - u_{n-2}
which funnily enough, yields every other Fibonacci number :-)
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Today's Puzzle:
Arrange red, yellow, or green dots in a row with no red dot immediately to the right of a green dot.
21 such arrangements with 3 dots.
How many with 4 dots in a row? 5? 6?
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Growing Graphs demo is finally out! 🕸️✨
🔗 znah.net/graphs/
Videos from a few months ago finally meet a finished implementation, thanks Gemini for doing the boring parts.
Inspired by Paul Cousin's Graph-Rewriting Automata: like a Game of Life, but cells can split if they want to
#GenerativeArt #WASM #SwissGL
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@Math_files This is actually true for 2-adic numbers (for which the sum converges).
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