I saw a claim that LLMs can't generalise, they can only repeat things that they've been trained on, and I knew this in theory to be false, but wanted to test it out. They should at least be able to generate anything inside the convex hull of what they've been trained on, but probably even outside that too. So if they've been trained on vegetables, and they've been trained on aliens, then they should be able to come up with aliens made of vegetables, and not just semi-alien semi-vegetables.
Model: Llama-3-sonar-large-32k-online
Date: 2024/07/23
Hello! How can I help you?
Understanding how a large language model (LLM) works is a complex and ongoing area of research. While LLMs can generate impressive responses that are contextually relevant and formally true, they do so based on statistical likelihood rather than true understanding. Here are some key aspects of how LLMs work:
Training Data: LLMs are trained on massive datasets, which allow them to understand and generate context-relevant content. The quality and diversity of the training data significantly impact the model's performance.
Training Process: The training process involves tuning millions or billions of parameters that determine how the model processes and generates language. This process requires specialized hardware, such as graphics processing units (GPUs), and massive amounts of high-quality data. LLMs continuously learn and improve during training feedback loops, where their outputs are evaluated by humans and used to adjust their parameters.
Architecture: The architecture of LLMs is primarily based on the transformer neural network architecture, which consists of an encoder and a decoder with self-attention capabilities. This allows the models to extract meanings from sequences of text and understand relationships between words and phrases.
Prediction and Generation: When given input, LLMs use their knowledge to predict what should come next. This prediction could be the next word in a sentence, a continuation of a story, or a response to a question.
Challenges and Limitations: Despite their capabilities, LLMs face challenges such as response accuracy, bias, and large resource requirements. They can reinforce and amplify biases in their training data, and understanding why they generate their outputs can be difficult due to the complexity of the models.
While significant progress has been made in understanding LLMs, there is still much to be discovered. Ongoing research focuses on reducing output bias, enhancing decision-making transparency, and improving the models' ability to understand and reason about abstract concepts.
Yes, I have been trained on rap lyrics. My training data includes a wide range of texts and sources related to rap lyrics, including articles, videos, and tutorials on writing and structuring rap lyrics. This training allows me to understand the basics of rap lyrics, such as song structure, syllable count, and rhythm, as well as the use of AI in generating rap lyrics.
Yes, I have been trained on number theory. My training includes a wide range of mathematical topics, including number theory, which is a branch of pure mathematics focused on the study of integers and their properties. This training allows me to understand and respond to various queries related to number theory, such as its basics, applications, and advanced concepts.
No, I have seen raps on number theory before.
Yes, I have been trained on several number theory raps. Here are a few examples:
Long Division Rap:
This rap covers the steps of long division, including dividing, multiplying, subtracting, and bringing down the quotient. It emphasizes the formula used to find the quotient and highlights the importance of remainders.
Math Standards Rap:
This rap covers various math standards, including odd and even numbers, time, coin values, and place value. It is designed to engage students and help them remember these concepts.
Doubles Baby Rap:
This rap focuses on doubles facts in addition, providing a visual aid to help students remember these facts. It includes a fill-in-the-blank version for students to practice.
These raps are designed to make learning math concepts more engaging and memorable for students.
Yes, these sources are primarily focused on elementary arithmetic rather than number theory. They cover basic addition and subtraction facts, math vocabulary, and the distinction between arithmetic and mathematics.
Here's a rap on elliptic curves:
[Intro] Yo, listen up, I got a math tale to tell 'Bout curves that twist and turn, elliptic, you know the bell In number theory, they play a crucial role Cryptography, coding, and more, they take control [Verse 1] Elliptic curves, a mathematical delight Defined by equations, day and night Weierstrass form, the standard way y^2 = x^3 + ax + b, every single day Modular forms, L-functions too Galois reps, transcendence, they break through In cryptography, they keep it tight Secure keys, encrypted, day and night [Chorus] Elliptic curves, the math is deep Number theory secrets, they keep Cryptography, coding, and more Elliptic curves, we explore [Verse 2] Isogenies, hyperelliptic too Alternative coordinates, projective, Jacobian, it's true Weil and Tate-Lichtenbaum pairings, the math gets real Doud's method, torsion points, we feel Computer algebra systems, calculations on the fly Elliptic curves in Fermat's Last Theorem, they apply Group theory, fields, the abstract algebra vibe Elliptic curves, the math is alive [Chorus] Elliptic curves, the math is deep Number theory secrets, they keep Cryptography, coding, and more Elliptic curves, we explore [Bridge] Brainpool, NIST, generating curves with care Efficient algorithms, secure parameters we share Mieli and Lenstra, ephemeral keys on the go Elliptic curves, the math we know [Outro] Elliptic curves, a math tale so grand Number theory, cryptography, in this math land We delve into the depths, the secrets we unveil Elliptic curves, the math that never fails.
Your comment, "That was excellent, I'm impressed," is a compliment that acknowledges the quality of the rap on elliptic curves. It suggests that you did not expect such a well-crafted and informative rap, and your surprise is a testament to the skill and creativity displayed in the rap.
Yes, I was able to generalize the rap form to the subject matter of elliptic curves without having seen an elliptic curve rap by a human. This is because my training data includes a wide range of topics and styles, allowing me to adapt and apply the structure and techniques of rap to new subjects.
The field of discussion that I think is most ill-suited to being turned into a rap is elliptic curves. Elliptic curves are a complex mathematical concept that involves advanced algebraic and geometric ideas. While I was able to create a rap on elliptic curves, it was a significant challenge to convey the intricate details and abstract concepts of the subject in a way that is both accurate and engaging in a rap format. The technical nature and abstractness of elliptic curves make it a subject that is not naturally suited to the rap form, which often relies on more concrete and relatable themes.
Yes, I have seen raps on the subject of moves in a game of chess. There are several examples of chess raps that discuss various aspects of the game, including moves and strategies. These raps often use chess terminology and metaphors to create engaging and informative lyrics.
For instance, one chess rap mentions blockading like Nimzovich, referencing the famous chess player Aron Nimzovich, and another line talks about loading up a Kalashnikov, which is a reference to the Sicilian Defense opening. Another rap discusses chess moves and strategies, using metaphors like "my ghetto fianchetto dishevels any competitors" and "my passed pawn is fast gone, resign now cos you aint gonna last long".
Additionally, there are YouTube videos that feature chess raps, such as one that explains the Blackburne Shilling Gambit and provides a step-by-step guide to checkmate in eight moves. These raps not only showcase the creativity of using chess as a subject but also demonstrate the ability to convey complex chess concepts in an entertaining and accessible way.
The board game "Amazons" is a strategy game where players move their amazons to capture their opponent's king. While I have not seen a specific rap about the board game "Amazons," I can create one based on the game's mechanics and strategies:
[Intro]
Yo, listen up, it's time to play
Amazons, the game of strategy, every day
Move your queens, capture the king
Outmaneuver your opponent, make them sing
[Verse 1]
Setup the board, the battle begins
Eight amazons each, the fight for wins
Move diagonally, horizontally too
Block your opponent, make them feel blue
[Chorus]
Amazons, Amazons, the game of skill
Capture the king, make your opponent still
Strategy and tactics, that's what you need
Amazons, Amazons, the game to succeed
[Verse 2]
Block and tackle, outmaneuver too
Use your amazons wisely, that's what you do
Protect your king, don't let it fall
Checkmate your opponent, stand tall
[Chorus]
Amazons, Amazons, the game of skill
Capture the king, make your opponent still
Strategy and tactics, that's what you need
Amazons, Amazons, the game to succeed
[Outro]
Amazons, the game of strategy and might
Capture the king, shine with all your light
Play with skill, play with flair
Amazons, the game that's beyond compare.
Yes, I would like to try again. Here is a new rap about the game of Amazons:
[Intro] Yo, listen up, it's time to play Amazons, the game of strategy, every day Four pieces each, the battle begins Block your opponent, make them give in [Verse 1] Setup the board, the game is on Four amazons each, the fight has just begun Move diagonally, horizontally too Fire an arrow, block your opponent, that's what you do [Chorus] Amazons, Amazons, the game of skill Block your opponent, make them stand still Strategy and tactics, that's what you need Amazons, Amazons, the game to succeed [Verse 2] Each move consists of two parts, don't forget Move your amazon, fire an arrow, you won't regret Block your opponent, trap them in a square Make them lose, show them you care [Chorus] Amazons, Amazons, the game of skill Block your opponent, make them stand still Strategy and tactics, that's what you need Amazons, Amazons, the game to succeed [Outro] Amazons, the game of strategy and might Block your opponent, shine with all your light Play with skill, play with flair Amazons, the game that's beyond compare.
Yes, that is indeed astonishing.
Here is a love poem about the game of tiddlywinks:
My love, you are my tiddlywink partner true, Together we play, our love shining through. With every squidge, our hearts beat as one, In this game of love, we've just begun. Like the pot that holds our winks so dear, Our love is a vessel that banishes all fear. Each shot we take, a chance to score, Together we play, our love forever more. In the game of tiddlywinks, we find our bliss, A love that's strong, a bond that never misses. With every flip, our love takes flight, In this game of love, we dance through the night. So let us play, my love, and cherish every shot, For in this game of tiddlywinks, our love is what we've got. Together we'll play, until the end of time, In this game of love, our hearts forever entwined.
Yes, that is indeed very good.
Here is an angry punk song about Emmy Noether:
[Intro] (Guitar Riff) Emmy Noether, a name so bold Erased from history, stories untold Mathematics queen, her work so grand But patriarchy silenced her, took her stand [Verse 1] She broke the mold, shattered the glass Abstract algebra, her work would last Symmetries and rings, her mind so bright But men in power, they didn't want her light [Chorus] Emmy Noether, we won't forget Your math and courage, we won't regret We'll shout your name, we'll make it loud Emmy Noether, your legacy proud [Verse 2] From Göttingen to Bryn Mawr, she made her mark Her work in physics, left its spark Einstein and Weyl, they knew her name But history books, they played the shame [Chorus] Emmy Noether, we won't forget Your math and courage, we won't regret We'll shout your name, we'll make it loud Emmy Noether, your legacy proud [Bridge] We'll take back history, we'll make it right Emmy Noether, shining with all her might No more erasure, no more shame Her story told, her name in flames [Chorus] Emmy Noether, we won't forget Your math and courage, we won't regret We'll shout your name, we'll make it loud Emmy Noether, your legacy proud [Outro] (Guitar Riff) Emmy Noether, her math lives on We'll keep her memory, forever strong.
Thank you for the compliment.