Authors

Announcements

April 22, 2024

Introducing Prime Intellect

Prime Intellect is building the infrastructure for decentralized AI development at scale. We aggregate global compute and enable researchers to collaboratively train state-of-the-art models through distributed training across clusters.

Through Prime Intellect, anyone will be able to contribute compute, capital and code to collaboratively train open AI models and share in their ownership and benefits. We envision this enabling a new wave of open AI progress, from community-driven language models to scientific breakthroughs.

Our Masterplan

1. Aggregate global compute (live in beta): Our platform brings together a diverse array of GPUs, from on-demand, spot to different durations.

2. Develop distributed training frameworks to enable collaborative model development across global, heterogeneous hardware. (In development)

3. Collaboratively train and contribute to open AI models in high-impact domains like language, agents, code, and science.

4. Launch a decentralized protocol for collective ownership of AI models. Collaboratively build towards aligned AGI that benefits all of humanity.

Aggregating Global Compute and Enabling Distributed Training

Our platform (live in beta) aggregates global supply from leading centralized and decentralized GPU providers. This allows us to offer the most cost-effective, scalable on-demand compute. We're preparing to provide access to bigger clusters of 16-128+ GPUs. This scale will enable the development of groundbreaking AI models that were previously out of reach for most researchers and organizations.

We are also developing a framework to enable distributed training across multiple clusters. While there are significant challenges to solve, we believe this is key to making large-scale AI development more accessible. We've begun testing early approaches and are working towards a production-ready orchestration solution.

Read our deep dive into the state of decentralized training.

Intelligence: Developing Impactful Collectively-owned AI Models

Through Prime Intellect, anyone can contribute resources to train impactful AI models. We are starting with AI model efforts in the following areas. Apply to join our research efforts and receive a fast compute grant to work on some of the highest impact AI research and models.

Build large language models like open-source software, allowing for continual improvement and model merging. We envision a future where all training compute can be built upon by everyone so that all efforts towards intelligence are cumulative. (Inspired by Colin Raffel).
Build coding agents that automate software development by deeply understanding code, boosting productivity. This paves the path to higher level reasoning and economically valuable work.
Create scientific foundation models to accelerate research in longevity drug discovery, materials science and other scientific areas.

Protocol: Enabling Collective Ownership and Governance

The Prime Intellect (PI) protocol offers the infrastructure and crypto-economic building blocks for decentralized AI development. It will reward participants for contributing compute, code, and capital, and enables collective governance of AI models and the value they generate:

Scalable, distributed compute marketplaces for accessible, affordable global AI training
Collectively owned AI models, rewarding contributions of resources and improvements.
Sustainable AI model funding via programmable licenses.
Exploring decentralized governance frameworks to align AI progress with collective human values.

Our Investors

We've raised $5.5M in seed funding from investors who share our vision of democratizing AI, co-led by Distributed Global and Coinfund with participation from Compound, Collab+Currency and Juan Benet with Protocol Labs.

As well as exceptional angels such as Clem Delangue (Huggingface), Dylan Patel (SemiAnalysis), Shivani (Nous Research), Riva Tez (Layerzero), Erik Voorhees (Shapeshift), Dcbuilder (Worldcoin), Robert Drost (Eigenlayer), Ben Fielding (Gensyn), IDTheory, Scott Moore (Gitcoin), Andrew Kang (Mechanism Capital), Joe Lallouz (Coinbase Cloud), Tyler Golato and Paul Kohlhaas (Molecule), Bool Capital (Wormhole), DCF God, Fabian0x (Tribute Labs), Steve Waterhouse (Orchid), Sami Kassab (OSS), Yoni Ben-Shimon, Justin Mares, Janine Leger, Gmoney and many more.

The backing of this diverse group of mission-aligned builders and investors accelerates Prime Intellect's development, helping to make transformative AI accessible to everyone.

Founders and Team

Our team combines deep expertise in state-of-the-art AI foundation models, distributed training systems, decentralized AI and science, tokenizing and rethinking intellectual property, DAOs, and decentralized networks.

Johannes' research experience on scalable AI foundation model training at Aleph Alpha uniquely positions us to drive unprecedented decentralized AI development. Vincent's prior experience leading AI and ecosystem at Molecule, as well as co-initiating the decentralized science collective VitaDAO, provides experience in building global research communities.

Join Us in Building the Open Future of AI

The power to shape the future of AI should not be concentrated in the hands of a few, but open to anyone with the ability to contribute. We invite you to join us in building a more distributed and impactful future for AI:

If you are relentlessly ambitious and want to make this happen, apply for our open roles.
Collaborate on our AI model initiatives.
Sign up to contribute compute or capital and earn ownership in groundbreaking models.

‍

Onwards,
‍Vincent Weisser + Johannes Hagemann
‍

Join our community!

Website: primeintellect.ai‍

Twitter / X: x.com/primeintellect

Discord: https://discord.gg/RC5GvMbfDf

Mail: contact@primeintellect.ai

Careers: https://jobs.ashbyhq.com/PrimeIntellect

Disclaimer: This announcement is for informational purposes only and does not constitute investment advice or an offer to sell securities. The views expressed are subject to change.

Eurus-2-PRIME

System Prompt

When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process. [ASSESS] [ADVANCE] [VERIFY] [SIMPLIFY] [SYNTHESIZE] [PIVOT] [OUTPUT] You should strictly follow the format below: [ACTION NAME] # Your action step 1 # Your action step 2 # Your action step 3 ... Next action: [NEXT ACTION NAME]

User

Quadratic polynomials $P(x)$ and $Q(x)$ have leading coefficients $2$ and $-2,$ respectively. The graphs of both polynomials pass through the two points $(16,54)$ and $(20,53).$ Find $P(0) + Q(0).$

Eurus-2-PRIME

[ASSESS]

We are given two quadratic polynomials $P(x)$ and $Q(x)$ with leading coefficients $2$ and $-2$, respectively. The graphs of both polynomials pass through the points $(16,54)$ and $(20,53)$. We need to find the value of $P(0) + Q(0)$.

[ADVANCE]

Let's express the quadratic polynomials $P(x)$ and $Q(x)$ in the general form:
$ P(x) = 2x^2 + bx + c $
$ Q(x) = -2x^2 + dx + e $

Since the graphs of both polynomials pass through the points $(16,54)$ and $(20,53)$, we can substitute these points into the equations of $P(x)$ and $Q(x)$ to form a system of equations.

For $P(x)$:
$ P(16) = 2(16)^2 + 16b + c = 54 $
$ 512 + 16b + c = 54 $
$ 16b + c = -458 \quad \text{(Equation 1)} $

$ P(20) = 2(20)^2 + 20b + c = 53 $
$ 800 + 20b + c = 53 $
$ 20b + c = -747 \quad \text{(Equation 2)} $

For $Q(x)$:
$ Q(16) = -2(16)^2 + 16d + e = 54 $
$ -512 + 16d + e = 54 $
$ 16d + e = 566 \quad \text{(Equation 3)} $

$ Q(20) = -2(20)^2 + 20d + e = 53 $
$ -800 + 20d + e = 53 $
$ 20d + e = 853 \quad \text{(Equation 4)} $

[ADVANCE]

Now, we can solve the system of equations for $P(x)$:
Subtract Equation 1 from Equation 2:
$ (20b + c) - (16b + c) = -747 - (-458) $
$ 4b = -289 $
$ b = -\frac{289}{4} $

Substitute $b = -\frac{289}{4}$ into Equation 1:
$ 16\left(-\frac{289}{4}\right) + c = -458 $
$ -1156 + c = -458 $
$ c = 698 $

So, for $P(x)$, we have:
$ P(x) = 2x^2 - \frac{289}{4}x + 698 $
$ P(0) = 698 $

Next, we can solve the system of equations for $Q(x)$:
Subtract Equation 3 from Equation 4:
$ (20d + e) - (16d + e) = 853 - 566 $
$ 4d = 287 $
$ d = \frac{287}{4} $

Substitute $d = \frac{287}{4}$ into Equation 3:
$ 16\left(\frac{287}{4}\right) + e = 566 $
$ 1148 + e = 566 $
$ e = -582 $

So, for $Q(x)$, we have:
$ Q(x) = -2x^2 + \frac{287}{4}x - 582 $
$ Q(0) = -582 $

[ADVANCE]

Finally, we can find $P(0) + Q(0)$:
$ P(0) + Q(0) = 698 + (-582) = 116 $

So, the value of $P(0) + Q(0)$ is $\boxed{116}$.

INTELLECT-MATH-7B-SFT (ours)

System Prompt

Solve the following math problem efficiently and clearly. Think carefully and step by step about your response and reason before providing a final response. Conclude your response with: \n\nTherefore, the final answer is: $\\boxed{answer}$. I hope it is correct.\n\nWhere [answer] is just the final number or expression that solves the problem.

User

Quadratic polynomials $P(x)$ and $Q(x)$ have leading coefficients $2$ and $-2,$ respectively. The graphs of both polynomials pass through the two points $(16,54)$ and $(20,53).$ Find $P(0) + Q(0).$

INTELLECT-MATH-7B-SFT

So I've got this problem here about quadratic polynomials $P(x)$ and $Q(x)$. $P(x)$ has a leading coefficient of $2$, and $Q(x)$ has a leading coefficient of $-2$. Both polynomials pass through the points $(16,54)$ and $(20,53)$. I need to find $P(0) + Q(0)$.

First, since both $P(x)$ and $Q(x)$ are quadratic polynomials, I can express them in the general form:

$P(x) = 2x^2 + bx + c$

$Q(x) = -2x^2 + dx + e$

Wait, actually, the leading coefficient is the coefficient of the highest power of $x$, which for a quadratic is $x^2$. So yes, $P(x) = 2x^2 + bx + c$ and $Q(x) = -2x^2 + dx + e$.

Now, both polynomials pass through the points $(16,54)$ and $(20,53)$. That means when $x=16$, $P(16)=54$, and when $x=20$, $P(20)=53$. Similarly for $Q(x)$.

So, I can set up equations using these points.

First, for $P(x)$:

$P(16) = 2(16)^2 + b16 + c = 54$

Similarly, $P(20) = 2(20)^2 + b20 + c = 53$

Let me calculate $16^2$ and $20^2$:

$16^2 = 256$

$20^2 = 400$

So,

$P(16): 2256 + 16b + c = 54 \Rightarrow 512 + 16b + c = 54 \Rightarrow 16b + c = 54 - 512 \Rightarrow 16b + c = -458$

$P(20): 2400 + 20b + c = 53 \Rightarrow 800 + 20b + c = 53 \Rightarrow 20b + c = 53 - 800 \Rightarrow 20b + c = -747$

Now, I have two equations:

1) $16b + c = -458$

2) $20b + c = -747$

I can subtract equation 1 from equation 2 to eliminate $c$:

$(20b + c) - (16b + c) = -747 - (-458)$

$20b + c - 16b - c = -747 + 458$

$4b = -289$

So, $b = -289 / 4 = -72.25$

Wait, but coefficients are usually integers, but maybe not. Let me check.

Now, plug $b$ back into one of the equations to find $c$. Let's use equation 1:

$16(-72.25) + c = -458$

$-1156 + c = -458$

$c = -458 + 1156 = 698$

So, $P(x) = 2x^2 - 72.25x + 698$

Hmm, $P(0)$ would be $c$, which is $698$.

Now, let's do the same for $Q(x)$.

$Q(16) = -2*(16)^2 + d16 + e = 54 \Rightarrow -2256 + 16d + e = 54 \Rightarrow -512 + 16d + e = 54 \Rightarrow 16d + e = 54 + 512 \Rightarrow 16d + e = 566$

$Q(20) = -2*(20)^2 + d20 + e = 53 \Rightarrow -2400 + 20d + e = 53 \Rightarrow -800 + 20d + e = 53 \Rightarrow 20d + e = 53 + 800 \Rightarrow 20d + e = 853$

Now, equations for $Q(x)$:

1) $16d + e = 566$

2) $20d + e = 853$

Subtract equation 1 from equation 2:

$(20d + e) - (16d + e) = 853 - 566$

$4d = 287$

$d = 287 / 4 = 71.75$

Now, plug $d$ back into equation 1:

$1671.75 + e = 566 \Rightarrow 1148 + e = 566 \Rightarrow e = 566 - 1148 = -582$

So, $Q(x) = -2x^2 + 71.75x - 582$

Therefore, $Q(0) = e = -582$

Now, $P(0) + Q(0) = 698 + (-582) = 116$

Wait, but the problem says "present the answer in LaTeX format: \boxed{Your answer}"

So, I should write $\boxed{116}$

But let me double-check my calculations to make sure I didn't make any mistakes.

First, for $P(x)$:

$P(16) = 2(256) + 16b + c = 512 + 16b + c = 54 \Rightarrow 16b + c = -458$

$P(20) = 2*(400) + 20b + c = 800 + 20b + c = 53 \Rightarrow 20b + c = -747$

Subtracting: $4b = -289 \Rightarrow b = -72.25$

Then, $c = -458 - 16*(-72.25) = -458 + 1156 = 698$

Similarly for $Q(x)$:

$Q(16) = -2*(256) + 16d + e = -512 + 16d + e = 54 \Rightarrow 16d + e = 566$

$Q(20) = -2*(400) + 20d + e = -800 + 20d + e = 53 \Rightarrow 20d + e = 853$

Subtracting: $4d = 287 \Rightarrow d = 71.75$

Then, $e = 566 - 16*71.75 = 566 - 1148 = -582$

So, $P(0) = 698$, $Q(0) = -582$, sum is $116$.

Seems correct.

Final Answer

$\boxed{116}$

INTELLECT-MATH-7B (ours)

System Prompt

User

Quadratic polynomials $P(x)$ and $Q(x)$ have leading coefficients $2$ and $-2,$ respectively. The graphs of both polynomials pass through the two points $(16,54)$ and $(20,53).$ Find $P(0) + Q(0).$

INTELLECT-MATH-7B

So I have two quadratic polynomials, $P(x)$ and $Q(x)$, with leading coefficients 2 and -2, respectively. Both pass through the points $(16,54)$ and $(20,53)$. I need to find $P(0) + Q(0)$.

First, since both are quadratic polynomials, I can express them in the general form:

$P(x) = 2x² + bx + c$

$Q(x) = -2x² + dx + e$

But since both pass through the points $(16,54)$ and $(20,53)$, I can set up equations using these points.

For $P(x)$:

$P(16) = 2*(16)² + b \cdot 16 + c = 54$

$P(20) = 2(20)² + b \cdot 20 + c = 53$

Similarly for $Q(x)$:

$Q(16) = -2(16)² + d \cdot 16 + e = 54$

$Q(20) = -2(20)² + d \cdot 20 + e = 53$

Let's compute the squares:

$16² = 256$

$20² = 400$

So for $P(x)$:

$2256 + 16b + c = 54 \Rightarrow 512 + 16b + c = 54 \Rightarrow 16b + c = 54 - 512 = -458 \quad ...(1)$

$2400 + 20b + c = 53 \Rightarrow 800 + 20b + c = 53 \Rightarrow 20b + c = 53 - 800 = -747 \quad ...(2)$

For $Q(x)$:

$-2256 + 16d + e = 54 \Rightarrow -512 + 16d + e = 54 \Rightarrow 16d + e = 54 + 512 = 566 \quad ...(3)$

$-2400 + 20d + e = 53 \Rightarrow -800 + 20d + e = 53 \Rightarrow 20d + e = 53 + 800 = 853 \quad ...(4)$

Now, I have two systems of linear equations:

For $P(x)$:

$16b + c = -458 \quad ...(1)$

$20b + c = -747 \quad ...(2)$

Subtract equation (1) from equation (2):

$(20b + c) - (16b + c) = -747 - (-458)$

$4b = -289 \Rightarrow b = -\frac{289}{4}$

Now plug $b$ back into equation (1):

$16\left(-\frac{289}{4}\right) + c = -458 \Rightarrow -1156 + c = -458 \Rightarrow c = -458 + 1156 = 698$

So $P(x) = 2x² - \frac{289}{4}x + 698$

For $Q(x)$:

$16d + e = 566 \quad ...(3)$

$20d + e = 853 \quad ...(4)$

Subtract equation (3) from equation (4):

$(20d + e) - (16d + e) = 853 - 566$

$4d = 287 \Rightarrow d = \frac{287}{4}$

Now plug $d$ back into equation (3):

$16\left(\frac{287}{4}\right) + e = 566 \Rightarrow 1148 + e = 566 \Rightarrow e = 566 -1148= -582$

So $Q(x)=-2x^{2}+\frac{287}{4}x-582$.

Now, $P(0)=c=698$.

$Q(0)=e=-582$.

Therefore, $P(0)+Q(0)=698+(-582)=116$.

Final Answer

$\boxed{116}$.

Authors

Vincent

Johannes

Acknowledgements

SYNTHETIC-1 Release: Two Million Collaboratively Generated Reasoning Traces from Deepseek-R1

We are releasing SYNTHETIC-1, the largest open reasoning dataset generated from Deepseek-R1, collaboratively generated by compute contributors across the globe.