#alphageometry

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The AI Scientist

A model that can produce novel AI papers plus some really cool papers and tech releases this week.

Next Week in The Sequence:

Edge 423: We explore the fundamentals of state space models including the fmaous S4 paper. The tech section provides an overview of NVIDIA’s NIM framework.

Edge 424: We dive into the DeepMind’s amazing AlphaProof and AlphaGeometry-2 that achieved silver medal in the latest international math olympiad.

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📝 Editorial: The AI Scientist

If you read this newsletter, you know that I firmly believe discovering new science might be the ultimate test for AGI. While we are still far from having AI that can formulate something like the Riemann Hypothesis or the Theory of General Relativity, we have made tremendous progress in proving and validating scientific ideas across disciplines such as mathematics, physics, biology, chemistry, and others.

The reason science presents such a challenging bar for AI is that it involves aspects like long-term planning, creativity, multidisciplinary knowledge, multi-step fact-checking, and many other components that are still in the very early stages of development in generative AI.

However, progress is being made.

This week, the Japanese AI startup Sakana AI, in collaboration with several other AI labs, published a paper detailing The AI Scientist, a framework for open-ended scientific discovery. The AI Scientist is capable of conducting open-ended research, executing experiments, generating code, visualizing results, and even presenting them in full reports. In the initial demonstrations, The AI Scientist made several contributions across different areas of AI research, including diffusion models, transformers, and grokking.

The core ideas behind The AI Scientist resemble models such as DeepMind’s Alpha Geometry, AlphaProof, or the NuminaMath model that recently won first prize in the AI Math Olympiad. These models use an LLM for idea formulation, combined with more symbolic models for experimentation. The biggest challenge with this approach is whether the idea-generation portion will quickly hit its limits. Some of the most groundbreaking scientific discoveries in history seem to involve a component of human ingenuity that doesn’t yet appear to be present in LLMs. However, this path holds great potential for exploring new ideas in scientific research.

For now, The AI Scientist represents an exciting advancement in open-ended scientific research.

🔎 ML Research

The AI Scientist

Researchers from Sakana AI, Oxford, University of British Columbia and several other institutions published a paper unveiling the AI Scientist, a pipeline for open ended scientific research using LLMs. The AI Scientist injects AI in different area of scientific research such as ideation, a literature search, experiment planning, experiment iterations, manuscript writing, and peer reviewing —> Read more.

Imagen 3

Google published the technical report of Imagen 3, their marquee text-to-image model. The paper details the training and evaluation details behind Imagen 3 as well as some of the challenges around safety —> Read more.

Mitigating Hallucinations

Google Research published a paper detailing HALVA, a contrastive tuning method that can mitigate hallucinations in language and image assistants. Like other contrastive learning methods, HALVA generates alternative representations of factual tokens with the objective of boosting the probability of the model identifying the correct token —> Read more.

Your Context is Not an Array

Qualcomm Research published a paper that explores the limitations of transformers. The paper suggest that some of the generalization challenges of transformers are related with the inability to perform random memory access within its context window —> Read more.

Mutual Reasoning in LLMs

Microsoft Research published a paper introducing rStar, a self-play multi reasoning approach that seems to improve reasoning capabilities in small language models. rStar uses a generation-discrimination process to decouple the different steps in the reasoning process —> Read more.

Pretraining vs. Fine Tuning

Researchers from Johns Hopkins University published a paper exploring the relationship between pretraining and fine-tuning in LLMs. The paper explores the diminishing returns of fine-tuning after certain scale —> Read more.

🤖 AI Tech Releases

Grok-2

xAI unveiled a new version of Grok that matches the performance of top open source models —> Read more.

SWE-Bench

OpenAI released a subset of the famous SWE-Bench benchmark with human verification —> Read more.

Claude Prompt Caching

Anthropic unveiled prompt caching capabilities for Claude 3.5 Sonnet and Claude 3 Haiku —> Read more.

Airflow 2.10

Apache Airflow 2.10 arrived with a strong focu on AI workflows —> Read more.

AI Risks Database

MIT open sourced a database of over 700 AI risks across different categories —> Read more.

🛠 Real World AI

Image Animation at Meta

Meta discusses the AI techniques used for image animation at scale —> Read more.

Model Reliability at Salesforce

Salesforce discusses the methods used to ensure AI model reliability and performance in their internal pipelines —> Read more.

📡AI Radar

Fei-Fei Li’s World Labs raised $100 million at a $1 billion valuation.

Decentralized AI startup Sahara AI raised $43 million in new funding.

Snowflake announced its Cortex Analyst solution to power self-service analytics with AI.

AI observaility platform Goodfire raised $7 million in new funding.

AI-focused VC Radical Ventures raised a new $800 million fund.

Raunway Gen-3 Turbo showcased very impressive capabilities.

AI-based stock evaluator TipRanks was acquired for $200 million.

Real Estate AI company EliseAI raised $75 million at $1 billion valuation.

Encord, an AI data development platform, raised a $30 million Series B.

RAG as a service platform Ragie raised $5.5 million.

CodeRabbit raised $16 million for using AI to automate code reviews.

AI-based scientific research platform Consensus raised an $11.5 million Series A.

O raciocínio matemático é um aspecto vital das habilidades cognitivas humanas, impulsionando o progresso em descobertas científicas e desenvolvimentos tecnológicos. À medida que nos esforçamos para desenvolver inteligência artificial geral que corresponda à cognição humana, equipar a IA com capacidades avançadas de raciocínio matemático é essencial. Embora os sistemas de IA atuais possam lidar…

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AI at the International Mathematical Olympiad: How AlphaProof and AlphaGeometry 2 Achieved Silver-Medal Standard

Mathematical reasoning is a vital aspect of human cognitive abilities, driving progress in scientific discoveries and technological developments. As we strive to develop artificial general intelligence that matches human cognition, equipping AI with advanced mathematical reasoning capabilities is essential. While current AI systems can handle basic math problems, they struggle with the complex reasoning needed for advanced mathematical disciplines like algebra and geometry. However, this might be changing, as Google DeepMind has made significant strides in advancing an AI system’s mathematical reasoning capabilities. This breakthrough is made at the International Mathematical Olympiad (IMO) 2024. Established in 1959, the IMO is the oldest and most prestigious mathematics competition, challenging high school students worldwide with problems in algebra, combinatorics, geometry, and number theory. Each year, teams of young mathematicians compete to solve six very challenging problems. This year, Google DeepMind introduced two AI systems: AlphaProof, which focuses on formal mathematical reasoning, and AlphaGeometry 2, which specializes in solving geometric problems. These AI systems managed to solve four out of six problems, performing at the level of a silver medalist. In this article, we will explore how these systems work to solve mathematical problems.

AlphaProof: Combining AI and Formal Language for Mathematical Theorem Proving

AlphaProof is an AI system designed to prove mathematical statements using the formal language Lean. It integrates Gemini, a pre-trained language model, with AlphaZero, a reinforcement learning algorithm renowned for mastering chess, shogi, and Go.

The Gemini model translates natural language problem statements into formal ones, creating a library of problems with varying difficulty levels. This serves two purposes: converting imprecise natural language into precise formal language for verifying mathematical proofs and using predictive abilities of Gemini to generate a list of possible solutions with formal language precision.

When AlphaProof encounters a problem, it generates potential solutions and searches for proof steps in Lean to verify or disprove them. This is essentially a neuro-symbolic approach, where the neural network, Gemini, translates natural language instructions into the symbolic formal language Lean to prove or disprove the statement. Similar to AlphaZero’s self-play mechanism, where the system learns by playing games against itself, AlphaProof trains itself by attempting to prove mathematical statements. Each proof attempt refines AlphaProof’s language model, with successful proofs reinforcing the model’s capability to tackle more challenging problems.

For the International Mathematical Olympiad (IMO), AlphaProof was trained by proving or disproving millions of problems covering different difficulty levels and mathematical topics. This training continued during the competition, where AlphaProof refined its solutions until it found complete answers to the problems.

AlphaGeometry 2: Integrating LLMs and Symbolic AI for Solving Geometry Problems

AlphaGeometry 2 is the latest iteration of the AlphaGeometry series, designed to tackle geometric problems with enhanced precision and efficiency. Building on the foundation of its predecessor, AlphaGeometry 2 employs a neuro-symbolic approach that merges neural large language models (LLMs) with symbolic AI. This integration combines rule-based logic with the predictive ability of neural networks to identify auxiliary points, essential for solving geometry problems. The LLM in AlphaGeometry predicts new geometric constructs, while the symbolic AI applies formal logic to generate proofs.

When faced with a geometric problem, AlphaGeometry’s LLM evaluates numerous possibilities, predicting constructs crucial for problem-solving. These predictions serve as valuable clues, guiding the symbolic engine toward accurate deductions and advancing closer to a solution. This innovative approach enables AlphaGeometry to address complex geometric challenges that extend beyond conventional scenarios.

One key enhancement in AlphaGeometry 2 is the integration of the Gemini LLM. This model is trained from scratch on significantly more synthetic data than its predecessor. This extensive training equips it to handle more difficult geometry problems, including those involving object movements and equations of angles, ratios, or distances. Additionally, AlphaGeometry 2 features a symbolic engine that operates two orders of magnitude faster, enabling it to explore alternative solutions with unprecedented speed. These advancements make AlphaGeometry 2 a powerful tool for solving intricate geometric problems, setting a new standard in the field.

AlphaProof and AlphaGeometry 2 at IMO

This year at the International Mathematical Olympiad (IMO), participants were tested with six diverse problems: two in algebra, one in number theory, one in geometry, and two in combinatorics. Google researchers translated these problems into formal mathematical language for AlphaProof and AlphaGeometry 2. AlphaProof tackled two algebra problems and one number theory problem, including the most difficult problem of the competition, solved by only five human contestants this year. Meanwhile, AlphaGeometry 2 successfully solved the geometry problem, though it did not crack the two combinatorics challenges

Each problem at the IMO is worth seven points, adding up to a maximum of 42. AlphaProof and AlphaGeometry 2 earned 28 points, achieving perfect scores on the problems they solved. This placed them at the high end of the silver-medal category. The gold-medal threshold this year was 29 points, reached by 58 of the 609 contestants.

Next Leap: Natural Language for Math Challenges

AlphaProof and AlphaGeometry 2 have showcased impressive advancements in AI’s mathematical problem-solving abilities. However, these systems still rely on human experts to translate mathematical problems into formal language for processing. Additionally, it is unclear how these specialized mathematical skills might be incorporated into other AI systems, such as for exploring hypotheses, testing innovative solutions to longstanding problems, and efficiently managing time-consuming aspects of proofs.

To overcome these limitations, Google researchers are developing a natural language reasoning system based on Gemini and their latest research. This new system aims to advance problem-solving capabilities without requiring formal language translation and is designed to integrate smoothly with other AI systems.

The Bottom Line

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A Silent Evolution in AI: The Rise of Compound AI Systems Beyond Traditional AI Models

As we navigate the recent artificial intelligence (AI) developments, a subtle but significant transition is underway, moving from the reliance on standalone AI models like large language models (LLMs) to the more nuanced and collaborative compound AI systems like AlphaGeometry and Retrieval Augmented Generation (RAG) system. This evolution has gained momentum in 2023, reflecting a paradigm shift on how AI can handle diverse scenarios not solely through scaling up models but through the strategic assembly of multi-component systems. This approach leverages the combined strengths of different AI technologies to tackle complex problems more efficiently and effectively. In this article, we’ll explore the compound AI systems, their advantages, and challenges in designing such systems.

What is Compound AI System (CAS)?

Compound AI System (CAS) is a system that integrates different components, including but not limited to, AI models, retrievers, databases, and external tools to tackle AI tasks effectively. Unlike older AI systems that use just one AI model like the Transformer based LLM, CAS emphasizes integration of multiple tools. Examples of CAS include AlphaGeometry where an LLMs is combined with a traditional symbolic solver to tackle Olympiad problems, and RAG system where an LLM is combined with a retriever and database for answering question related to given documents. Here, it is important to understand the distinction between multimodal AI and CAS. While multimodal AI focuses on processing and integrating data from various modalities—text, images, audio—to make informed predictions or responses like Gemini model, CAS integrates multiple interacting components like language models and search engines to boost performance and adaptability in AI tasks.

Advantages of CAS

CAS offers many advantages over traditional single model-based AI. Some of these advantages are as follows:

Enhanced Performance: CAS combine multiple components, each specialized in a particular task. By leveraging the strengths of individual components, these systems achieve better overall performance. For example, combining a language model with a symbolic solver can lead to more accurate results in programming and logical reasoning tasks.

Flexibility and Adaptability: Compound systems can adapt to diverse inputs and tasks. Developers can swap or enhance individual components without redesigning the entire system. This flexibility allows for rapid adjustments and improvements.

Robustness and Resilience: Diverse components provide redundancy and robustness. If one component fails, others can compensate, ensuring system stability. For instance, a chatbot using retrieval-augmented generation (RAG) can handle missing information gracefully.

Interpretable and Explainable: Using multiple components allows us to interpret how each component contributes to the final output, making these systems interpretable and transparent. This transparency is crucial for debugging and trust.

Specialization and Efficiency: CAS uses multiple components specializing in specific AI tasks. For example, a CAS designed for medical diagnostics might incorporate a component that excels in analyzing medical images, such as MRI or CT scans, alongside another component specialized in natural language processing to interpret patient histories and notes. This specialization allows each part of the system to operate efficiently within its domain, enhancing the overall effectiveness and accuracy of the diagnostics.

Creative Synergy: Combining different components unleashes creativity, leading to innovative capabilities. For instance, a system that merges text generation, visual creation, and music composition can produce cohesive multimedia narratives. This integration enables the system to craft complex, multi-sensory content that would be challenging to achieve with isolated components, showcasing how the synergy between diverse AI technologies can foster new forms of creative expression.

Building CAS: Strategies and Methods

To leverage the benefits of CAS, developers and researchers are exploring various methodologies for their construction. Mentioned below are the two key approaches:

Neuro-Symbolic Approach: This strategy combines the strengths of neural networks in pattern recognition and learning with the logical reasoning and structured knowledge processing capabilities of symbolic AI. The goal is to merge the intuitive data processing abilities of neural networks with the structured, logical reasoning of symbolic AI. This combination aims to enhance AI’s capabilities in learning, reasoning, and adapting. An example of this approach is Google’s AlphaGeometry, which uses neural large language models to predict geometric patterns, while symbolic AI components handle logic and proof generation. This method aims to create AI systems that are both efficient and capable of providing explainable solutions.

Language Model Programming: This approach involves using frameworks designed to integrate large language models with other AI models, APIs, and data sources. Such frameworks allow for the seamless combination of calls to AI models with various components, thereby enabling the development of complex applications. Utilizing libraries like LangChain and LlamaIndex, along with agent frameworks such as AutoGPT and BabyAGI, this strategy supports the creation of advanced applications, including RAG systems and conversational agents like WikiChat. This approach focuses on leveraging the extensive capabilities of language models to enrich and diversify AI applications.

Challenges in CAS Development

Developing CAS introduces a series of significant challenges that both developers and researchers must address. The process involves integrating diverse components, such as the construction of a RAG system involves combining a retriever, a vector database, and a language model. The availability of various options for each component makes design of compound AI system a challenging task, demanding careful analysis of potential combinations. This situation is further complicated by the necessity to carefully manage resources like time and money to ensure the development process is as efficient as possible.

Once the design of a compound AI system is set, it typically undergoes a phase of refinement aimed at enhancing overall performance. This phase entails fine-tuning the interplay between the various components to maximize the system’s effectiveness. Taking the example of a RAG system, this process could involve adjusting how the retriever, vector database, and LLMs work together to improve information retrieval and generation. Unlike optimizing individual models, which is relatively straightforward, optimizing a system like RAG presents additional challenges. This is particularly true when the system includes components such as search engines, which are less flexible in terms of adjustments. This limitation introduces an added layer of complexity to the optimization process, making it more intricate than optimizing single-component systems.

The Bottom Line

AI Masters Olympiad Geometry The team behind Google’s Deep Mind have just released details of a new AI system:  AlphaGeometry This has been specifically trained to solve classical geometry problems – and already is now at the level of a Gold Medalist at the International Olympiad (considering only geometry problems).  This is an incredible achievement – as in order to solve classical geometry…

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AlphaGeometry: How DeepMind’s AI Masters Geometry Problems at Olympian Levels?

In the ever-evolving landscape of artificial intelligence, the conquest of cognitive abilities has been a fascinating journey. Mathematics, with its intricate patterns and creative problem-solving, stands as a testament to human intelligence. While recent advancements in language models have excelled in solving word problems, the realm of geometry has posed a unique challenge. Describing the visual and symbolic nuances of geometry in words creates a void in training data, limiting AI’s capacity to learn effective problem-solving. This challenge has prompted DeepMind, a subsidiary of Google, to introduce AlphaGeometry—a groundbreaking AI system designed to master complex geometry problems.

The Limitations of Symbolic AI in Geometry

The prevailing AI approach for geometry relies heavily on rules crafted by humans. While effective for simple problems, this symbolic AI encounters difficulties in flexibility, particularly when faced with unconventional or new geometric scenarios. The inability to predict hidden puzzles or auxiliary points crucial for proving complex geometry problems highlights the limitations of relying solely on predefined rules. Moreover, creating exhaustive rules for every conceivable situation becomes impractical as problems increase in complexity, resulting in limited coverage and scalability issues.

AlphaGeometry’s Neuro-Symbolic Approach

DeepMind’s AlphaGeometry combines neural large language models (LLMs) with symbolic AI to navigate the intricate world of geometry. This neuro-symbolic approach recognizes that solving geometry problems requires both rule application and intuition. LLMs empower the system with intuitive abilities to predict new geometric constructs, while symbolic AI applies formal logic for rigorous proof generation.

In this dynamic interplay, the LLM analyzes numerous possibilities, predicting constructs crucial for problem-solving. These predictions act as clues, aiding the symbolic engine in making deductions and inching closer to the solution. This innovative combination sets AlphaGeometry apart, enabling it to tackle complex geometry problems beyond conventional scenarios.

AlphaGeometry’s neuro-symbolic approach aligns with dual process theory, a concept that divides human cognition into two systems—one providing fast, intuitive ideas, and the other, more deliberate, rational decision-making. LLMs excel at identifying general patterns but often lack rigorous reasoning, while symbolic deduction engines rely on clear rules but can be slow and inflexible. AlphaGeometry harnesses the strengths of both systems, with the LLM guiding the symbolic deduction engine towards likely solutions.

To overcome the scarcity of real data, researchers at DeepMind trained AlphaGeometry’s language model using synthetic data. Nearly half a billion random geometric diagrams were generated, and the symbolic engine analyzed each diagram, producing statements about its properties. These statements were then organized into 100 million synthetic data points to train the language model. The training occurred in two steps: pretraining the language model on all generated synthetic data and fine-tuning it to predict useful clues required for solving problems using symbolic rules.

AlphaGeometry’s Olympiad-Level Performance

AlphaGeometry is tested based on the criteria established by the International Mathematical Olympiad (IMO), a prestigious competition renowned for its exceptionally high standards in mathematical problem-solving. Achieving a commendable performance, AlphaGeometry successfully solved 25 out of 30 problems within the designated time, demonstrating a performance on par with that of an IMO gold medalist. Notably, the preceding state-of-the-art system could only manage to solve 10 problems. The validity of AlphaGeometry’s solutions was further affirmed by a USA IMO team coach, an experienced grader, recommending full scores for AlphaGeometry’s solutions.

The Impact of AlphaGeometry

AlphaGeometry’s remarkable problem-solving skills represent a significant stride in bridging the gap between machine and human thinking. Beyond its proficiency as a valuable tool for personalized education in mathematics, this new AI development carries the potential to impact diverse fields. For example, in computer vision, AlphaGeometry can elevate the understanding of images, enhancing object detection and spatial comprehension for more accurate machine vision. AlphaGeometry’s ability for dealing with complicated spatial configurations hold the potential to transform fields like architectural design and structural planning. Beyond its practical applications, AlphaGeometry could be useful exploring theoretical fields like physics. With its capacity to model complex geometric forms, it could play a pivotal role in unraveling intricate theories and uncovering novel insights in the realm of theoretical physics.

Limitations of AlphaGeometry

While AlphaGeometry showcases remarkable advancements in AI’s ability to perform reasoning and solve mathematical problems, it faces certain limitations. The reliance on symbolic engines for generating synthetic data poses challenges for its adaptability in handling a broad range of mathematical scenarios and other application domains. The scarcity of diverse geometric training data poses limitations in addressing nuanced deductions required for advanced mathematical problems. Its reliance on a symbolic engine, characterized by strict rules, could restrict flexibility, particularly in unconventional or abstract problem-solving scenarios. Therefore, although proficient in “elementary” mathematics, AlphaGeometry currently falls short when confronted with advanced, university-level problems. Addressing these limitations will be pivotal for enhancing AlphaGeometry’s applicability across diverse mathematical domains.

The Bottom Line