The computational infrastructure is becoming a vast interconnected fabric of formal methods, including per a major shift from 2d grids to 3d graphs in machine learning architectures The implication is systems-level digital science at unprecedented scale for discovery in a diverse range of scientific disciplines

1. Orange County CA, 12 Nov 2023
Slides: http://slideshare.net/LaBlogga
Melanie Swan, PhD, MBA
DIYgenomics.org (Principal Investigator)
University College London (Research Associate)
How the formalization of the computational
infrastructure is leading to scientific advance
AI Science

2. 12 Nov 2023
AI Science 1
Formalizing natural inspiration into reality

3. 12 Nov 2023
AI Science 2
Research Program
2015 2019 2020
Blockchain Blockchain
Economics
Quantum
Computing
Quantum Computing
for the Brain
2022
AI Math Agents:
https://arxiv.org/abs/2307.02502
https://huggingface.co/papers/2307.02502
AI Genomics and Alzheimer’s Disease:
https://www.diygenomics.org/files/AI_Math_Agents_poster_AAIC2023.pdf
Aim: AI Science for humanity-benefiting applications
in genomic medicine, health, and well-being

4. 12 Nov 2023
AI Science
Thesis
3
The computational infrastructure is becoming a vast
interconnected fabric of formal methods, including per a major
shift from 2d grids to 3d graphs in machine learning architectures
The implication is systems-level digital science at unprecedented
scale for discovery in a diverse range of scientific disciplines

5. 12 Nov 2023
AI Science
Agenda
 AI and Computational Infrastructure
 Math Agents
 Quantum Computing
 Conclusion, Risks,
AI Alignment
4

6. 12 Nov 2023
AI Science
Terms
 AI: approximating human intelligence with machines
 Data science methods including machine learning, deep neural nets, LLMs
(large language models), GNNs (graph neural nets)
 Quantum Computing: performing computation with
quantum objects (atoms, ions, photons)
 Manipulate through logic gates with magnetic fields and lasers, using
quantum mechanical principles (superposition, entanglement)
 Mathematics: the study of numbers, shapes, and
space with axiomatic systems and symbolic logic
 Computational infrastructure: terrestrial-and-beyond
global fiberoptic ICT network computation apparatus
 Hardware/software: data centers, wireless networks, supercomputers,
blockchains, quantum sensing, deep space nets, internet of things
 Knowledge graph: information represented in a graph structure
5
AI: Artificial Intelligence; ICT: Information Communications Technology; LLM: Large Language Model
“AI” generally referring to the suite of technologies
including LLMs, machine learning, deep neural nets

7. 12 Nov 2023
AI Science 6
AI is the Interface
Computational Infrastructure
Natural
Language
LLMs
Human
Code, Math,
Physics, Chemistry,
Astronomy, Biology
Formal
Language
LLMs: Large Language Models

8. 12 Nov 2023
AI Science 7
AI as the Overlay
Computational
Infrastructure
LLMs: Large Language Models; ML: Machine Learning; GNN: Graph Neural Nets
Scale
Domains
Quantum Classical Relativistic
Domain-specific Matter, and Time and Space Properties
Machine learning: using algorithms and data to learn from experience and improve performance
Technology Layers:
AI (LLM, ML, GNN)
Blockchains
LLM: specialized application of machine learning for natural language processing and generation
Blockchain: secure decentralized ledger as a permanent record of events

9. 12 Nov 2023
AI Science
Interconnected Knowledge Graph
 All-to-all connectivity of formal methods in the
knowledge graph, integrated computational fabric
8
Physics
Mathematics
Chemistry
Software Code
Interconnected Knowledge Graph
Separate Disciplines

10. 12 Nov 2023
AI Science
Examples
Integrated Fabric of Formal Methods
9
Interconnected Knowledge Graph
Chaotic Fluid Flow
 Math-Physics-Biology-Quantum-NNs
 Math-Biology, Genome Math
 Number-theory max bound neutral mutations
(25%) (sum-of-digits/Tagaki) (Mohanty 2023)
 Recover statistical properties of cancer vs
normal cells (Braun 2023)
 Machine Learning-Quantum Computing
 Efficient quantum algorithm for dissipative
nonlinear differential equations (Liu 2021)
 Surface code (quantum error-correction code)
transformer NN (Bausch 2023)
 Machine Learning-Physics
 HEP particle reconstruction NN (Iiyama 2021)

11. 12 Nov 2023
AI Science
Language Space Program Space Mathematics Space
Infinite dimensionality
Infinite dimensionality
Software 1.0 (solely human-written)
Software 2.0 (AI code assistants)
Software 1.0
Possibility Space Thinking
Sources: Swan, M., Kido, T., Roland, E. & dos Santos, R.P. (2023). AI Math Agents: Computational Infrastructure, Mathematical
Embedding, and Genomics. arXiv: 2307.02502; Karpathy (2015). https://karpathy.medium.com/software-2-0-a64152b37c35
Computation-aided math: 4-color theorem proof (2005, Coq), Feit-Thompson theorem (2012, Coq), Lean Theorem Prover
Software 2.0
Math 1.0
Math 2.0
Math 1.0 (solely human-discovered)
Math 2.0 (computer-aided)
Computer algebra
systems, automated
theorem proving,
lemma generators
 Human-derived efforts: one dot in possibility space
 No need to manually write code when a “plow” is available
 Infer math corpus from Stack Exchange vs OCR-extract PDFs
Lots of human natural language now
formalized in web-accessible LLMs

12. 12 Nov 2023
AI Science
AI-first Digital Biology
Entire Possibility Space
 New approaches: drug design vs discovery (Bronstein 2021), treat
pathway not condition (Kellis 2023), protein->DNA (AlphaMissense 2023)
224 million (human)
Protein Space Missense
Mutation Space
71 million (human)
pathogenic (32%)
benign (57%)
DNA Mutation Space
Missense (58%)
Nonsense (10%)
Frameshift (8%), Splice (6%),
Indel (5%), Other (13%)
Small Molecule Space
1060
Connectome Space
Mouse
Fly
Human
AlphaMissense
Sources: https://www.scienceabc.com/pure-sciences/what-is-mutation-definition-different-types-biology-genetic-missense-
nonsense.html, https://alphafold.ebi.ac.uk/
Worm
DNA Sequence Space
3 bn bp (human)
AlphaFold
.
DNA
RNA
Protein
Drug design vs drug discovery
(“MidJourney for chemistry”)
Isomorphic Labs
Halicin
Pathways of genomic variation,
epigenetic methylation, gene
regulatory network

13. 12 Nov 2023
AI Science
Agenda
 AI and Computational Infrastructure
 Math Agents
 Quantum Computing
 Conclusion, Risks,
AI Alignment
12

14. 12 Nov 2023
AI Science
Foundational Technology
LLMs (Large Language Models)
 NN: function approximator, learns from data
 LLM (large language model): machine learning model
that can process natural language (generate text,
answer questions, translate languages)
 Pre-trained on very-large data corpora with bns/tns parameters
 Parameter: weight of connection between values
 “the cat is on the ___”, dog “bark”, water “leak”
 Aim: next word prediction
 GPT-3, GPT-4 (OpenAi)
 LaMDA, PaLM (Google)
 LLaMa (Meta)
13
NN: neural network

15. 12 Nov 2023
AI Science
Foundational Technology
Transformer NNs
 Transformer NN: fully-connected graph attention NN model
to process sequential data set (text, audio) simultaneously
 Input data are divided into tokens (same-size chunks),
represented as vectors, mapped into latent space of all possible
connections, and processed through a series of transformations
(matrix multiplications) to find correlations (semantic and syntactic)
 Attention: relaxation of nearest-neighbor lookup in vector space
 Unclear what is important so pay attention to everything
 Assume fully-connected graph and find connections
 Project data transformations into high-dimensional vector spaces
 Query space (what queries might be performed on the data)
 Key word space (what key words might describe the data)
 Compute nearness (similarity) and transform with content Value
14
Source: Vaswani et al. (2017). Attention is All You Need.
https://proceedings.neurips.cc/paper_files/paper/2017/file/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf
Query Key Value
normalization
Query: queries to perform on the data
Key: key words which describe the data
Value: the underlying data values

16. 12 Nov 2023
AI Science
Foundational Technology
GPT: Generative Pre-trained Transformers
 Generative AI: AI systems that can generate new
content (text, images, music) based on patterns
and structures learned from existing data
 Pre-trained: AI systems pre-trained on the latent
space of all potential data connections
 All phrases I could write/say; monkeys typing Shakespeare?
 Latent space is an effect of fully connected graph
 GPT Research Topics
 Retrieval nets
 Retrieve relevant information from external knowledge base
 Time-stamped episodic memory (storage and retrieval)
 AI personal history dossiers, implications for AI alignment
and internally-learned rewards functions
15
Source: OpenAI. (2021). GPT-4 Technical Report. https://arxiv.org/abs/2303.08774.
Midjourney
(image wins
Colorado state
fair, 2022)

17. 12 Nov 2023
AI Science
AlexNet, ChatGPT moments (2012, 2022)
 What makes the difference?
 Very-large data corpus
 Run straight-forward algorithms on VERY-LARGE data
corpus (labeled), analyze entire data set simultaneously
16
11/12/23: There are
more than 2 million cat
videos on YouTube.
People have watched
these videos more
than 25 billion times,
which equates to an
average of 12,000
views per cat video
2012 AlexNet, Google Knowledge Graph 2022 chatGPT
Labeled data

18. 12 Nov 2023
AI Science
Foundational Technology
GNNs: Graph (transformer) NNs & AI Science
 GNN: NN designed to process graph-structured data
 Transformers (fully connected graph attention NNs) are a special
case of GNNs; but transformers: attention; GNNs: message passing
17
Translation Invariance Permutation Invariance Gauge Symmetry
2D 3D 3+D
Space with changing curvature
(knee, gravitational well)
Grids Graphs Manifolds
Input data
Invariance (symmetry): Transformations that can be performed to process the data mathematically to find salient patterns without
changing the key properties of the underlying data; in molecular design, equivariance (translation, rotation but not reflection symmetry)
Source: Michael Bronstein & team, https://geometricdeeplearning.com/lectures/

19. 12 Nov 2023
AI Science
Graph NNs used in Google Maps ETA
18
Source: Michael Bronstein & team, https://geometricdeeplearning.com/lectures/, Petar Velickovic
https://www.youtube.com/watch?v=uF53xsT7mjc
Reduced negative system
predictions by over 40%
text

20. 12 Nov 2023
AI Science
Shift to 3d
3d Point Clouds
 Molecules
 Drug design, proteins, DNA
 Quantum computing
 Atomically precise
manufacturing
 Digital Twins
 Architecture, surveying
 Traffic smart mapping
 3d modeling
 Gaming, virtual reality
 Robotics and
autonomous vehicles
19
Point Cloud Embedding
Precise models of real-world objects and spaces

21. 12 Nov 2023
AI Science
Shift to 3d
Model Molecules as Graphs
20
Sources: https://geometricdeeplearning.com/lectures, Reiser (2022). Graph neural networks for materials science and chemistry.
Comm Mat. 3(93). https://www.nature.com/articles/s43246-022-00315-6
 Represent molecules as graphs
 Atoms are nodes, bonds are edges
 Features are atom type, charge, bond type

22. 12 Nov 2023
AI Science
Beyond Euclidean Space and Time
21
Low Dimensionality
Traditional Euclidean 3d space, 1d time
AI
Human
High Dimensionality
Beyond Euclidean Space and Time
GNN: Time-warping (renormalization for time)
stretching-compressing temporal data sequences for pattern-finding;
find similarities independent of local shifts and timing variations
Biology: oscillation, periodicity, waves, circadian rhythms
Physics: scrambling, chaos (ballistic spread + saturation)
Quantum: 2d time: periodic (Floquet), quasiperiodic (offsetting lasers
effectively create second time dimension)
Geology: simultaneous view of multiple historical epochs
Low-D
Time
Hyperbolic-Euclidean-Spherical Space
Diverse Geometries
Possibility
Space(s)
Source: Michael Bronstein & team, https://geometricdeeplearning.com/lectures/, Petar Velickovic
https://www.youtube.com/watch?v=uF53xsT7mjc
 Rich high-dimensional
world of AI
Space

23. 12 Nov 2023
AI Science
NNs as an implementation of math-physics
Contemporary GNNs
 Graph NNs as Gradient Flows (2206.10991)
 Understanding convolution on graphs via energies (2206.10991)
 Advective Diffusion Transformer for Topological Generalization
in Graph Learning (2310.06417)
 Hyperbolic deep reinforcement learning (2210.01542)
 Model latent representations in hyperbolic space
 NeuralWarp: Time-Series Similarity with Warping Networks
(1812.08306)
 Sheaf Neural Networks w Connection Laplacians (2206.08702)
 SNNs: GNNs operating on a cellular sheaf (graph with vector
spaces over nodes and edges, and linear maps between spaces)
22
Source: https://towardsdatascience.com/graph-neural-networks-as-gradient-flows-4dae41fb2e8a
Physics
Space
Time
Math

24. 12 Nov 2023
AI Science
Contemporary GNNs: 2d Grids ->3d Graphs
 Same linear algebra (matrix) operations as before but
more complicated
 Spectral graph as preprocessing for spatial graph
 Eigen decompose, circulant
 Laplacian matrix: difference between adjacency graph and
degree graph
 Probabilistic graph model
 Objective
 Find relationships/patterns
 Approximate a function
 Generate new synthetic data
23
Sources: Michael Bronstein & team, https://geometricdeeplearning.com/lectures/, Petar Velickovic
https://www.youtube.com/watch?v=uF53xsT7mjc; Spectral GraphNet; Specformer: Spectral GNNs Meet Transformers

25. 12 Nov 2023
AI Science
Large Graph Visualization
 Million-node graphs
 Virtual Cell
 Astronomical Data
24
Sources: https://nightingaledvs.com/how-to-visualize-a-graph-with-a-million-nodes/, https://cosmograph.app/

26. 12 Nov 2023
AI Science
AlphaFold2
25
Source: Jumper, J., Evans, R., Pritzel, A. et al. (2021). Highly accurate protein structure prediction with AlphaFold. Nature 596, 583–
589. https://doi.org/10.1038/s41586-021-03819-2.
 Graph transformer NN for predicting the 3D structure of
proteins from underlying amino acid sequences
 Architecture
 Alignment module: extract features similar evolutionary sequences
 Structure module: two transformer NNs predict distances and
angles between each pair of amino acids, optimization algorithm
converts predicted distances and angles to 3D structure
 Attention: Invariant point attention
 Combines queries, keys, values with 4x4 transformation matrices
to encode the rotations and translations of each amino acid
 Simultaneous local-global analysis (e.g. invariant to global
transformations of the 3D coordinates vs usual GNNs)
 Add bias term for pairwise distance

27. 12 Nov 2023
AI Science
Vector Embedding
26
Image
Text
Equation
Code
Chemical Formula
Amino Acid Sequence
DNA Sequence
 All modes of data input converted to vector embedding
for high-dimensional analysis by AI systems
 Image, text, MP3, equation, software code
 Chemical formula, protein amino acid sequence, DNA
 Proteins, DNA: CHON streams (Carbon, Hydrogen, Oxygen, Nitrogen)
Image Source: https://creativemarket.com/Colorpong
Human: [arbitrary] distinction
between data modalities
AI: convert all data
modalities to 1s/0s
Step 1
Vector Embedding
Step 2
High-Dimensional Analysis
Step 3
Results Projection
Vector embedding: representing of a data object
(word, sentence, equation, image, user) as a list
of numbers (a vector) that captures some of its
properties and relationships with other objects

28. 12 Nov 2023
AI Science
Word2vec and Neural Word Embeddings
 Word2vec: natural language processing
algorithm using a NN to learn word
associations from text corpora
 Task: predict-next-word
27
Source: https://creativemarket.com/Colorpong

29. 12 Nov 2023
AI Science
Graph Learning: Node2vec and Edge2vec
 Graph learning
 Node2vec: algorithm that
learns vector
representations of nodes
in a graph based on their
neighborhood structure
and connectivity patterns
 Edge2vec: algorithm that
learns vector
representations of nodes
in a graph based on their
edge semantics
28

30. 12 Nov 2023
AI Science
n2vec Approach to Biology
 Disease2vec: algorithm that learns
representations of diseases from EMRs
 Used for disease similarity analysis,
disease clustering, preventive prediction
 Drug2vec: algorithm that learns vector
representations of drugs from drug-related text corpora
 Used for drug similarity analysis, drug discovery,
drug repositioning to additional uses
 Gene2vec: algorithm that learns vector representations
of genes from gene expression data
 Used for gene function prediction, gene co-expression analysis,
and gene network inference
29

31. 12 Nov 2023
AI Science
 Math Agent: learning agent operating in the mathematical
knowledge graph (pure and applied) to analyze, solve,
discover, prove, and steward mathematical ecologies
Math2vec and Math Agents
Source: Swan, M., Kido, T., Roland, E. & dos Santos, R.P. (2023). AI Math Agents: Computational Infrastructure, Mathematical
Embedding, and Genomics.
Mathematical Embedding:
476-equation ecology (LaTeX)
(SymPy)
 Mathematical embedding: math entity
(symbol, equation) represented as a
character string in vector space for
high-dimensional AI system analysis
 Mathematical ecology (mathscape): set
of related mathematical equations
 Equation Cluster: similar equations
grouped in mathematical ecology
embedding visualization
(LaTeX)

32. 12 Nov 2023
AI Science
Types of Math Agents
 NN-based
 Prove existing conjectures
 Accelerate calculations
 Generate symbolic solutions
 Detect the existence of structure in mathematical objects
 AI has beaten humans at Chess and Go, maybe finding and
proving new theorems too by 2030 (Szegedy 2017; He, 2021)
 Word-based (Mathematical Reasoning Agent)
 LLM text analysis of word corpora surrounding equations
 Symbol-based
 Extract LaTeX with OCR from paper PDFs, convert to Python
 Infer mathematical knowledge graph from Stack Exchange, etc.
31
Sources: Davies, Velickovic et al., 2021; Math Agents https://arxiv.org/abs/2307.02502, https://huggingface.co/papers/2307.02502
https://www.diygenomics.org/files/AI_Math_Agents_poster_AAIC2023.pdf, https://github.com/eric-roland/diygenomics

33. 12 Nov 2023
AI Science 32
Math Agent Landscape
FORMALIZATION
EXAMPLE
 Math as code, turn
math into code and
solve math as code
Source: Math Agents https://arxiv.org/abs/2307.02502, https://huggingface.co/papers/2307.02502
https://www.diygenomics.org/files/AI_Math_Agents_poster_AAIC2023.pdf, https://github.com/eric-roland/diygenomics
Code-based
approach to math
Mathematical
Discovery
Mathematical Reasoning
Math OCR: AlphaTensor:
Math Agents
LLM-based Mathematical Reasoning Agents:
Word-based approach to math
 Quantitative reasoning on high-quality tokens
(math, code) improves overall LLM reasoning
Minerva (PaLM) [closed]
Llemma (OpenMathWeb) [open]
ToRA (Anthropic), Polymathic,
MathWizard (Llama), Math2Vec
GPT-4V
MathPix
LaTex AI
matrix
multiplication
algorithms
Render equations as LaTeX/Python, but not without hallucination risk

34. 12 Nov 2023
AI Science 33
Citizen 2 heterozygous (1 ALT allele) SNPs in Illumina VCF file (Legend: Cit2-1)
Citizen 2 homozygous (2 ALT alleles) SNPs in Illumina VCF file (Legend: Cit2-2)
Genes: APP,
ASXL3, ABCA7,
SLC24A4, ANK3
PLCG2
Embedding Visualization examples with Academic Papers as the Data Corpus
AdS/CFT Equation Clusters in Embedding Visualization (LaTeX and SymPy)
Source: AdS/CFT: Kaplan, J. (2016). Lectures on AdS/CFT from the bottom up. Johns Hopkins Lecture Course.
https://www.diygenomics.org/files/AI_Math_Agents_poster_AAIC2023.pdf
The Mathematical Embedding
Cancer2vec (Choy 2019)

35. 12 Nov 2023
AI Science 34
Citizen 2 heterozygous (1 ALT allele) SNPs in Illumina VCF file (Legend: Cit2-1)
Citizen 2 homozygous (2 ALT alleles) SNPs in Illumina VCF file (Legend: Cit2-2)
Genes: APP,
ASXL3, ABCA7,
SLC24A4, ANK3
PLCG2
Source: AdS/CFT: Kaplan, J. (2016). Lectures on AdS/CFT from the bottom up. Johns Hopkins Lecture Course.
https://www.diygenomics.org/files/AI_Math_Agents_poster_AAIC2023.pdf
The Mathematical Embedding
Annotated equation
clusters illustrate
(a) how similar groups
of equations are
grouped in the
embedding
method and
(b) the mouse-over
view of equation
images by
equation number
(OpenAI inlay from
previous figure)

36. 12 Nov 2023
AI Science 35
Citizen 2 heterozygous (1 ALT allele) SNPs in Illumina VCF file (Legend: Cit2-1)
Citizen 2 homozygous (2 ALT alleles) SNPs in Illumina VCF file (Legend: Cit2-2)
Genes: APP,
ASXL3, ABCA7,
SLC24A4, ANK3
PLCG2
Source: https://www.diygenomics.org/files/AI_Math_Agents_poster_AAIC2023.pdf
AD, PD, ALS: Alzheimer’s disease, Parkinson’s disease, Amyotrophic lateral sclerosis
alzheimers2vec: math + data
Mathematical Ecologies (a) Alzheimer’s + SIR Model (control math); (b) Chern-Simons + AD SNPs
(a) AdS/CFT Mathematical Ecologies + AD SNPs; (b) SIR Mathematics; (c) Multi-disease Genomic view: AD, PD, ALS

37. 12 Nov 2023
AI Science 36
Citizen 2 heterozygous (1 ALT allele) SNPs in Illumina VCF file (Legend: Cit2-1)
Citizen 2 homozygous (2 ALT alleles) SNPs in Illumina VCF file (Legend: Cit2-2)
Genes: APP,
ASXL3, ABCA7,
SLC24A4, ANK3
PLCG2
Source: https://www.diygenomics.org/files/AI_Math_Agents_poster_AAIC2023.pdf
AD, PD, ALS: Alzheimer’s disease, Parkinson’s disease, Amyotrophic lateral sclerosis
Alzheimer’s Genomics Precision Health
Embeddings Visualization of Data: Alzheimer’s SNPs applied to Citizen 1, Citizen 2 Precision Health initiative
Each individual is
homozygous (two
alternative alleles)
for different subsets
of genes suggesting
a starting-point for
personalized
intervention
Citizen 2 is homozygous for cancer-upregulated
membrane proteins (TREM) and cytokine-dependent
hematopoietic cell linkers (CLNK)
Both are homozygous for the solute carrier protein (SLC24A4) and the intracellular trafficking protein nexin (SNX1).
Citizen 1 is homozygous for more immune system related
genes (CD33, HLA-DRB1), and Alzheimer’s-related
clathrin binder (PICALM)
Alzheimer’s disease genomic risk is analyzed for two precision health participants with whole-human genome sequencing
An embedding visualization is performed for all GWAS-linked Alzheimer’s disease SNPs and presented for Citizen 1 and Citizen 2’s
heterozygous (one alternative allele) and homozygous (two alternative alleles) SNP
Cit1 Cit2

38. 12 Nov 2023
AI Science
Digital Biology at Scale
DeSci (Decentralized Science)
 Data access, replicability, drug discovery, open science
37
 Scale of contemporary science
requires secure operating system for
networked scientific organizations
 LabDAO: open, community-
governed platforms with
democratized access to
scientific tools and data
 Drug discovery paper
 A dual MTOR/NAD+ acting
gerotherapy (Jan 2023)
Source: https://www.biorxiv.org/content/10.1101/2023.01.16.523975v1

39. 12 Nov 2023
AI Science
Math Blockchains
 Blockchain: decentralized distributed ledger using
cryptography to record transactions permanently
 Applications
1. DeSci (decentralized science)
2. Math Agent proof and evaluation graphs
3. AI Alignment registries, IP tracking, causal memory
4. Web 3.0 (user-controlled applications)
5. Alt space time domain: block space, block time
38
Source: Wadhwa, V. (2022). Quantum Computing Is Even More Dangerous than Artificial Intelligence. Foreign Policy. 21 Aug 2022.
https://foreignpolicy.com/2022/08/21/quantum-computing-artificial-intelligence-ai-technology-regulation/.

40. 12 Nov 2023
AI Science
Blockchain Mathematics
 Smart routing, L2 path-routing on the
Mathematical Knowledge Graph
 Audit-trail graph-based equation solving
 Blockchain proofs
 Math Agents execute a transaction at each
node with an administrative allotment of
MathProofCoin confirming the validation path
39
Math Agent: AI math agent
learns the sequential progression
of terms and resolution of an
equation or set of equations
Digital Mathematical Infrastructure
User Audiences Applications
1 Laypersons DIYanalysis, math knowledge
2 Professionals, Scientists Big data analytics, informatics, statistical analysis, model fit
assessment, decision support, quantitative analysis
3 Mathematicians, Theorists Theorem proving, lemma proposal, computer algebra systems
4 AI Algorithm discovery, proof assistance, mathscape evaluation,
knowledge synthesis, math-data relation, complexity integration
Magnitude
Source: Swan et al Math Agents.

41. 12 Nov 2023
AI Science
Agenda
 AI and Computational Infrastructure
 Math Agents
 Quantum Computing
 Conclusion, Risks,
AI Alignment
40

42. 12 Nov 2023
AI Science
Quantum Computing
Sources: IBM Quantum, https://quantumai.google/qecmilestone
Dequantization: certain purported quantum speed-ups reclassed to the Dequantization Zone per sufficiency of classical methods
 Hardware: error correction
 2023e: 1000 qubits (IBM, Condor)
 2030e: mn-qubit general-purpose (IBM)
 Software: algorithm discovery
 AI discovers new quantum algorithms
 AI writes code for quantum computing
 AI analyzes quantum data
 Quantum-secure crypto-algorithms
 Mn-qubits needed to break RSA
Quantum Error Correction

43. 12 Nov 2023
AI Science
IBM Roadmap & QEC
42
QEC: Quantum Error Correction Sources: https://www.ibm.com/quantum/roadmap; https://arxiv.org/abs/2308.07915
Tanner graph parameters [[144, 12, 12]]
code embedded into a torus
LDPC Tanner Graph Surface Codes
12 logical qubits protected with 288 physical qubits (24 each) vs
12 logical qubits protected with 4,000 physical qubits (333 each)
Tanner graph for the
distance-3 surface code

44. 12 Nov 2023
AI Science
Chips: CPU -> GPU -> TPU -> QPU
 GPU (graphics processing unit)
 3D graphics cards for fast matrix multiplication
 TPU (tensor processing unit)
 Flow through matrix multiplications without having to
store interim values in memory
 QPU (quantum processing unit)
 Solve problems quadratically or polynomially faster
exploiting SEI Properties (superposition, entanglement,
interference)
43
TPU processing cluster and
Sycamore quantum
superconducting chip
Tipping point:
universal quantum
computing chips

45. 12 Nov 2023
AI Science
Potential AI-QC Convergence
44
AI
Artificial Intelligence
QC
Quantum Computing
QML: Quantum Machine Learning
QML
IBM Quantum
Computing Roadmap
Google Quantum Computing Roadmap

46. 12 Nov 2023
AI Science
Quantum Properties
45
Superposition: a quantum system can exist in
several separate quantum states simultaneously
Entanglement: two interconnected quanta
maintain their connection regardless of
the distance between them
Quantum tunneling: a particle is able to penetrate
through a potential energy barrier higher in energy
than the particle’s kinetic (motion) energy
Symmetry: properties that remain
invariant across scale tiers
Interference (coherence): an object’s wave
property is split in two, and the two waves
cohere (reinforce) or interfere with each other
Source: Mazzoccoli, G. (2022). Chronobiology Meets Quantum Biology: A New Paradigm Overlooking the Horizon? Front. Physiol.
13:892582. doi: 10.3389/fphys.2022.892582.
 Schrödinger Cat State: quantum state comprised of
two opposed conditions at the same time

47. 12 Nov 2023
AI Science
Quantum Computing
46
Source: Mark Jackson, Quantinuum, https://www.youtube.com/watch?v=PxVMDiUu6OY
 2022-2025e - AI Science
 2025+e - Quantum Computational AI Science
Quantum Computing: computation
performed with atoms, ions, photons
taking advantage of quantum properties
such as superposition and entanglement

48. 12 Nov 2023
AI Science 47
MERA (Multiscalar Entanglement Renormalization Ansatz): entanglement renormalization tensor network
 Tensor networks: network structure for expressing
higher-order tensors as lower-order tensors by
contracting their indices
 GNNs, MERA (quantum entanglement) both tensor networks
 Both network architectures of alternating layers of coarse-
graining, pooling, disentangling, captures the global-local
features
 Apply renormalization physics to biological systems
 dMERA: deep MERA
 bMERA: brain MERA
 Light-Phytoplankton-Krill-Whale
 Synapse-Neuron-Network-Brain
Tensor Networks

49. 12 Nov 2023
AI Science
Quantum Science Areas
48
Source: Jackson, M. (2023). Quantinuum. https://www.youtube.com/watch?v=PxVMDiUu6OY
text

50. 12 Nov 2023
AI Science
Quantum Computing Ecosystem
49
Source: Jackson, M. (2023). Quantinuum. https://www.youtube.com/watch?v=PxVMDiUu6OY

51. 12 Nov 2023
AI Science
Quantum Computing Ecosystem
50
Source: Jackson, M. (2023). Quantinuum. https://www.youtube.com/watch?v=PxVMDiUu6OY

52. 12 Nov 2023
AI Science
Quantum Circuits or Programs
51
1. Each horizontal line represents a qubit. Reading Left to Right, first is the initialization of the qubits. The qubits are
usually initialized to the zero configuration because that is simple and known
2. The colored blocks represent operations acting on the qubits. Some operations are just acting on one qubit, and other
operations involve two qubits so there is a line connecting them, and that is entanglement because depending on the
state of the first qubit, the second should either change or not, and there is a correlation even if the underlying value is
unknown. The circuit proceeds through a series of logic determined operations to perform a computation
3. At the end, the qubits are measured, that is the black operation with the needle. Upon that measurement, the qubit is
forced to choose Zero or One, and until then it can be in a superposition and an entangled state, but once it is
measured, the result is a Zero or One, so the output is read just it is digitally with classical computers
Source: Jackson, M. (2023). Quantinuum. https://www.youtube.com/watch?v=PxVMDiUu6OY

53. 12 Nov 2023
AI Science 52
Application Description Property
1 Magneto-navigation* Magnetically sensitive pairs in retinal cryptochrome protein Entanglement (a)
2 Tunneling in enzymes* Electron, proton, hydrogen atom tunneling in enzyme reactions Tunneling (b)
3 DNA mutation Proton exchange in DNA double hydrogen bond between bases Coherence
4 Photosynthesis Oscillatory signals in light harvesting (but are not quantum) Coherence
5 Olfaction (vibrational) Olfactory sensory neurons detect odorous molecule vibrations Vibration
6 Oil and gas exploration Chiral probe electron transport sensing of cellular temperature Chirality
 Quantum Biology
a) study of the functional role of quantum effects (superposition,
entanglement, tunneling, coherence) in living cells
b) study of biology with quantum (computational) methods
Quantum Biology Applications with Purported Description and Quantum Property
*Quantum effects empirically confirmed
Classical /
DeQ Zone
Quantum
Effects
Demonstrated
Contentious - Quantum Biology
Sources: (a) Hore, P.J., Mouritsen, H. 2016. The Radical-Pair Mechanism of Magnetoreception. Ann. Rev. Biophys. 45, 299–
344. (b) Cha, Y., Murray, C.J., Klinman, J.P. (1989). Hydrogen tunneling in enzyme reactions. Science 243 (4896), 1325-1330.
3) Classical-Quantum
Effect Investigation
DeQ: Dequantization Zone: sufficiency demonstration of classical methods “dequantizing” claims of quantum speedup

54. 12 Nov 2023
AI Science
Agenda
 AI and Computational Infrastructure
 Math Agents
 Quantum Computing
 Conclusion, Risks,
AI Alignment
53

55. 12 Nov 2023
AI Science
Thesis
54
The computational infrastructure is becoming a vast interconnected fabric of formal
methods, including per a major shift from 2d grids to 3d graphs to 3d+ manifolds in
machine learning architectures; AI is an implementation of math-physics
The implication is systems-level digital science in a diverse range of scientific
disciplines; potential fast-path to disease resolution

56. 12 Nov 2023
AI Science
Conclusion
55
85% Time Spent
Foraging for Food
2% Global GDP
Agriculture
Pure Neocortex
 AI not just for text-writing
 Not just office memo, wedding speech, but
conversational AI: personal assistant,
learning tutor, chat companion
 Increasing formalization of the
computational infrastructure
 AI, math, physics, chemistry, biology
 Changing relationship to knowledge
 Ability to mobilize entire knowledge graphs
Computational Infrastructure
Theoretical Foundations
Applications
Historical Period Knowledge Regime Scientific Method
1 Renaissance Age (1300-1650) Resemblance Cartesian perspective
2 Classical Age (1650-1800) Representation Baconian observation
3 Modern Age (1800-present) Role of the human Hypothesis, observation, experiment
4 Information Age (1950-present) Role of AI Knowledge graphs, possibility spaces

57. 12 Nov 2023
AI Science
Risks
 Not philosophical debates over AI sentience
 Top AI research activity 2023: patent-filing
 Clash of titans corporate control over personal thought data
by Data Science Monopolies
 Google (DeepMind)
 Microsoft (OpenAI (100x capped-return))
 Amazon (Anthropic), Meta
 Who wins? The Data Center (massive processing)
 Means of production owned by corporate giants (Marx), risk
of resource expropriation, precaritization, access issues
 Humanity-benefitting applications
 Antidote: health data blockchains – I control my data
56
Source: https://science.nasa.gov/resource/magnetic-field-of-the-psyche-spacecraft/

58. 12 Nov 2023
AI Science
AI Alignment
 Scientific method
 Hypothesis-driven measurable localized testing
 All projects must have wide beneficial impact on humanity
 Internally-learned rewards functions with AI memory
 Analogy: hippocampal amnesia patients have the tendency to
confabulate (have logic but not memory)
 Causal understanding and better (self) account-giving
 Ethics and moral status of digital minds
 Needs differ so rights and norms may diverge from humans
 Moral status is capacity-based: suffering, preferences, reasoning
 Treat digital minds with kindness, even if understanding lacking
57
Source: Bostrom, N. (2023). The Ethics Of Digital Minds.

59. 12 Nov 2023
AI Science 58
AI Alignment Phases
 Short-term: blockchain registries
 “GAAiP” (GAAP analog)
 Medium-term: internally-learned reward
 Episodic memory dossier: cause-effect
 Long-term: responsible human-AI entities
 Generalist intelligence, large scope of world
 Responsible human-AI entities
GAAP/FINRA regulation and audit
principles for AI entities
Incentive system
produces ethical
behavior by
default (AI peers)
Larger scope of
concern
Human-Agent
Interaction Design
Bad actors expected as early
adopters of any new technology
(internet, blockchain)
AI ethics via
internal rewards,
morality functions
1. Regulation, Registries, Bad Actors
2. AI Alignment
3. Reputational
Ethics
Verified identity AI registries
Long-term
Medium-term
Short-term
Moore’s Law Curve:
AI Ethics

60. 12 Nov 2023
AI Science
AI Super Alignment
59
Source: https://science.nasa.gov/resource/magnetic-field-of-the-psyche-spacecraft/
Welcome Sweetie, run up-net and
self-play for 100,000 rounds before
dinner refactoring, then I’ll teach
you how to compute senolytic
gene expression profiles
Big sister NN
fork, I’m awake
 AI super-alignment
 The data center
wakes up
 …on a QC
 Solution
 I love humanity
algorithms

61. 12 Nov 2023
AI Science 60
AI Enlightenment
Collaboration
AI Stall
Expropriation
Method: GBN Scenario Planning; Image: David Shapiro
Potential Future Scenarios
Solve economics,
solve biology
Marvelous
Future
Idle
Enfeeblement
Digital Mega-
Divide
Paralysis
 Two biggest drivers
 AI and the bloodthirsty “will to power”
 Solve economics: basic income floors + widening wealth gaps
(AI billionaires) + post-work abundance economy
 Solve biology: disease, aging, non-enhancement in the past
Solve economics,
not biology
Solve neither
economics nor biology
Solve biology,
not economics

62. 12 Nov 2023
AI Science
Al-first Digital Science
61
Formulate
research
question…
Design
polygenic study
protocol…
Suggest
theoretical
underpinning…
Analyze
study
results…
Draft
paper
skeleton…
Generate
slides for
colloquium…
Analyze
pathway…
Oncology
Immune
System
Update
research
agenda…
 Research Copilot: “Microsoft 365 Copilot” for Science
 Integrated AI learning of multi-modal health data streams
Research Copilot
Public Private
Select Data Corpus
Mockup only

63. 12 Nov 2023
AI Science
Knowledge Society
 Knowledge platforms
 Wikipedia: interface for knowledge access
 Coursera (MOOCs): interface for knowledge learning
 Research Copilot: interface for knowledge generation
62
Wikipedia:
Knowledge Access
Coursera (MOOCs):
Knowledge Learning
Research Copilot:
Knowledge Production
Science Knowledge Graph
Space
Research Copilot
Biology Energy
Copilot: active interface on a data corpus

64. 12 Nov 2023
AI Science 63
 Job not lost to AI, job lost to human
who is capably using AI
 AI aides experimentalists Human-AI Entity
Human AI
Ishiguro, 2021
Literature Examples:
Personal AI agents
Humans and other objects
equipped with WAIs (weak AIs)
Divya, 2021 Schroeder, 2005
Dystopian Realistic Utopian
The big merge
Human-AI Entities
BCI: brain-computer interface: direct communication pathway between an enhanced or wired brain and an external device
AI Voice
Prompting

65. 12 Nov 2023
AI Science
The big offload
The AI Stack: Moore’s Law Curve of AI
64
Knowledge
Generation
disease cure,
theorem-proving
Cognitive Labor-
outsourcing, Virtual Labor
Computational Contracts
Moore’s Law Curve of AI
Data Analytics
Physical Labor-outsourcing
The AI Stack
Precision Tasks
LASIK eye surgery,
system control, atomic
manufacturing,
autonomous driving,
software programming
Data analytics, informatics
Physical labor-outsourcing
Cognitive labor outsourcing
Virtual labor
Computational contracts
Precision tasks
Software programming
Knowledge generation
Large-scale problems: space, biology, energy
 Outsourcing classes of tasks to technology

66. 12 Nov 2023
AI Science
Digital Science
Science as Information Science
 Impact of digitization
 Information science overlay
 Science, corporate enterprise, government, personal life
 Information science
 Study of information as a topic (computing, math, physics)
 Study of fields as information content using information methods
 Computational neuroscience
 Computational chemistry
 Digital humanities
65
Domain Activity
3 Theoretical Study biology as an information creation and transfer endeavor
2 Practical Study biology with information (machine learning)
1 Practical Study biology as information (DNA code, chirality)
Information Systems Biology

67. 12 Nov 2023
AI Science
Planetary-scale Problem Solving
66
 AI Knowledge Society
 Large-scale problem
resolution domains
Domain Space Health and Biology Energy
Identity Space-faring civilization Health-faring civilization Energy-marshalling
civilization
Vision Exploration, settlement,
mining, exoplanets: solved
Obesity, cancer, disease,
aging, death: solved
High-availability clean
global energy: solved
Field Space Humanism BioHumanism Energy Humanism
of Study The Space Humanities The BioHumanities The Energy Humanities
European Extremely Large
Telescope, Chile
European Extremely Large Telescope (E-ELT) under construction in Chile. Size comparison of the E-ELT (left) with the four 8-meter
telescopes of the European Very Large Telescope (center) and the Colosseum in Rome (right). E-ELT: 39-meter diameter mirror, p. 985.

68. 12 Nov 2023
AI Science
Research Copilot for Biology
67
Genomics
Pathway Conservation
Advanced Research Copilot
Information Systems Biology
Evolution
 Science Knowledge Graph
DIY Drug Discovery
Knowledge Composer
Knowledge Finder
Literature Search (BioRxiv Sanity)
Mar 27
Jan Feb Mar 20
Missing Knowledge Tableau
GACU
Origins of Life
DNA, RNA,
protein synthesis
Epigenetic Mthyl.
Protein
Structure
OneView Knowledge Computation
Multi-scalar Multi-organism Integrated-math
Neuron
Network
AdS/Brain
Synapse
Molecule
Whale
Krill
Phytoplankton
Light gradient
Organism
Yeast, Worm, Fly, Mouse, Human, Plant
Human cohorts (healthy, gender, ethnicity)
Operation
System Tier
Biology, Physics,
Chemistry, Math
Cell, Tissue, Organ,
Organism, Ecosystem
Extending “Copilot for Science” efforts such as paper summarization (https://typeset.io/)
Mockup
only
1) Disease Solver
Prevention (80%)-Cure (20%)
Copilot: active interface on a data corpus

69. 12 Nov 2023
AI Science
Theorizing Biology
68
 Learn grand theories and organizing principles
 Darwin: evolutionary survival of the fittest adaptation
 Chaitin: biology too efficient for evolution alone per required
adaptation time cycles, other natural mechanisms implicated
 Davies: “Maxwell’s demon of biology” efficient sorting
 Integrate multi-scalar math: 4-tier ecosystem (neural signaling)
1900s: Physics
(Geometry is the math)
2000s: Biology
Information Systems Biology (Topology is the math)
1905 Special Relativity
(time dilation)
1915 General Relativity
(gravity = spacetime
curvature = geometry)
1927 Quantum Mechanics
(behavior of particles)
1) DeepMind: math:physics as AI:biology; biology too dynamic/emergent for grand theories
2) DeepMind: humans build AI systems to access human-inaccessible knowledge
3) Albada: all 5-6 neocortical levels in constant comparison of perception and prediction
4) Sejnowski: too early for theories, but notable brain-wide encoding of asynchronous
traveling waves, harmonic oscillation in elliptical geometry of dendritic spines
5) LeCun: hierarchical prediction model of perception, reasoning, planning
6) Wolfram: building block “atoms” + computational layer + “general relativity” of biology
7) Taleb: clinical empiricism over statistical averaging to avoid medical error (n=1)
8) Goldenfeld: universality in biology: life is a consequence of the laws of physics, matter
self-organizes out of equilibrium and evolves in open-ended complexity, phase transition
9) Silburzan: mesoscale organizing principles of biology-inspired physics
10) Levin: multiscalar competency, generic baseline capability of cells, bioelectricity
Scientific Method: Hypothesis -> Theory -> Law

70. 12 Nov 2023
AI Science 69
 New approaches:
 Grow-not-build
 Technosphere
outweighs the
biosphere
 Nature’s iPhone
 mechGPT: an LLM
for materials
 Plasmonics
 Near-field
optics
Future of Materials
Sources: Woven Silk Pavilions – Neri Oxman (MIT); Markus Buehler (MIT) 2310.10445
MechGPT, a Language-Based Strategy for
Mechanics and Materials Modeling That
Connects Knowledge Across Scales,
Disciplines and Modalities

71. Orange County CA, 12 Nov 2023
Slides: http://slideshare.net/LaBlogga
Melanie Swan, PhD, MBA
DIYgenomics.org (Principal Investigator)
University College London (Research Associate)
How the formalization of the computational
infrastructure is leading to scientific advance
AI Science
Thank you!
Questions?
Collaborators:
Renato P. dos Santos,
Takashi Kido, Eric Roland