Vladimir Viktor Mirjanić

Work Experience

• Research Assistant

  Oct 2023 – Sept 2024
  University of Cambridge
  • Created a novel ML approach to discovering formulas for Ricci-flat metrics on Calabi-Yau manifolds
  • Uncovered new patterns and approximations for the flat metric on highly symmetric K3 manifolds
  
  
• Software Engineering Intern

  July–Sept 2021
  Microsoft Development Center Serbia
  • Developed proof-of-concept for an Azure SQL C++ backend issue that had been outstanding for 3 years
  • Decreased migration downtime from on-premises to Premium tier databases down to 3-5 minutes
  
  

Teaching Experience

• Multiple Roles

  Jan 2024 – Present
  University of Cambridge, Department of Computer Science and Technology
  • Undergraduate course supervisor: mentoring students in Discrete Maths, Algorithms I, Algorithms II
  • Project supervisor for L65 Geometric Deep Learning Course: designed a course research project in Neural Algorithmic Reasoning and mentored master's students on it over 8 weeks
  • Teaching Assistant for L65 Geometric Deep Learning
  • Team coach for ICPC and regional competitions, organizer for subregional UKIEPC qualifiers at Cambridge
• Tutorial Lead for Geometric Deep Learning

  July 2024
  EEML 2024
  • Created a PyTorch tutorial to teach basics of Graph Neural Networks and GDL
  • Led the GDL workshop, where I presented problems and model solutions to the students
  • Coordinated with teaching assistants to provide live assistance and Q&A
• Lecturer at the Computer Science Week 6

  Apr 2021
  Mathematical Grammar School, Serbia
• Presenter at Science Through Entertainment Exhibition

  Sept 2017
  Serbian Academy of Sciences and Arts & University of Stuttgart

Publications

• Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces

  Dec 2024
  V. V. Mirjanić, C. Mishra

  arXiv preprint

  Ever since Yau’s non-constructive existence proof of Ricci-flat metrics on Calabi-Yau manifolds, finding their explicit construction remains a major obstacle to development of both string theory and algebraic geometry. Recent computational approaches employ machine learning to create novel neural representations for approximating these metrics, offering high accuracy but limited interpretability. In this paper, we analyse machine learning approximations to flat metrics of Fermat Calabi-Yau n-folds and some of their one-parameter deformations in three dimensions in order to discover their new properties. We formalise cases in which the flat metric has more symmetries than the underlying manifold, and prove that these symmetries imply that the flat metric admits a surprisingly compact representation for certain choices of complex structure moduli. We show that such symmetries uniquely determine the flat metric on certain loci, for which we present an analytic form. We also incorporate our theoretical results into neural networks to achieve state-of-the-art reductions in Ricci curvature for multiple Calabi-Yau manifolds. We conclude by distilling the ML models to obtain for the first time closed form expressions for Kahler metrics with near-zero scalar curvature.

• Latent Space Representations of Neural Algorithmic Reasoners

  Nov 2023
  V. V. Mirjanić, R. Pascanu, P. Veličković

  Second Learning on Graphs Conference (LoG 2023)

  Neural Algorithmic Reasoning (NAR) is a research area focused on designing neural architectures that can reliably capture classical computation, usually by learning to execute algorithms. A typical approach is to rely on Graph Neural Network (GNN) architectures, which encode inputs in high-dimensional latent spaces that are repeatedly transformed during the execution of the algorithm. In this work we perform a detailed analysis of the structure of the latent space induced by the GNN when executing algorithms. We identify two possible failure modes: (i) loss of resolution, making it hard to distinguish similar values; (ii) inability to deal with values outside the range observed during training. We propose to solve the first issue by relying on a softmax aggregator, and propose to decay the latent space in order to deal with out-of-range values. We show that these changes lead to improvements on the majority of algorithms in the standard CLRS-30 benchmark when using the state-of-the-art Triplet-GMPNN processor.

Projects

• Curvature for Information propagation in GNNs

  Feb-Mar 2023

  Master's group project

  • Studied how curvature affects learning of sheaf structure GNN latent spaces
  • Augmented Graph Attention Networks with curvature information and rotational attentions
  • Reduced loss on ZINC dataset by over 40% compared to vanilla Graph Attention Networks

• Super-Efficient Super-Resolution in JAX

  Jan 2023

  Master's group project

  • Replicated SESR, one of the leading super-resolution models, in JAX
  • Decreased training time by 15% compared to the original TensorFlow implementation
  • Extended the paper to support collapsible convolution blocks with bias terms

• From Mode-Connecting Paths to Mode Connecting Sub-Spaces

  Jan 2023

  Master's group project

  • Showed that mode connecting paths are sampled from multi-dimensional sub-spaces of low loss
  • Created a working prototype to recover these sub-spaces of low loss in function space

• A Secure USB Port

  July-Sept 2021

  BA Dissertation

  • Designed and constructed a hardware firewall for USB connections and wrote firmware in C
  • Achieved defence against three most common USB attacks while keeping cost under $16

Honours and Awards

• IAIFI Summer School Hackathon Winner — MIT, Boston MA

  Aug 2024
• Internal Graudate Studentship — Trinity College, Cambridge

  July 2024
  • PhD tuition studentship
• Highly Commended MEng Project (1/27) — University of Cambridge

  June 2023
  • Awarded for the highest scoring master's dissertation
• Dositeja Award — Fund for Young Talents of Serbia

  Dec 2022
  • Contribution toward master's tuition scholarship
• Senior Scholar — Trinity College, Cambridge

  July 2021
  • Elected due to high performance in Part IB of the Computer Science Tripos
  • Re-elected in July 2022 and Dec 2023 due to high performance in Parts II and III
• Best Part IB Group Project (1/21) — University of Cambridge

  Apr 2021
  • Voted the most technically impressive project by faculty and students
• Bronze Medal — 60th International Mathematical Olympiad

  July 2019
• Bronze Medal — 36th Balkan Mathematical Olympiad

  June 2019
• Best Final Year Project in the Area of Astronomy — Mathematical Grammar School

  June 2019
• Henry VIII Bursary — Trinity College, Cambridge

  Mar 2019
  • Four-year tuition scholarship
• 99th Percentile (1520/1600) — SAT

  Oct 2018
• English Proficiency (7.5/9) — IELTS

  Aug 2018
• English Proficiency (112/120) — TOEFL

  Aug 2018
• Honourable Mention — 35th Balkan Mathematical Olympiad

  May 2018
• Dositeja Award — Fund for Young Talents of Serbia

  2016 – 2020
  • High School and University Performance Based Stipend