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

• Tutorial Lead for Geometric Deep Learning

  Jul 2024
  EEML 2024
• Project Supervisor for L65 Geometric Deep Learning

  Jan–Apr 2024
  University of Cambridge, Department of Computer Science and Technology
• 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

• 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

• Discovering Flat Metrics with Symbolic Regression

  Mar 2023

  Master's individual project

  • Created a novel pipeline using symbolic regression and machine learning to discover formulas for Ricci-flat metrics on Calabi-Yau manifolds
  • Demonstrated that the pipeline is capable of recovering the known metric for toric Calabi-Yau in
    $\mathbb{CP}^2$
  • Uncovered approximations for the Fermat quartic, and an exact formula for its determinant. Proposed a generalisation to higher dimensions

• 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 — IAIFI

  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