Microsoft Research Blog

Solving a 31-year-old grand challenge in mathematics – the KLS conjecture 

October 21, 2026 | Xinzhi Zhang
For decades, a fundamental question about the difficulty of computing in high-dimensional spaces has resisted proof. New research resolves this question, removing a major theoretical obstacle to understanding the efficiency of randomized algorithms used across science and computing. The Kannan–Lovász–Simonovits (KLS) conjecture was proposed in…

Recent Posts

  1. Side-by-side diagrams compare a flat cut and a curved cut through the same convex geometric shape. The left panel, labeled “Flat cut,” shows a diamond-shaped cross-section with a cut area of 0.2500. The right panel, labeled “Smallest Curved Cut,” shows a curved, ribbon-like cross-section with a smaller cut area of approximately 0.2173. Below the diagrams, text summarizes the KLS Conjecture: among cuts that divide a convex body into two equal volumes, the best flat cut has area at most a universal constant times the smallest possible cutting area in any dimension.

    Solving a 31-year-old grand challenge in mathematics – the KLS conjecture 

    October 21, 2026 | Xinzhi Zhang

    For decades, a fundamental question about the difficulty of computing in high-dimensional spaces has resisted proof. New research resolves this question, removing a major theoretical obstacle to understanding the efficiency of randomized algorithms used across science and computing. The Kannan–Lovász–Simonovits (KLS) conjecture was proposed in…

  2. Magnetar proves a program's execution and returns a small proof that anyone can check, with security resting only on standard hash functions.

    Proof-based general-purpose computing with Magnetar 

    October 15, 2026 | Srinath Setty

    Zero-knowledge proofs can verify computing results without rerunning workloads or exposing sensitive data. Magnetar helps bring them into the mainstream with support for standard programming languages, major speed gains, and quantum-resistant security.

  3. Diagram showing tutor guidance to student and real student feedback to tutor being hard to scale. With AI Student Simulator, fast proxy feedback is provided.

    Simulating student learning for better AI tutoring 

    October 12, 2026

    StudentSim is a research system for evaluating and improving AI tutoring tools before they are tested with learners. It models how individuals may engage with tutors, giving feedback to improve tutor performance across subjects like chess, writing, and mathematics.

  4. GridSFM diagram depicting the workflow

    Forecasting space weather risks on power grids 

    September 30, 2026 | Rohan Kannan

    Extreme space-weather events can damage power systems on Earth and degrade GPS accuracy and satellite operations. A new machine learning system can predict where damage is likely to occur 30-60 minutes before a storm arrives.

  5. Two images showing the robot performing the same task of handing over a tape from one robot arm to another. The videos show that while the task succeeds when the inference latency is low, the handover fails with high inference latency as is the case with onboard robot GPUs.

    Offloaded inference for real-world physical AI robotics 

    September 23, 2026

    Robots are getting smarter, but how can their hardware match that growth? New Microsoft Research findings show that moving AI inference beyond the robot can improve task success, boost efficiency, and support more advanced physical AI workloads.

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