Research Portfolio

Emma Leonhart

My work sits at the intersection of neurosymbolic AI, interpretability, and AI safety — three problems I see as a single problem. Geometric tensor languages and grounded retrieval are the tools I build to attack them.

01 — About

I think neurosymbolic AI, interpretability, and safety are the same problem viewed from three angles. A model whose reasoning we can’t inspect can’t be aligned; a model that can’t be grounded in symbolic structure can’t be inspected; and the structure has to be load-bearing inside the computation, not bolted on after the fact.

My working thesis: what looks like reasoning in modern language models is mostly continuous geometric operations on embedding spaces. The path forward is to make that geometry explicit, so it can be read, constrained, and grounded against external symbolic structure. Geometry isn’t the goal — it’s the substrate that makes the other three goals tractable.

Why now: post-hoc interpretability methods have reached the ceiling of what they can recover from opaque models, and substrate-level designs (where the program is its own trace) are the natural next move.

That shows up as Sutra, a language where programs are visible tensor arithmetic instead of opaque control flow; Yantra, an operating system written in Sutra where the whole machine is one differentiable tensor graph; Loka, vector retrieval grounded in a typed knowledge graph; interactive tutorials, interpretability you can drag with your mouse; and Wikidata pipelines for the symbolic side of the loop.

02 — Flagship work

📜 Sutra In development
A geometric tensor programming language.

Every value is a tensor. Every operation is tensor arithmetic in a geometric space. There is no print, no if, no while — branches are continuous weighted blends and loops are geometric rotations. Programs compile to straight-line tensor operations, which makes them GPU-native and end-to-end differentiable by construction.

I’m building the reference compiler (PyTorch backend), the IntelliJ and VS Code plugins, the language specification, and the interactive demos — plus Loka, the bundled vector database. The name comes from the Sanskrit sūtra, the word used for Pān&dotbelow;ini’s grammar of Sanskrit, the earliest known formal grammar of any language.

Yantra Building now
A neuro-symbolic, GPU-native operating system written in Sutra.

The whole running system (kernel, processes, IPC, GUI) is one differentiable tensor-op graph, and a small CPU exists only to boot and orchestrate the GPU. Processes exchange axons (structured embeddings), so a local AI model integrates with no translation layer.

Built so far: a v0.0 kernel with real Sutra compute on torch tensors, disc-to-GPU storage-tier moves on real hardware, and a bootloader verified in QEMU. Aimed at critical systems where predictable latency and a readable verification surface matter more than mass-market compatibility.

03 — Research Directions

04 — Explainers

Interactive ML Tutorials
14 hands-on visualizers covering vector math, neural networks, training dynamics, and modern architectures. Drag, click, change the inputs, watch the math.
Loka Theory
Eight interactive explainers for the database internals: HNSW in RDF, subgraph SIMD indexing, SPARQL exit conditions, and how graph and vector databases differ.

05 — Projects

Projects
Every project — the geometric language, the triplestore, the research artifacts, and the AI-workflow tools — each on its own emmaleonhart.com subdomain, ranked by stars.

06 — Other Projects

07 — Links

emmaleonhart.com