PhD Position: World Models for Software Architecture Synthesis (Constructor Fabric)

Constructor Labs · Bremen · €1,650/month (stated in the posting)

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Supervisor: Prof. Dr. Alexander Tormasov

About the Position

Constructor Knowledge Labs (CKL), in collaboration with Constructor Technology, invites applications for a PhD position in machine learning for software engineering and formal methods, on the Constructor Fabric project.

Constructor Fabric turns a company's informal knowledge into production software through a pipeline of composable capability units called gears: requirements → architecture → product fit → framework (G1) → application → runtime. We are building a World Model over that pipeline — a model that does not just generate code, but predicts the consequences of an architectural decision: total cost of ownership, unintended side effects, latency and failure behaviour, and whether a proposed composition is even admissible.

The central object is not a digital twin of the application but its formal architectural skeleton: gear contracts (GearSpec), a typed attributed hypergraph of the application (AppGraph), a composition algebra that defines which assemblies are legal, and several semantic projections (types, protocols, resources, security) over which properties are proved, refuted by counterexample, or reported as an explainable gap. All of it is written in a domain-specific language whose syntax trees and graphs we keep in a projectional editor (JetBrains MPS) — so the DSL is not a convenience layer, it is the thing that defines the model's state space and the boundary of what the model is allowed to propose.

What you will work on
Depending on your background, one or two of:

1. Formal skeleton and composition — GearSpec as a contract $(Requires, Provides, State, Effects, Assumptions, Guarantees, Parameters)$; AppGraph as a typed attributed hypergraph; an algebra of assembly (sequential, parallel, feedback, refinement); semantic projections and system-level invariants over trajectories.
2. Architecture synthesis as an inverse problem — given a specification, load and constraints, find the composition of gears that realises it. Constraint solving and MCTS as the baseline; a learned transition/value model for ranking and pruning; LLM proposals treated strictly as candidate hypotheses that a DSL parser, type checker and property checks must then admit or reject.
3. DSL design and language engineering — the gear DSL and its glue layer decide which AppGraphs are expressible at all, and therefore where the search space ends. This thread covers the abstract syntax and static semantics of that DSL; the requirement that an architectural decision be unbypassable by construction (you must not be able to wire authentication around the Auth Resolver); what happens to the language when gear contracts change or a 201st gear is added; projectional representation of graphs with cycles; and the open hypothesis that a specialised G1-DSL is generated together with every G1.
4. Local transition models and pipeline surrogates — fast approximate predictors for single pipeline steps (spec change → code quality, architecture → product fit, app → runtime outcome), with calibrated uncertainty, validated against real telemetry.
5. Data — reconstructing (specification → architecture) pairs from open repositories at scale, plus synthetic project generation from a fixed gear set and DSL grammar to cover rare transitions, gaps and counterexamples.

Profile

• MSc (or equivalent) in computer science, mathematics, or a mathematical natural science.
• Coursework in compilers, programming-language theory, language design or model-driven engineering is a strong positive signal, half of this project is deciding what a formal architecture description is allowed to say.
• Evidence that you finish things: a maintained open-source repository, a peer-reviewed publication, or a strong competition result.
• Fluent technical English.
• Most importantly: the habit of stating an assumption explicitly and designing an experiment that could falsify it.

Required mathematical background

Core skills:

• Probability and statistics. Estimation, Bayesian inference, uncertainty quantification and calibration (proper scoring rules, reliability diagrams, ECE), experiment design and significance testing. A prediction we cannot calibrate is not usable here.
• Linear algebra and multivariate calculus at the level needed to derive, not just call, a training objective: matrix calculus, gradients, stochastic optimisation, conditioning.
• Discrete mathematics and graph theory. Typed and attributed graphs and hypergraphs, subgraph matching and isomorphism, graph rewriting, reachability, basic complexity classes.
• Mathematical logic and formal methods. First-order logic, type systems, SAT/SMT, temporal logic (LTL/CTL) and model checking, pre/post-conditions, invariants, refinement.
• Sequential decision making. MDP/POMDP, dynamic programming, model-based RL, latent state-space (world) models, Monte-Carlo Tree Search.

Strong command of at least one, working knowledge of a second:

• Formal languages, semantics and language engineering — grammars (context-free, attribute and graph grammars), derivation and reachability, parsing; abstract versus concrete syntax; operational and denotational semantics; metamodelling, model-driven engineering, model-to-model transformation, and projectional (structural) editing of the kind JetBrains MPS implements. We are asking for the education, not the tool: you should know why a projectional editor exists, what a metamodel buys you over a text grammar, and how a language evolves without breaking its existing models. Hands-on MPS experience is explicitly not required — we will teach it.
• Category theory for compositional systems — monoidal and traced monoidal categories, functors as semantic projections, string diagrams, operads. This is the language of our assembly algebra.
• Causal inference — structural causal models, do-calculus, counterfactuals, identifiability. Required for the "what happens if we replace this technology / move on-premises" class of questions, which similarity search alone cannot answer.
• Queueing theory and applied stochastic processes — M/M/1 and networks of queues, heavy tails, retries, timeouts, partial failure and reliability models. This is the resource and stochastic projection.
• Combinatorial optimisation, constraint programming and program synthesis theory — CEGIS, version-space algebras, symmetry breaking, search heuristics.
• Representation learning theory — VAEs and latent dynamics, GNN expressiveness (Weisfeiler-Leman hierarchy), permutation equivariance, embedding migration under a changing vocabulary.

Required hands-on programming skills

This is an engineering-heavy PhD. We expect code that another person can clone, run and reproduce — not notebooks that worked once.

Must have:

• Python (professional level). Type hints, packaging, `pytest`, profiling, `asyncio`, memory-aware data structures. You write unbuffered, logged, restartable long-running jobs by default.
• Training loops written from scratch, custom datasets and collation, mixed precision, multi-GPU; experiment tracking (W&B or MLflow), configuration management (Hydra), strict seed and artefact reproducibility.
• Graph machine learning. PyTorch Geometric or DGL — message passing, heterogeneous and typed graphs, graph transformers, handling graphs whose node vocabulary changes between versions.
• Solvers and verification tooling driven from Python. Z3 or cvc5 hands-on; demonstrated exposure to at least one model checker (TLA+/TLC, SPIN, NuSMV, Alloy) or proof assistant (Lean, Coq, Isabelle).
• Code as data. AST manipulation, `tree-sitter`, static analysis, dependency and interface graph extraction, large-scale repository mining.
• Parallel data pipelines. `multiprocessing`, Ray or Dask; checkpointing, heartbeats, cost estimation before launching a run that touches millions of files.
• LLM engineering. API orchestration, structured and grammar-constrained decoding, evaluation harnesses, token/cost accounting — with the discipline to treat model output as a hypothesis subject to formal checks.
• Linux, git, code review, shell.

Desirable:

• Language tooling you have actually used: ANTLR, Xtext, Lark, or a parser, type checker or interpreter you wrote yourself. Our internal representation of gear syntax trees and graphs lives in JetBrains MPS — again, we do not ask for MPS experience, only that you are comfortable reading and extending a metamodel; Java/Kotlin literacy helps once you get there.
• JAX, or compiler / SAT-SMT internals.
• Infrastructure literacy — Docker, Kubernetes, Terraform, OpenTelemetry/Prometheus — since the resource projection is calibrated against real deployment telemetry.
• One systems language (Rust, Go or C++) for performance-critical search.
• Prior experience with production software architecture, or with a brownfield system you had to change without breaking.

Funding

The appointment provides full financial coverage through a dedicated fellowship, comprising:

• Monthly stipend of €1,650
• Monthly research-cost allowance of €100 (Forschungskostenpauschale)
• Health-insurance subsidy of €100 per month

Location: Bremen, Germany

Duration: 3 years, full time

Start date:  November 2026

Application package must include

• CV, including publications, code, or research projects.
• Cover letter (1–2 pages) explaining your motivation, research interests, and fit with the project.
• A link to code you have written.
• A one-page research statement picking one open research question from the project and sketching how you would approach it.
• Master’s and Bachelor’s degree certificate and transcripts.
• Contact information for 2–3 academic referees.

Applications are reviewed on a rolling basis. Shortlisted candidates will be invited to interviews.

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