We introduce MLFMF, a collection of data sets for benchmarking recommendation systems used to support formalization of mathematics with proof assistants. These systems help humans identify which previous entries (theorems, constructions, datatypes, and postulates) are relevant in proving a new theorem or carrying out a new construction. Each data set is derived from a library of formalized mathematics written in proof assistants Agda or Lean. The collection includes the largest Lean 4 library Mathlib, and some of the largest Agda libraries: the standard library, the library of univalent mathematics Agda-unimath, and the TypeTopology library. Each data set represents the corresponding library in two ways: as a heterogeneous network, and as a list of s-expressions representing the syntax trees of all the entries in the library. The network contains the (modular) structure of the library and the references between entries, while the s-expressions give complete and easily parsed information about every entry.We report baseline results using standard graph and word embeddings, tree ensembles, and instance-based learning algorithms. The MLFMF data sets provide solid benchmarking support for further investigation of the numerous machine learning approaches to formalized mathematics. The methodology used to extract the networks and the s-expressions readily applies to other libraries, and is applicable to other proof assistants. With more than $250\,000$ entries in total, this is currently the largest collection of formalized mathematical knowledge in machine learnable format.

Large language models (LLMs) excel at generating code from natural language (NL) descriptions. However, the plain textual descriptions are inherently ambiguous and often fail to capture complex requirements like intricate system behaviors, conditional logic, and architectural constraints; implicit data dependencies in service-oriented architectures are difficult to infer and handle correctly. To bridge this gap, we propose a novel step-by-step code generation framework named UML2Dep by leveraging unambiguous formal specifications of complex requirements. First, we introduce an enhanced Unified Modeling Language (UML) sequence diagram tailored for service-oriented architectures. This diagram extends traditional visual syntax by integrating decision tables and API specifications, explicitly formalizing structural relationships and business logic flows in service interactions to rigorously eliminate linguistic ambiguity. Second, recognizing the critical role of data flow, we introduce a dedicated data dependency inference (DDI) task. DDI systematically constructs an explicit data dependency graph prior to actual code synthesis. To ensure reliability, we formalize DDI as a constrained mathematical reasoning task through novel prompting strategies, aligning with LLMs' excellent mathematical strengths. Additional static parsing and dependency pruning further reduce context complexity and cognitive load associated with intricate specifications, thereby enhancing reasoning accuracy and efficiency.

We introduce MLFMF, a collection of data sets for benchmarking recommendation systems used to support formalization of mathematics with proof assistants. These systems help humans identify which previous entries (theorems, constructions, datatypes, and postulates) are relevant in proving a new theorem or carrying out a new construction. Each data set is derived from a library of formalized mathematics written in proof assistants Agda or Lean. The collection includes the largest Lean 4 library Mathlib, and some of the largest Agda libraries: the standard library, the library of univalent mathematics Agda-unimath, and the TypeTopology library. Each data set represents the corresponding library in two ways: as a heterogeneous network, and as a list of s-expressions representing the syntax trees of all the entries in the library.

Those of you subscribing to the nupic-theory mailing list are aware that a new research paper describing a mathematical model for the spatial pooler (SP) has emerged. Many of us have asked "What is the math behind the SP?" or "How can I use the SP for machine learning". The goal of this paper is to address those very questions, bridging the gap between HTM and the machine learning community. This work is part of a much larger body of work being conducted by the Rochester Institute of Technology's (RIT's) NanoComputing Research Lab. Our lab is specifically focused on designing energy efficient hardware circuits and architectures that are biologically inspired.