Skill-describing phrases for course comparison and credit transfer

A central application of 3A-LLM is the semantic comparison of university course offerings and the support of credit transfer. We evaluate this use case on a supplementary corpus of skill-describing phrases. In this corpus, each phrase is represented as an acyclic directed graph: every node has either two children (Subject and Object) or no children. The maximum height of such a graph is \lceil\log_2(n)\rceil, where n is the number of words in the phrase. Terminal leaf nodes always contain semantic primes from the LDV that are not further decomposable; each node may additionally hold translations in arbitrary languages. This structure is analogous to 3A-LLM's a(b) compounding. We use approximately ten phrases from the \texttt{input} field that describe skills in computing, software development, hardware and software, and mathematics (equations, formulas, expressions, linear algebra). 3A-LLM supports query expansion (T1) and implicit concept prediction (T2) for these skill descriptions; the nested Subject--Object structure aligns with functional compounding and yields interpretable neighbourhoods. The following paragraphs detail the use case and worked examples.

Use-case: comparing course offerings and credit qualification. A central application is the semantic comparison of university course offerings. Course descriptions (learning outcomes, syllabi) can be mapped to skill-describing phrases and their implicit concepts; 3A-LLM then supports (i) comparing which courses at different institutions cover equivalent or related skills, and (ii) assessing whether a student has acquired enough credits for a bachelor or master degree, or how many credits are still missing. International standards apply: the European Credit Transfer and Accumulation System (ECTS) [EC2023ECTS] defines one academic year as 60 credits (approx. 1,500--1,800 hours workload); a bachelor degree typically requires 180--240 ECTS, a master 60--120 ECTS. ECTS is designed for transparency and recognition across the European Higher Education Area (EHEA). A further use-case is credit transfer: when a student moves from one university to another, the semantic alignment of course descriptions (via shared implicit concepts and 3A-LLM neighbourhoods) supports decisions on which completed modules can be recognised and how many credits count toward the target degree. The deterministic, explainable concept structure of 3A-LLM allows institutions to trace why two courses were deemed equivalent or how a credit gap was computed.

(1) Software development and lifecycle. “Students know the life cycle of software and master processes and methods of software development”: implicit concepts include software, process, method, development; 3A-LLM returns software, tool, artifact and related concepts from the neighbourhood of life cycle and development. “Students understand the concepts of software development tools and programming environments”: gold concepts software, tool, programming, environment; 3A-LLM expands development and programming to include tool and artifact.

(2) Planning and implementation. “Students independently plan and implement software projects including the necessary cost estimation based on a given problem”: implicit software, project, plan, cost, problem; 3A-LLM links project and implement to software and artifact. “They can structure and coordinate the design of complex systems”: implicit design, system, structure; 3A-LLM gives system, structure and design-related concepts in the neighbourhood.

(3) Data and representation. “They are able to prepare and graphically represent larger data sets and to analyze and interpret results”: implicit data, representation, analysis, result; 3A-LLM expands data and represent to result, measure and related terms. “Data processing design and implementation: basics of CV design, data modeling, table objects and relationship classes, dialog objects, design patterns, user manuals”: implicit data, model, object, design, pattern; 3A-LLM returns data, model, artifact and design in top-k.

(4) Programming and technologies. “Experience with HTML and CSS as well as API technologies such as REST / SOAP”: implicit technology, software, interface; 3A-LLM links API and technology to software and tool. “Programming skills in JavaScript and ideally Java”: implicit programming, software, language; 3A-LLM gives programming, software and language-related concepts. “Programming interfaces of network operating systems, client-server programming based on the transport layer, use of remote procedures and methods”: implicit network, system, programming, interface; 3A-LLM expands to network, system, software and interface.

(5) Mathematics: equations, formulas, linear algebra. “Linear algebra: systems of equations, Gaussian methods, operations on matrices and vectors”: implicit equation, matrix, vector, algebra, mathematics; 3A-LLM returns equation, formula, expression, matrix and mathematics in the neighbourhood. “Numerical methods: numerical computation and errors, iteration methods, linear systems of equations, numerical integration, interpolation, differential equation”: implicit equation, method, computation, mathematics; 3A-LLM links numerical and equation to mathematics, method and computation. “Students master the arithmetic operations of matrices and apply arithmetic rules for determinants”: implicit matrix, determinant, arithmetic, mathematics; 3A-LLM gives matrix, mathematics and operation-related concepts. “Functions in multiple derivatives: partial derivative, partial and full differential, chain rule, derivative of implicit functions, extrema”: implicit function, derivative, expression, mathematics; 3A-LLM expands to function, formula, mathematics and expression.

(6) Abstraction and algorithmic problem-solving. “Graduates of this module possess the ability to formulate more complex problems mathematically and solve them algorithmically”: implicit mathematics, algorithm, problem; 3A-LLM returns mathematics, algorithm, problem and method. “They develop skills for thinking in structures and for abstracting problems”: implicit structure, abstraction, problem; 3A-LLM links structure and problem to abstraction and method. “Discrete representation of an aspect of the meaning of a word”: implicit representation, meaning, word; 3A-LLM gives meaning, representation and word in the neighbourhood.

(7) Worked example: decomposing a complex skill phrase. Consider the phrase “Students can independently solve statistical problems in the field of economics.” In the corpus it is represented as a multi-level Subject--Object tree: statistical(students(can(independently_solve(problems))))(the_field(economics)). Inner nodes include students (plural of student), can (modal + ability), independently_solve (adverb independently + verb solve), problems (plural of problem), and the_field(economics) (prepositional “field of economics”). The root applies the adjective statistical (from statistics) to the clause and attaches the domain “in the field of economics.” Implicit concepts extracted for T2 are student, ability, independence, solution, problem, statistics, field, economics; 3A-LLM returns these in the neighbourhood and supports both query expansion (e.g. from statistical to mathematics, method) and credit-matching across course descriptions that use similar phrasing. The full decomposition is shown in the Appendix.

For all phrases above, the Subject--Object decomposition in the corpus (e.g. software(development), equation(system), matrix(operation)) aligns with 3A-LLM‘s functional view; T2 gold sets for skill-describing sentences were derived from the taxonomy and manual annotation. Mean derivation path length for 3A-LLM T2 predictions is 2.3 edges. The taxonomy-based gold sets align well with 3A-LLM’s graph structure where concepts are mapped; remaining errors are mostly due to missing mapping for rare types or disambiguation in homonymous contexts.