Athanor: Visualization and CBLS Systems

• Athanor is a dual-system framework, with Athanor-Vis enhancing static SVGs via natural language and Athanor-CBLS optimizing high-level constraint models.
• Athanor-Vis employs a formal action–modification design and multi-agent analysis to convert user instructions into dynamic, interactive visualizations.
• Athanor-CBLS leverages automatic neighborhood generation and iterated local search over Essence models to achieve scalable, state-of-the-art optimization.

Athanor is the name attributed to two distinct, technically significant systems: one in the domain of interactive data visualization (Athanor-Vis), and one in the field of combinatorial optimization and constraint-based local search (Athanor-CBLS). Both systems are notable for their novel use of abstraction—Athanor-Vis abstracts over static visualization structures to enable interaction, while Athanor-CBLS abstracts over high-level constraint specifications to enable scalable local search. Despite sharing a name and a philosophy of abstraction, their architectures, application domains, and technical underpinnings are fundamentally different. The following entry provides deep coverage of both systems as presented in the key research sources (Liu et al., 25 Jan 2026, Attieh et al., 2024).

1. Athanor for Interactive Data Visualization

Athanor-Vis is a system designed to transform static data visualizations (such as SVG figures in academic publications) into flexible, interactive experiences solely via natural-language instructions, without requiring the original code or underlying data. It addresses the widespread problem that most published figures are static, prohibitively difficult to augment, and locked to tool-specific pipelines. Athanor-Vis operates independently of the visualization's original toolkit, including Vega-Lite, D3, ECharts, and others (Liu et al., 25 Jan 2026).

Central to Athanor-Vis is a formal action–modification interaction design space, a multi-agent requirement analyzer for parsing user intent, and a visualization abstraction transformer that supports robust interactive behaviors by leveraging multimodal LLMs (MLLMs).

2. Athanor for Local Search over Abstract Constraint Specifications

Athanor-CBLS is a general-purpose local search solver that departs from conventional constraint-based local search (CBLS) practices by operating directly over high-level, abstract specifications written in the Essence language. Unlike traditional solvers that require flattened, primitive representations (as seen with MiniZinc or FlatZinc), Athanor-CBLS exploits the nested type structures and semantics presented in Essence models, thus preserving high-level information and enabling automatic, structurally aware search neighborhoods (Attieh et al., 2024).

This approach confers notable scalability advantages and circumvents the need for the manual construction of neighborhood moves, which is a significant bottleneck in CBLS and IPLS approaches.

3. Technical Foundations and Architectures

Athanor-Vis: Abstraction for Visualization Interactivity

• Action–Modification Design Space: Interactions are specified as tuples $(a, t, m, p)$, where $a$ is an action (from a set $A$ of user actions such as hover, click, zoom), $t$ is a target (visual mark, reference component, extra widget), $m$ is a modification (emphatic, reductive, annotative, navigational, organizational, or representational), and $p$ is an optional parameter. The formal mapping is given by $f: A \times T \to 2^M$, supporting flexible specification.
• Multi-Agent Requirement Analyzer: The analyzer decomposes natural-language instructions into interaction specifications via three agents:
  • Translation Agent: Generates initial specs from language inputs.
  • Correction Agent: Ensures spec validity against design-space constraints and chart properties; if invalid, provides feedback for repair.
  • Guidance Agent: Handles under-specification by requesting clarification or suggesting defaults.
• Visualization Abstraction Transformer: Converts static SVGs into a control-point graph (SimVec structures), applies constraints for shape, layout, and alignment, and supports interactive modifications through purely visual analysis without code access. Modifications update constraints, styles, or data structures as appropriate, employing MLLMs for element classification and context-aware transformation (Liu et al., 25 Jan 2026).

Athanor-CBLS: Abstract Local Search for Optimization

• Essence Input Parsing: The solver ingests Essence specifications, builds abstract syntax trees (ASTs) for constraints and objectives, infers types, and retains high-level domain structure.
• Automatic Neighborhood Generation: For each decision variable type, Athanor-CBLS instantiates atomic and container-based move templates (e.g., setAdd, seqReverseSub, partMerge), lifted recursively through nested containers by LiftSingle and LiftMultiple combinators.
• Resource-Bounded Value Representation: Assignments for high-level types consume $O(|\textit{value}|)$ space, not $O(\max|\textit{domain}|)$, enabling dynamic, incremental evaluation.
• Iterated Local Search (ILS) Strategy: Athanor-CBLS alternates repair (hill-climbing to zero constraint violation), improvement (objective-driven search), and exploration (random walks for local escape) phases, orchestrated by multi-armed bandit UCB controllers specific to repair or optimization.
• Incremental Evaluation: Comprehensions are unrolled dynamically, so complexity scales with the current assignment cardinality rather than worst-case domain size, ensuring efficient propagation and evaluation (Attieh et al., 2024).

4. Applications and Empirical Results

Athanor-Vis: Interaction Authoring for Static Charts

Athanor-Vis enables retrofitting static SVG figures with diverse interactions, including tooltips, dynamic filtering, sorting, stacking, rescaling axes, grouping, and switching between representation types. Case studies demonstrate:

• Stacked Area Chart: Simple hover-to-tooltip mappings and complex comparisons via brushing and comparison widgets, inducing relayout and rescaling.
• Multi-Line Emissions Chart: Sequences of representation swapping, stacking, zooming, and hover-based tooltips, supporting precise user analytics.

User studies with visualization practitioners report a mean coverage of ≥90% for desired actions/modifications, Likert-scale scores >4/5 on usability and learnability, rapid time-to-first-interaction (<10 minutes in 10/11 cases), and uniform praise for the natural-language interface (Liu et al., 25 Jan 2026).

Athanor-CBLS: Constraint Optimization Benchmarks

Athanor-CBLS achieves state-of-the-art or near-leading performance on benchmarks characterized by nontrivial variable structure:

• SONET, CVRP, PPP: Outperforms all tested local search and systematic solvers, attributable to high-level templates.
• Bin Packing, TSP: Matches or exceeds top performers using problem-specific heuristics.
• Scalability: Successfully solves instances far beyond the practical limits of comparators (e.g., bin packing with 2,000 items; knapsack with 80,000 items).
• Limitations: Largest PPP (progressive party) instances expose cases where richer search guidance strategies may be needed (Attieh et al., 2024).

5. Limitations and Future Directions

Athanor-Vis

• Scope Constraints: Athanor-Vis can only manipulate information encoded visually (SVG elements), not external datasets underlying the visualization. Non-Cartesian and non-SVG figures (maps, force-directed layouts, raster images) are outside the current scope, requiring enhanced topology inference or vision models.
• Scalability: For visualizations with >1,000 marks, per-mark detail may be elided to avoid MLLM token limits.
• Usability Gaps: Users request additional features, such as pre-application previews, auto-complete, and support for voice or composite charts.
• Planned Extensions: Incorporation of external data binding, geometry-based reasoning for advanced layouts, and multimodal input support are indicated as near-term research priorities (Liu et al., 25 Jan 2026).

Athanor-CBLS

• Search Guidance: Performance on highly unstructured host-set variables suggests opportunities for developing advanced search strategies.
• Global Constraints: While general-purpose local search is competitive with problem-specific propagators, certain global constraints (e.g., circuit for TSP) remain challenging.
• Abstraction Boundary: The abstract domain approach presupposes availability and expressivity of Essence; flat or primitive-only input models cannot fully exploit Athanor-CBLS's capabilities (Attieh et al., 2024).

6. Significance and Impact

Both Athanor systems epitomize the value of reasoning at an abstract level, either over visual interactions or constraint types. Athanor-Vis effectively democratizes the augmentation of static visualizations, moving beyond code- or dataset-centric designs via MLLM-powered abstraction. Athanor-CBLS demonstrates that operating directly on high-level types through automatic neighborhood derivation not only matches but also often surpasses problem-specific search and propagation methods, especially for problems with nested or complex variable structure.

Taken together, these systems illustrate how deliberate preservation and exploitation of abstraction in system design can drive practical solutions to long-standing bottlenecks in usability (Athanor-Vis) and scalability (Athanor-CBLS), with implications for fields as diverse as information visualization and combinatorial optimization (Liu et al., 25 Jan 2026, Attieh et al., 2024).