Non-AI Expressive Mapping

• Non-AI expressive mapping is a method that uses explicit rules and parameterized functions to transform high-level expressive inputs into nuanced outputs across domains like music, robotics, and rhetoric.
• It emphasizes transparency and direct human control, avoiding data-driven AI to provide interpretable and predictable mappings through handcrafted logic.
• Evaluation metrics such as accuracy, negative log-likelihood, and reward-based measures validate these mappings, establishing robust baselines and clear design principles in each domain.

Non-AI expressive mapping refers to the systematic, fully interpretable transformation of high-level expressive inputs or intentions into nuanced outputs—such as musical performance attributes, robot movement trajectories, or rhetorical strategies—using explicit rules, parameterized functions, or handcrafted mapping logic, rather than any form of machine learning or data-driven AI. These mappings are foundational to domains where transparency, predictability, and human-understandable structure are critical, providing robust baselines, interpretability, and direct control over expressive affordances across fields including music technology, robotics, human-computer interaction, and computational rhetoric.

1. Formal Foundations and Representative Domains

Non-AI expressive mapping universally entails the definition of a target representation space (e.g., dynamics/timbre vectors, movement primitives, rhetorical configuration), the specification of explicit mappings from input features to output behavior, and domain-specific design criteria for expressivity and functionality.

• Expressive performance mapping in music: Given a fixed musical score (symbolic notes and timing), the objective is to map these to expressive parameters such as velocity and timbre, often for each voice and time step. The NES-MDB framework exemplifies this, defining a mapping $f: C \rightarrow P$ where $C$ is the score and $P$ encodes vectors of dynamics and timbre for the NES's Pulse, Triangle, and Noise voices, parameterized at $24$ Hz, with categories as fine as $$V_{t,v} \in \{0 \dots 15\},\ T_{t,v} \in \{0 \dots 3\}$$ or $\{0,1\}$ (Donahue et al., 2018).
• Expressive motion and gesture in robotics: The ELEGNT framework specifies movement as a sequence of time-indexed state/action tuples in an MDP. Here, expressive mapping is realized as a deterministic or handcrafted policy that injects spatial and temporal "primitives"—e.g., amplitude and speed of a head nod or arm wave—into the trajectory plan, balancing user-defined weights on functional and expressive reward (Hu et al., 21 Jan 2025).
• Instrumental and interface sonification: The MindCube system maps IMU, button, and joystick readings via piecewise linear or exponential normalization to low-level synthesis controls (VCV Rack CVs for cutoff, LFO, panning, etc.), each mapping being fully specified and invertible (Liu et al., 22 Jun 2025).
• Linguistic and rhetorical structure: Expressive mapping operates as an algebra of operators (split, unite, invert, etc.) over a discrete atomic/compound set of rhetorical modes, with subsequent organization into a pyramid comprising rhetorical (surface), cognitive (function), and epistemic (purpose) layers (Wu, 10 Nov 2025).

2. Mapping Architectures and Algorithmic Strategies

Non-AI expressive mapping architectures generally fall into one or more of the following algorithmic types, depending on domain constraints and expressive requirements:

• Rule-based mapping: Explicit if-then or state machine logic, e.g., "if pitch changes, reset velocity to training-set median; else, retain current velocity" (Donahue et al., 2018).
• Simple statistical models: Unigram and bigram counts as baseline estimators—i.e., $P(V_{t,v}=x) = \operatorname{freq}(x)$ or $P(V_{t,v}=x|V_{t-1,v}=y)$—offering interpretable, data-grounded mappings (Donahue et al., 2018).
• Multinomial regression: Linear softmax models with interpretable feature sets (such as one-hot note embeddings, previous state variables) directly mapping input context to expressive outputs (MultiReg Note+Auto), without hidden layers or stochasticity (Donahue et al., 2018).
• Parameter normalization and mapping functions: Linear/exponential conversion from physical sensor readings to control values, such as mapping $(\phi, \theta)$ (roll, pitch) continuously to $(\text{cutoff}, \text{LFO rate})$ using fixed scaling/offset formulas (Liu et al., 22 Jun 2025).
• Operator calculus over categorical structures: For complex cognitive regimes, mapping is formalized as operator sequences acting on base mode sets, e.g., split–unite duality to generate new rhetorical hybrids or expansion–reduction to navigate expressive scale (Wu, 10 Nov 2025).
• Trajectory waypoint injection: Primitives instantiated as explicit geometric/temporal parameters (e.g., head nod amplitude, speed, pause length) are inserted into MDP-based planners as regularized waypoints (Hu et al., 21 Jan 2025).

A representative table summarizing algorithmic families:

Architecture Type	Example Domains	Representative Papers
Rule/statistical models	NES music, linguistics	(Donahue et al., 2018, Wu, 10 Nov 2025)
Parameterized function mapping	Sonification, robotics	(Liu et al., 22 Jun 2025, Hu et al., 21 Jan 2025)
Operator calculus	Rhetorical mode systems	(Wu, 10 Nov 2025)

3. Evaluation Metrics and Benchmarks

Non-AI expressive mapping frameworks employ domain-specific, quantitative evaluation metrics to assess output plausibility, fidelity, and expressive capacity.

• Music expressive mapping (NES-MDB): The primary metrics are negative log-likelihood (NLL) and framewise/POI accuracy. NLL is defined as $C$0, while accuracy is given as a normalized count of correct matches. Special attention is paid to "Points of Interest" (POI), frames at which a pitch change triggers a likely expressive change. Baselines achieved: bigram model with NLL/all=4.57, accuracy/all=0.741 but accuracy/POI=0.000, indicating mere copying behavior; MultiReg Note+Auto with NLL/all=4.32, accuracy/all=0.752, but accuracy/POI=0.137 (Donahue et al., 2018).
• Robot movement (ELEGNT): Evaluation is multi-modal: combined reward function $C$1, plus qualitative user studies reporting perception metrics (e.g., engagement, character, human-likeness; expression-driven: mean score 56.16 vs. function-only: mean 28.77, $C$2 across several metrics) (Hu et al., 21 Jan 2025).
• Sonification controllers: While the MindCube system lacks formal user study results, future directions include expression quantification (e.g., range, control smoothness), and possible adoption of standard expressive range evaluations (Liu et al., 22 Jun 2025).
• Expressive mode operations in rhetoric: Expressive diversity is quantified in combinatorial terms (total possible mode sets $C$3) and measured in bits of Shannon entropy. Hierarchical mapping reduces cognitive complexity: entropy in flat selection ($C$4) versus hierarchical selection ($C$5 for cognitive clusters of size $C$6), demonstrating distinct reductions in uncertainty (Wu, 10 Nov 2025).

4. Design Principles and Domain-Specific Implementation Strategies

Distinct domains highlight unique design recommendations rooted in empirical results:

• Temporal structure and context separation: In music, do not overweight rare but salient POIs as this destabilizes output; instead, use score for POI detection and past expressive state for parameter value determination (Donahue et al., 2018).
• Waypoint/primitive reasoning in robotics: Expressive intention mapping proceeds from category (attention, attitude, emotion) to primitive selection, low-level parameterization, and waypoint injection in planned trajectories. Trades off are managed by the scalar $C$7 controlling expressivity versus efficiency (Hu et al., 21 Jan 2025).
• Mapping space modeling in sonification: Transparent, continuous mappings from sensor dimensions to synthesis parameters enable immediate audition and control. Calibration routines, layering, and dynamic mapping extension are suggested routes for refinement (Liu et al., 22 Jun 2025).
• Hierarchical selection and expressivity scaling in rhetoric: Organizing generated modes in a pyramid (rhetorical/cognitive/epistemic) systematically narrows choices, providing a quantifiable measure of expressive growth (Marginal Rhetorical Bit, $C$8 bit per mode; rhetorical scaling $C$9 for $P$0 new modes per stage) (Wu, 10 Nov 2025).

5. Case Studies, Benchmarks, and Impact

Selected cases demonstrate the practical consequences and strengths of non-AI expressive mapping:

• NES-MDB mapping: Even a bigram model attains $P$1 global accuracy, but fails at POIs. MultiReg Note+Auto achieves $P$2 global accuracy but exhibits smoothing at salience boundaries, reinforcing the importance of explicit, context-sensitive rules (Donahue et al., 2018).
• ELEGNT robot: Expression-driven movement achieved statistically significant improvements in all perception metrics in social-oriented tasks, with case-specific gains up to $P$3 on a 0–100 scale (Hu et al., 21 Jan 2025).
• MindCube sonification: The non-AI mapping, while domain-transparent and immediately usable, lacks adaptive or context-sensitive mapping, motivating calibration and automated mapping extension in future work; expressive affordances are mediated strictly by the structure of sensor-to-CV mapping (Liu et al., 22 Jun 2025).
• Rhetorical operator calculus: Hierarchical mapping reduces entropy and cognitive load for both writers and readers, facilitating the design of scalable, dynamic discourse systems without requiring AI components (Wu, 10 Nov 2025).

6. Limitations, Extensions, and Outlook

Non-AI expressive mappings are valued for interpretability, transparency, and immediate control, but they reveal domain-characteristic limitations:

• Adaptivity and individualization: Handcrafted mappings lack adaptation to users, performers, or contexts; e.g., MindCube mappings require explicit calibration for optimal operation (Liu et al., 22 Jun 2025).
• Expressive resolution and complexity: Rule-based or statistical models quickly reach ceilings in domains with high temporal/semantic variability (e.g., music POIs), and operator-based systems risk combinatorial blowup without hierarchical constraint (Donahue et al., 2018); (Wu, 10 Nov 2025).
• Lack of data-driven nuance: These methods do not exploit the learning of subtler patterns or affordances that may emerge from large, complex datasets.

Nevertheless, non-AI expressive mapping provides essential baselines for evaluating AI-based methods, robust scaffolding for participatory and interdisciplinary design, and a framework for the quantification and structuring of expressive intent in domains where interpretability, transparency, and direct manipulation are paramount (Donahue et al., 2018); (Hu et al., 21 Jan 2025); (Liu et al., 22 Jun 2025); (Wu, 10 Nov 2025).