Expressive Range Analysis (ERA)

• Expressive Range Analysis (ERA) is a quantitative framework that maps generated outputs into low-dimensional descriptor spaces to measure variability, coverage, and density.
• ERA has evolved from classic procedural content generation in game levels to multidimensional applications in text-to-audio and speech expressiveness via metrics like emotion, prosody, and spontaneity.
• ERA functions both as an evaluative tool and a design space for controlled generation, with methodological challenges in metric selection and projection strategy influencing its insights.

Expressive Range Analysis (ERA) is a quantitative framework for characterizing the space of outputs that a generator can produce by mapping sampled artifacts into a descriptor space and examining variability, coverage, boundaries, density, clusters, and outliers. In its classical form within Procedural Content Generation (PCG), ERA is a two-metric visualization in which generated artifacts are plotted in a 2D plane or heatmap to support comparison of generators and reasoning about search space exploration. More recent work has extended ERA beyond game levels to fixed-prompt text-to-audio generation and to speech systems, where DeEAR operationalizes expressiveness as a multidimensional space over Emotion, Prosody, and Spontaneity rather than a single subjective score (Withington et al., 2023, Morse et al., 31 Oct 2025, Lin et al., 23 Oct 2025).

1. Origins in Procedural Content Generation

ERA is widely used in PCG research as a simple way to visualize the outputs of generative systems. The standard workflow is to sample a large set of artifacts, compute two quantitative metrics for each artifact, and plot the resulting points in a 2D space. The plot is then interpreted in terms of coverage, density, clusters, patterns, and outliers. In level generation, these metrics are often domain-specific and interpretable, such as linearity, leniency, number of enemies, counts of tile types, or agent-derived measures such as jump count and time taken (Withington et al., 2023).

A central conceptual distinction in the PCG literature is between a generator’s generative space, meaning the artifacts it can actually produce, and the broader possibility space, meaning all artifacts that could exist in the domain. ERA projects both into a lower-dimensional descriptor space. This makes the method useful for comparing systems, but it also creates a well-known methodological risk: if the chosen metrics compress the possibility space, induce redundant axes, or concentrate desirable content into a small region, the projection can make a rich generator appear narrow or misleadingly structured (Withington et al., 2023).

Within this tradition, ERA has been valued for three kinds of analysis. First, it supports judgments about creativity and diversity, asking whether a generator produces many distinct artifacts. Second, it supports judgments about fidelity, asking whether outputs are faithful to the intended domain or prompt. Third, it supports judgments about controllability, asking whether changes in parameters or stochastic seeds produce understandable changes in output. Later adaptations to audio retain these three concerns, although the descriptor spaces and validation procedures differ substantially from level generation (Morse et al., 31 Oct 2025).

2. Formal structure and families of measurements

In the classical 2D formulation, a generator $G$ produces artifacts $x \in X$, and two metrics $m_1$ and $m_2$ map artifacts to real values. The expressive range is the set

$$R = \{(m_1(x), m_2(x)) \mid x \in X_{\text{generated}}\}.$$

This representation is usually visualized as a point cloud or as a discretized 2D histogram. In level-generation work, the continuous metric space is often partitioned into bins, making occupancy and coverage directly visible (Bazzaz et al., 4 Apr 2025).

ERA has progressively expanded beyond simple 2D scatter plots. In fixed-prompt text-to-audio work, the generator is formalized as

$a = G(p, z),$

where $p$ is a text prompt and $z$ is stochastic input. A feature extractor produces $x = F(a) \in \mathbb{R}^d$, and for a fixed prompt $p$ the expressive range is the induced distribution $x \in X$0 over feature vectors. The empirical mean and covariance are then

$x \in X$1

with PCA used to visualize spread in a reduced space (Morse et al., 31 Oct 2025).

The families of measurements that recur across ERA variants are breadth, diversity, coverage, and boundaries. In 2D PCG practice these are typically expressed through occupied bins, density patterns, pairwise distances, and convex-hull area or volume. In text-to-audio ERA, the paper reports normalized total variance in PCA space,

$x \in X$2

with the ESC-50 reference set normalized to $x \in X$3 (Morse et al., 31 Oct 2025).

The speech-oriented extension in DeEAR makes the multidimensional structure explicit. For utterances $x \in X$4 and dimensions $x \in X$5 with scores $x \in X$6, the proposed ERA statistics include per-dimension range

$x \in X$7

mean

$x \in X$8

variance

$x \in X$9

and interquartile range

$m_1$0

After normalization to $m_1$1, coverage can be quantified by convex-hull coverage $m_1$2, grid coverage $m_1$3, and thresholded coverage $m_1$4, while controllability is captured by mean $m_1$5 error $m_1$6, success rate within an $m_1$7-ball $m_1$8, and per-dimension Spearman correlations between requested and achieved targets (Lin et al., 23 Oct 2025).

3. Metric selection as a methodological problem

A persistent issue in ERA is that the informativeness of a visualization depends heavily on the chosen descriptor pair. The metric-selection literature argues that ERA has often relied on established but unjustified norms, designer intuition, or exhaustive corner plots, even though different metric pairs can produce substantially different impressions of output diversity and search-space exploration (Withington et al., 2023).

One proposed remedy is to rank candidate metric pairs using three explicit criteria. Fitness Independence (FI) favors pairs for which fit or desirable artifacts are spread across the ERA plane rather than concentrated in a small region. In the Mario study, the plane is discretized into a $m_1$9 grid using min–max ranges, and each cell’s score is the average fitness of the artifacts falling into that cell, with empty cells depressing the overall score. Mutual Correlation (MC) penalizes redundancy between the two axes by computing $m_2$0 using Spearman’s $m_2$1. Alternative Metric Correlation (AMC) favors pairs that remain informative with respect to other unplotted metrics by averaging, over all alternative metrics, the larger absolute correlation with either axis (Withington et al., 2023).

The empirical study evaluates 153 metric pairs from 18 metrics over 9015 Mario levels generated by nine generators plus 15 original Nintendo levels. The best overall pair by average rank is Density–AverageY, with FI $m_2$2, MC $m_2$3, AMC $m_2$4, and AverageRank $m_2$5. The top FI pair is Density–JumpCount with FI $m_2$6; the top MC pair is EmptySpaceCount–MaxJumpAirTime with MC $m_2$7; and the top AMC pair is EmptySpaceCount–JumpCount with AMC $m_2$8. By contrast, Contiguity–BlockCount is presented as the worst overall pair because it yields a more redundant and less discriminative projection (Withington et al., 2023).

This work also identifies a recurrent structural pattern: mixed pairs combining one structural metric and one agent-extracted metric tend to rank well. Among the 20 pairs comprising the top-5 lists for each criterion plus the top-5 overall, 15 of 20 pairs are mixed, compared with only 2 structural–structural and 3 agent–agent pairs. The same paper notes a specific failure mode of FI: extreme outliers can stretch the min–max binning and depress the score, as illustrated by a level with MaxJumpAirTime of 148 frames against a usual range of 0–62 (Withington et al., 2023).

4. ERA as a design space for constrained generation

ERA has also been used not merely as an evaluation tool but as a conceptual design space to be actively traversed. In level generation with constrained expressive range, the expressive range is defined over two tile-count metrics—density, the number of non-background tiles, and difficulty, the number of enemy or hazard tiles including gaps—and the generator is directed toward underrepresented regions of that space rather than sampled opportunistically (Bazzaz et al., 4 Apr 2025).

The generator in this setting is Sturgeon, a constraint-based system with a mid-level API that compiles to low-level constraint satisfaction problems. Tile variables $m_2$9 are constrained by local pattern templates learned from Super Mario Bros. corpus segments and by global count constraints such as

$$R = \{(m_1(x), m_2(x)) \mid x \in X_{\text{generated}}\}.$$0

$$R = \{(m_1(x), m_2(x)) \mid x \in X_{\text{generated}}\}.$$1

Three pattern templates are studied: ring, block2, and nbr-plus. Ring is described as the most constrained, nbr-plus as the least constrained, and block2 as intermediate (Bazzaz et al., 4 Apr 2025).

Traversal is organized over a grid in the density–difficulty plane. Underrepresented cells are defined as bins with fewer than 10 levels. At each step, the procedure selects uniformly at random among cells with minimum occupancy, attempts to generate a level satisfying the target bin constraints, and places cells on a blocklist if generation fails or if the occupancy cap is reached. Each attempt has a 15-minute timeout, and each template is run for 12 hours (Bazzaz et al., 4 Apr 2025).

The quantitative results show clear trade-offs between structural fidelity and feasibility. From Table 1, ring makes 200 total attempts with 177 successes, 2 fails, 21 timeouts, average solve time 150.09 s, average fail time 73.73 s, and average time 374.61 s. Block2 makes 294 attempts with 282 successes, 2 fails, 10 timeouts, average solve time 8.36 s, average fail time 19.97 s, and average time 309.44 s. Nbr-plus makes 315 attempts with 313 successes, 2 fails, 0 timeouts, average solve time 0.98 s, average fail time 30.78 s, and average time 10.57 s. The paper interprets this as evidence that loosening local constraints expands coverage and speeds exploration, while stronger templates preserve corpus-faithful structure but leave holes in the expressive range (Bazzaz et al., 4 Apr 2025).

A major conceptual contrast is drawn with quality-diversity methods such as MAP-Elites. Rather than filling bins opportunistically through random generation and search pressure, constrained traversal directly targets underrepresented cells. This suggests a different use of ERA: not just post hoc diagnosis of what a generator produced, but prospective control over where generation is directed in a designer-defined behavior space (Bazzaz et al., 4 Apr 2025).

5. Adaptation to open text-to-audio models

Text-to-audio generation poses an ERA problem of a different kind because the output domain is extremely broad. The audio study therefore adopts a fixed-prompt ERA assumption: for a given prompt $$R = \{(m_1(x), m_2(x)) \mid x \in X_{\text{generated}}\}.$$2, the pair “model plus prompt” is treated as a generator, and stochastic sampling across seeds is used to characterize the expressive range for that semantic region. This makes the analysis tractable while preserving the core ERA question of how variable the outputs are, what part of the descriptor space they cover, and where the boundaries lie (Morse et al., 31 Oct 2025).

The experimental setup uses ESC-50 environmental sound labels with prompt templates of the form “Sound of [label].” Three models are evaluated—Stable Audio Open, MMAudio, and AudioLDM 2—using 50 prompts, 100 generated clips per prompt per model, and 10 s duration per clip, for a total of 15,000 generated clips. As reference data, 40 curated ESC-50 clips are used for each label, totaling 2,000 references. All audio is converted to mono, 22050 Hz (Morse et al., 31 Oct 2025).

Three acoustic feature families are extracted. Pitch uses pYIN with hop size 512, retaining only voiced frames and summarizing the mean, std, min, and max of $$R = \{(m_1(x), m_2(x)) \mid x \in X_{\text{generated}}\}.$$3 and its first- and second-order deltas, for 12 dimensions. Loudness uses A-weighted RMS energy with frame length 20248 and hop 512, again summarized by mean, std, min, and max of the signal and its deltas, for 12 dimensions. Timbre uses MFCCs derived from a mel spectrogram with 128 Mel bins, frame length 2048, hop 512, the first 13 MFCCs, plus deltas and delta-deltas, summarized to 156 dimensions. For each prompt and attribute, pooled data from all models and ESC-50 references are reduced to two principal components for visualization (Morse et al., 31 Oct 2025).

The study reports both prompt-specific and aggregate findings. For the prompt thunder, ERA is first constructed from two scalar descriptors: the loudness peak time $$R = \{(m_1(x), m_2(x)) \mid x \in X_{\text{generated}}\}.$$4 and the relative peak magnitude $$R = \{(m_1(x), m_2(x)) \mid x \in X_{\text{generated}}\}.$$5. Stable Audio Open typically produces a pronounced thunderclap in the first 2 seconds, clustering at early $$R = \{(m_1(x), m_2(x)) \mid x \in X_{\text{generated}}\}.$$6 with larger $$R = \{(m_1(x), m_2(x)) \mid x \in X_{\text{generated}}\}.$$7, whereas MMAudio rarely produces a pronounced thunderclap and often includes persistent rain, yielding smaller $$R = \{(m_1(x), m_2(x)) \mid x \in X_{\text{generated}}\}.$$8 and more dispersed peak timing. More generally, PCA-based ERA across prompts such as crying baby, dog, door knock, helicopter, and rain shows model-dependent spreads and overlaps with ESC-50 reference clouds; for example, MMAudio clusters tightly for rain in loudness and timbre PCA spaces, while Stable Audio Open shows broad spread for helicopter but reduced overlap with ESC-50 references (Morse et al., 31 Oct 2025).

Aggregated over all 50 prompts, the normalized total variance results establish a ranking by overall variation of Stable Audio Open > MMAudio > AudioLDM 2. The mean normalized variance across loudness, pitch, and timbre is 1.08 for Stable Audio Open, 0.86 for MMAudio, and 0.65 for AudioLDM 2, relative to ESC-50 at 1.00. All models exceed ESC-50 in pitch variation—1.69, 1.26, and 1.12 respectively—but fall short in loudness and timbre variation. The paper is explicit that no explicit fidelity metrics such as CLAP similarity, ESC-50 classifier accuracy, or FAD are reported; overlap with ESC-50 in PCA space is used qualitatively, and ERA as implemented measures expressive range rather than semantic correctness (Morse et al., 31 Oct 2025).

6. ERA for speech expressiveness through DeEAR

In speech systems, ERA is redefined as the quantitative assessment of the breadth, diversity, and controllability of a system’s expressiveness along perceptually grounded dimensions. DeEAR decomposes expressiveness into Emotion, Prosody, and Spontaneity, produces per-utterance sub-scores for these dimensions and a fused overall score on a 0–100 scale, and then uses the resulting score distributions to analyze breadth, diversity, coverage, and controllability. This formulation is motivated by the claim that MOS ratings are expensive, slow, and ambiguous, that low-level acoustic features correlate imperfectly with perceptual constructs of expressiveness, and that emotion recognition alone captures only one facet of expressiveness (Lin et al., 23 Oct 2025).

The DeEAR framework combines task-specific proxy scorers with a lightweight fusion model. Emotion, denoted $$R = \{(m_1(x), m_2(x)) \mid x \in X_{\text{generated}}\}.$$9, is modeled with a fine-tuned wav2vec2-large-robust-12-ft-emotion-msp-dim system, augmented with 12,000 Chinese samples from CNSCED and 2,000 English samples from IEMOCAP. Prosody, denoted $a = G(p, z),$0, is annotated by Gemini 2.5 Pro through carefully engineered prompts, and these labels achieve SRCC $a = G(p, z),$1 with human ratings. Spontaneity, denoted $a = G(p, z),$2, uses a two-stage approach: heuristic pseudo-labeling based on dataset-level spontaneity bases and DNSMOS-derived quality signals, followed by fine-tuning wav2vec2-large-robust on those pseudo-labels (Lin et al., 23 Oct 2025).

Overall expressiveness is learned from 480 clips rated by three expert annotators on overall expressiveness from 1 to 5, with Krippendorff’s alpha $a = G(p, z),$3. A lightweight XGBoost regressor fuses the three sub-scores:

$a = G(p, z),$4

trained by minimizing squared error to averaged human judgments. The deployed student model, DeEAR-Base, uses wav2vec2-large-xlsr-53 with three regression heads and is multi-task trained on 20,000 unlabeled utterances pseudo-labeled by the teacher. On utterance-level evaluation, DeEAR reports PCC $a = G(p, z),$5 and SRCC $a = G(p, z),$6 across 400 test items from four sets; at the system level, the ranking correlation with human judgments is SRCC $a = G(p, z),$7 (Lin et al., 23 Oct 2025).

The paper then uses these outputs for two canonical ERA tasks. The first is benchmarking. Seven S2S systems are evaluated on 20 prompts, and the resulting overall score gap between the top and bottom systems is about 60.1 points: Doubao has $a = G(p, z),$8, while Qwen2.5-Omni has $a = G(p, z),$9. The second is data curation. DeEAR selects 14k utterances totaling 51 hours, with EN/ZH approximately 1:1, from Expresso, NCSSD, M$p$0ED, MultiDialog, and IEMOCAP to form ExpressiveSpeech. Using a threshold of 63.5, the curated set reaches average $p$1, compared with source-set averages of 39.4–62.9, with DNSMOS P.835 OVRL average 3.17 and license CC BY-NC-SA 4.0 (Lin et al., 23 Oct 2025).

The same study reports downstream improvement from DeEAR-guided curation. Fine-tuning an S2S model, Expressive-FT, built from a 7B LLM and 1.5B ALM with S3tokenizer, on ExpressiveSpeech for one epoch at learning rate $p$2 improves overall $p$3 from 2.0 to 23.4. By dimension, Emotion rises from 5.7 to 15.9, Prosody from 35.7 to 36.7, and Spontaneity from 33.7 to 62.0; all gains are reported as $p$4. In human A/B tests, 78.5% prefer Expressive-FT, 10.0% prefer the baseline, and 11.5% are ties, again with $p$5 (Lin et al., 23 Oct 2025).

7. Limitations, misconceptions, and open directions

A recurrent misconception is to treat ERA as a direct measure of quality or correctness. The audio literature explicitly rejects this interpretation: ERA quantifies variation and coverage, not semantic correctness, so a generator can appear diverse because it sometimes produces off-prompt audio. In the ESC-50 study, this is why overlap with reference clouds is discussed only qualitatively and why future work is said to require pairing ERA with CLAP similarity, ESC-50 classifier agreement, or FAD (Morse et al., 31 Oct 2025).

A second misconception is that ERA plots are neutral summaries of a generator. The metric-selection literature shows that the opposite is often true: different axis pairs induce different accessible regions of the projected space, and poor pairs can compress the possibility space or create redundant axes. The proposed FI, MC, and AMC criteria are therefore not peripheral refinements but attempts to address a structural weakness in standard ERA practice (Withington et al., 2023).

A third limitation is that descriptor spaces remain domain-dependent and incomplete. In constrained level generation, density and difficulty are simple tile-count metrics that do not capture higher-level structural or experiential properties such as linearity, symmetry, or richer path-based behavior. The paper therefore presents the method as particularly well suited to metrics that can be expressed as global constraints, while recognizing that more complex descriptors are harder to enforce directly (Bazzaz et al., 4 Apr 2025).

The speech literature adds further robustness concerns. DeEAR is bilingual in English and Chinese, but further multilingual validation is stated to be necessary because emotion and prosody vary across cultures. Prosody labels are produced by Gemini 2.5 Pro with SRCC $p$6 against human ratings, so biases or failure modes in the LMM can propagate. The spontaneity heuristic penalizes “hyper-clean” incongruent speech, which raises the possibility that studio-quality expressive speech may require careful calibration. Although strong out-of-domain performance is reported, domains such as singing and dramatized speech are identified as needing explicit validation. Suggested validation strategies beyond SRCC include human A/B and MUSHRA-like tests targeted to each dimension, cross-dataset generalization, and reliability analyses such as Krippendorff’s alpha, test–retest stability, and sensitivity to loudness or normalization (Lin et al., 23 Oct 2025).

Taken together, these lines of work indicate that ERA is best understood as an exploratory and comparative methodology whose meaning depends on descriptor choice, projection strategy, and the relation between diversity and fidelity. The main trajectory across recent research is from 2D post hoc visualization toward multidimensional, task-grounded, and increasingly controllable analyses: metric-selection methods make classical PCG ERA more defensible, constrained generation turns ERA into a target space for synthesis, fixed-prompt text-to-audio ERA adapts the framework to multimodal generation, and DeEAR operationalizes a human-aligned ERA for speech expressiveness that supports benchmarking, curation, and control (Withington et al., 2023, Bazzaz et al., 4 Apr 2025, Morse et al., 31 Oct 2025, Lin et al., 23 Oct 2025).