Lyapunov-Inspired LyRIC Activation and GLARE Attention in Chaos-Guided State Space Modeling for EMG-To-Speech (ETS) Synthesis

1 Introduction and Related Work

• Prior ETS systems are described as smoothing frame-level predictions despite chaotic phonation, using parameter-heavy Transformers, and lacking evaluations of acoustic fidelity and objective intelligibility.The section links these gaps to muffled prosody and low-latency SSI constraints.Source: §1 · p. 1
• GLARE supplies localized attention, while GLAME fuses GLARE with Mamba and replaces SiLU with the LyRIC activation.The section reports a 77.63% reduced complexity for the LyRIC-based architecture.Source: §1 · pp. 1–2
• 4.69× higher intelligibility, 2.08× better spectral reconstruction, and 73.49% fewer parameters than recent baselines are reported for multilingual settings.The proposed system is supervised by LER and MSDFA.Source: §1 · p. 2
• LER aligns Lyapunov exponents across temporal resolutions, while MSDFA quantifies long-range fractal-like correlations overlooked by standard spectrogram losses.These objectives are introduced to constrain the network to deterministic chaotic invariants of speech.Source: §1 · p. 2

2 Overall Architecture

• The pipeline takes eight-channel EMG, preprocesses it, predicts mel-spectrogram bins, and converts them to audio with a HiFi-GAN vocoder.Source: §2 · p. 2

2.1 Design of the GLARE

• GLARE combines sliding-window masking, relative positional embeddings, and grouped-query attention, limiting context locally and halving key-value heads versus query heads.Source: §2.1 · pp. 2–3

2.2 Design of the LyRIC Activation

• LyRIC approximates logarithmic divergence with leading term x|x|^α; α > 0 ensures C1 continuity, and α = 1 costs 1 FLOP/element.Source: §2.2 · p. 4

2.3 Convolutional Feature Extraction (CFE)

• The CFE front end has three residual blocks, each with two 1D convolutional layers, ReLU, and a parameterized skip connection, at 512 channels.Source: §2.3 · p. 4

2.4 GLARE-fused Mamba Encoder–GLAME

• The four-layer GLAME encoder places GLARE in its first and third layers, ends with an FFN, and branches to acoustic and phoneme-supervision heads.Source: §2.4 · pp. 4–5

2.5 Design of the LER Loss

• LER penalizes differences in local divergence rates by comparing Lyapunov exponents for temporally aligned predicted and target audio features.Source: §2.5 · p. 5

2.6 Design of the MSDFA Loss

• MSDFA targets long-range temporal correlations by comparing multi-scale detrended fluctuations, which the authors say frame-level spectrogram losses overlook.Source: §2.6 · p. 5

2.7 Total Loss Function

• The total objective combines DTW alignment, pairwise-distance and phoneme losses, and the LER and MSDFA chaos-inspired losses.Source: §2.7 · p. 6

3.1 Evaluation Metrics / 3.2 Dataset and Hyperparameter

• Evaluation spans 19 hours of English and about 55 hours of six-channel Mandarin from 100 speakers, using ten metrics and DTW for framewise comparisons.DTW aligns post-vocoder output for sample-by-sample assessment; the metric suite includes acoustic, intelligibility, quality, error-rate, and efficiency measures.Source: §3.2 · p. 6, §3.1 · p. 6, §3.3 · p. 6

3.3 Comparative Analysis with Baselines

• STOI = 0.61 vs 0.13 and LSD = 1.08 vs 2.25 against P2 on English; Mandarin CER is 36.3% versus the baseline’s 38.0%.The English comparison is in Table 2; the Mandarin comparison is reported against Xie et al. (2025).Source: §3.3 · pp. 6–7, Table 2 · p. 6

3.4 Computational Complexity

• CGS-ETS yields a 73.5% decrease in total size (54.10M→14.34M), with FLOPs down 61.4% (2400M→926.6M), inference time of 5.61ms, and RTF of 0.0057.Source: §3.4 · p. 7

3.5.1 Chaos Loss Components

• LER lowers WER from 51.56% to 48.34%, MSDFA to 45.65%, and their joint configuration reaches 41.36% with STOI 0.61 and LSD 1.08.The ablation attributes localized gradient regularization to LER and macro-level fractal correlations to MSDFA.Source: §3.5.1 · p. 7, Table 4 · p. 7

3.5.2 Activation Functions / 3.5.4 Hyperparameter α in LyRIC Activation

• LyRIC-driven Mamba with GeLU yields WER 41.36%, NISQA 3.33, and RTF 0.0057; the quadratic α = 1 setting gives the best reported trade-off.The α ablation reports 926.6M FLOPs at α = 1, while α = 0 and higher orders worsen WER or gradient stability.Source: §3.5.2 · p. 7, Table 5 · p. 7, §3.5.4 · p. 8

3.5.3 GLARE Attention Depth

• Alternating GLARE in layers 1 and 3 achieves WER 41.36% and NISQA 3.33 with 14.34M parameters and 5.61ms inference.Removing attention raises WER to 73.22%, while applying it to every layer increases computation and redundancy.Source: §3.5.3 · p. 7, Table 6 · p. 8

3.5.5 Different Attention Mechanisms

• GLARE achieves WER 41.36% and SI-SDR -32.6 with 5.61ms inference and 926.6M FLOPs, outperforming the compared attention alternatives on the reported trade-off.All-layer MHA requires 1166M FLOPs; truncated MHA and MQA reach about 45% WER.Source: §3.5.5 · p. 8, Table 8 · p. 8

3.6 Statistical Analysis of MOS Scores / 3.7 Additional Ablation Study / 3.8 Subjective Mean Opinion Score (MOS)

• Subjective MOS is 4.25 versus 3.98; session-level NISQA spread is lower at SDv 0.059 versus 0.195, while utterance means are 3.329 versus 3.301 (p = 0.807).The additional ablation appendix examines channel capacity and GLAME hierarchical depth.Source: §3.8 · p. 8, §3.6 · p. 8, §3.7 · p. 8

4 Conclusion

• GLAME combines LyRIC and GLARE with the chaotic objectives LER and MSDFA.The conclusion presents these components as the paper’s chaos-theory-based architecture and objectives.Source: §4 · pp. 8–9
• On the Gaddy benchmark, CGS-ETS reports superior fidelity and intelligibility with 73.49% fewer parameters.The conclusion describes this as validating chaotic dynamics as an efficient prior for real-time SSIs.Source: §4 · p. 9

6 Limitations

• The datasets cover single-speaker English and multi-speaker Mandarin, but not multimodal inputs such as visual images or video.The design instead focuses on handling intrinsic physiological artifacts.Source: §6 · p. 9
• LER costs approximately 31.8 M MACs per segment, versus 0.358 M MACs for MSDFA, and both objectives are active only during training.Table 11 reports computational complexity per 200-frame utterance; pre-computed detrending kernels keep MSDFA overhead minimal.Source: §6 · p. 9, Table 11 · p. 9
• The fixed GLARE sliding window (k = 32) may restrict learning global prosodic variations across extremely long phonetic sequences.The architecture uses relative positional biases alongside this localized window.Source: §6 · p. 9

7 Potential Risks/Ethical Considerations

• The model could be misused for secret eavesdropping, impersonation, or deepfake audio generation, posing privacy and security risks.The stated research purpose is speech restoration.Source: §7 · p. 9
• The authors call for transparency, protecting consent, and following guidelines to address these risks.Source: §7 · p. 9

A.1 Convolutional Feature Extraction (CFE)

• Each of three CFE residual blocks uses two Conv-1D layers with ReLU and a parameterized skip connection, maintaining 512 channels.The first convolution downsamples by 2×, while the second preserves resolution; the skip projection matches the downsampling.Source: §A.1 · p. 10
• Table 12 is an ablation study on activation functions.Source: Table 12 · p. 11
• Table 13 is an ablation study on GLARE attention.Source: Table 13 · p. 11
• Table 14 is an ablation study comparing different attention mechanisms.Source: Table 14 · p. 11
• Table 15 is an ablation study on channel dimension.Source: Table 15 · p. 11

A.2 Activation Functions

• Table 12 presents activation-function ablation results across CGS-ETS blocks, with detailed discussion in Section 3.5.2.Source: §A.2 · p. 11

• Table 13 reports a comprehensive ablation study of GLARE attention layer depths; detailed findings are discussed in Section 3.5.3.Source: §A.3 · p. 11

• Table 14 summarizes an ablation study of attention mechanisms across layer depths; detailed results are discussed in Section 3.5.5.Source: §A.4 · p. 11

• Table 15 ablates internal channel capacity (CD) for continuous EMG modeling.Source: §A.5 · p. 11
• CD = 512 achieves the lowest WER (41.36%) and peak spectral fidelity (LSD: 1.08, SD: -32.61), while reducing P2’s footprint by 75%.Its reported IT is 5.61ms and RTF is 0.0057, maintaining real-time feasibility.Source: §A.5 · p. 11
• Small capacities (P0, P1 ≤256) cause phonetic collapse (WER > 52.14%, NISQA ≤3.20), while CD = 1024 (P2) overfits with WER at 45.10%.P2 uses 56.82M parameters and 3.69G FLOPs.Source: §A.5 · p. 11

A.6 Layer Count of GLAME

• 41.36% WER, STOI 0.61, PESQ 1.19, and NISQA 3.33 are achieved by P3 (Lc = 4) with 9.85M parameters and RTF 0.0057.P0 (Lc = 2) has 5.67M parameters but WER 55.94%; P2 (Lc = 5) reaches WER 41.91% but uses 14.18M encoder parameters, exceeds 1.1G FLOPs, and has NISQA 3.25.Source: §A.6 · pp. 11–12, Table 16 · p. 12

A.7.1 The Macro-Architectural Role of the GLAME Encoder

• 77.6% fewer parameters and 61.4% fewer FLOPs reduce the baseline encoder’s 44.03M parameters and 2400M FLOPs to 9.85M and 926.6M, respectively.The GLAME encoder supports real-time synthesis at RTF 0.0057 while retaining the acoustic fidelity reported in Table 2.Source: §A.7.1 · p. 12

A.7.2 The Role of Chaos-Informed Losses (LER & MSDFA)

• 41.36% WER, LSD 1.08, and STOI 0.61 result when LER and MSDFA are combined in P4.Individually, LER lowers WER to 48.34%, while MSDFA lowers it to 45.65% and boosts perceptual naturalness; the losses address short-term fluctuations and long-range phoneme dependencies, respectively.Source: §A.7.2 · p. 13

A.7.3 The Role of the LyRIC Activation Function

• 41.36% WER and 926.6M FLOPs result when LyRIC is placed in the Mamba state-space block and GeLU in the terminal FFN, reducing computation by over 111M FLOPs.Standard SiLU and SwiGLU routing incurs 1038M FLOPs and 51.16% WER; placing LyRIC in the CFE or FFN destabilizes the representation.Source: §A.7.3 · p. 13

A.7.4 The Role of GLARE Attention

• 41.36% WER, 9.85M encoder parameters, and 5.61ms latency are achieved with GLARE at alternating layers L ∈{1, 3}, reducing parameters by 32% and latency by 24%.By comparison, all-layer MHA uses 14.49M parameters and 1166M FLOPs for 43.32% WER and 7.42ms latency, while truncated MHA or MQA variants push WER to approximately 45%.Source: §A.7.4 · p. 13

A.8 EMG as A Chaotic Dynamical System

• Articulatory EMG is described as a nonlinear, non-stationary signal whose feedback-driven motor activity can be sensitive to initial conditions and enter chaotic regimes.The paper argues that reconstruction-only models average out jitter, aperiodic bursts, and rapid transitions, producing over-smoothed speech; it motivates explicit nonlinear constraints such as LER and MSDFA.Source: §A.8 · pp. 13–14

A.9 Theoretical and Empirical Analysis of the LyRIC Activation Function

• LyRIC’s Lyapunov-derived formulation preserves bilateral phase geometry and controls activation magnitude; at α = 1.0, its smooth surface retains sensitivity to EMG fluctuations.Direct evaluation of the log-divergence formulation costs 47 FLOPs per element versus 1–22 for standard activations, motivating the polynomial LyRIC approximation, set to α = 1 for 1 FLOP per element; its output variance is 0.35 versus 0.56–0.59 for standard activations.Source: §A.9.1 · p. 14, §A.9.2 · p. 15, §A.9.3 · pp. 16–17

A.10 Theoretical Analysis of the LER Loss

• LER penalizes the distance between predicted and ground-truth Lyapunov exponents, using reconstructed latent phase-space trajectories and Rosenstein-based divergence estimation.This supervision is intended to preserve chaotic source-signal structure, including sub-harmonic firing patterns, bifurcations, and timing irregularities, rather than collapsing to a stable equilibrium.Source: §A.10 · pp. 17–18

A.11.1 English Corpus

• The English Gaddy and Klein corpus contains nearly 20 hours of single-speaker EMG and parallel audio, with open-vocabulary data evaluated using an 8:1:1 train-validation-test split.DTW alignments from vocalized EMG-audio pairs transfer audio targets to silent EMG signals.Source: §A.11.1 · p. 18

A.11.2 Mandarin Corpus

• AVE-Speech provides over 55 hours per modality from 100 Mandarin speakers; adapting the pipeline required six-channel input and rate-matching changes, MFA phoneme alignments, and character-level evaluation.The corpus comprises 100,000 discrete utterances; the evaluation pipeline uses CER for Mandarin.Source: §A.11.2 · pp. 18–20

A.12 Dataset Class and DataLoader

• The EMGDataset uses deterministic shuffling, LRU caching, pinned-memory tensors, and frame-budget batching capped at 256,000 frames to limit OOM risk across variable-length sequences.Its collation function pads variable-length modalities and routes parallel acoustic targets for silent EMG inputs.Source: §A.12 · p. 20

A.13 Details on Computational Complexity

• 73.49% fewer parameters (14.34M vs. 54.10M) and 61.39% fewer FLOPs (926.55M vs. 2.40G) are reported for CGS-ETS versus baseline P0.CGS-ETS also has a 5.61 ms inference time per batch versus 5.97 ms for the baseline, while both report an RTF of 0.0057.Source: §A.13 · pp. 20–21
• LyRIC contributes 0.13M FLOPs, or 1 FLOP per element, while activation functions account for 1.74M FLOPs (0.19% of CGS-ETS’s 926.55M total).The reported FLOP counts use practical framework-level costs; high-density matrix operations dominate computation.Source: §A.13 · pp. 20–21

A.14 Hyperparameters and Configuration

• Experiments used Python 3.9, PyTorch (≥2.0.0), CUDA 11.8, and FP32 training on two NVIDIA RTX 4090 GPUs with distributed data parallelism.The appendix points to Table 19 for CGS-ETS training and model hyperparameters.Source: §A.14 · p. 21

A.15 Inference and Evaluation Workflow

• Inference predicts mel spectrograms and phoneme probabilities from EMG, aligns features with DTW, reconstructs waveforms using HiFi-GAN, and exports acoustic, ASR, CER, and perceptual metrics.Perceptual metrics are computed after downsampling waveforms to 16 kHz.Source: §A.15 · p. 22

A.16 Subjective Evaluation Details

• 5.52% higher subjective MOS was achieved by CGS-ETS than the established SOTA baseline in the listening test.Ten English-speaking volunteers rated 30 utterances in randomized baseline, CGS-ETS, and reference versions.Source: §A.16 · pp. 22–23

A.17.2 The Paired Wilcoxon Signed-Rank Framework

• H0 states that the median paired MOS difference between CGS-ETS and Gaddy-EMG is zero, while H1 posits a systematic perceptual-quality shift.Source: §A.17.2 · p. 24
• The test excludes zero differences, ranks the absolute remaining paired differences, and assigns each rank the sign of its original difference.Source: §A.17.2 · p. 24
• The framework sums positive and negative ranks as W+ and W−; under H0, these sums should be approximately equal, and T is the test statistic.W+ represents evidence favoring the proposed model, while W− represents evidence favoring the baseline.Source: §A.17.2 · p. 24
• With n = 99, p-values of 0.807 and 0.938 did not reject H0 at the 5% level, although CGS-ETS showed superior stability and a higher mean.The passage characterizes the models as operating within a comparable perceptual category for this dataset size.Source: §A.17.2 · p. 24