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

Sajid Fardin Dipto; Tarikul Islam Tamiti; Luke Baja-Ricketts; David Vergano; Anomadarshi Barua

cs.SDOct 6, 2026

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

Authors: Sajid Fardin Dipto, Tarikul Islam Tamiti, Luke Baja-Ricketts, David Vergano, Anomadarshi Barua

Organizations: Department of Cyber Security Engineering George Mason University Fairfax, VA, USA

Abstract

Electromyography-to-Speech (ETS) synthesis is typically a non-linear, chaotic dynamical system. However, no prior work has studied the chaotic behavior of ETS synthesis to date. Yet, prior works strictly rely on standard reconstruction metrics with parameter-heavy transformers that systematically over-smooth natural acoustic dynamics. To close this gap, for the first time, we propose a chaos-inspired Lyapunov-derived activation function (LyRIC) with two novel chaotic loss functions, Lyapunov Exponent Regularization and Multi-Scale Detrended Fluctuation Analysis, to explicitly capture the deterministic chaos of human phonation. In addition, we introduce a compressed novel encoder, GLAME, which synergizes global Mamba state-space modeling with localized GLARE attention. We comprehensively perform frame-level acoustic evaluation in a multilingual and multi-speaker setup using English and Mandarin datasets. The proposed system outperforms the established baseline with a 4.69x increase in objective intelligibility (STOI: 0.61 vs. 0.13) and a 2.08x improvement in spectral reconstruction (LSD: 1.08 vs. 2.25). Importantly, this improvement is achieved with 73.49% fewer parameters (14.34M vs. 54.10M), establishing a new baseline for ETS synthesis. To the best of our knowledge, this is the first work demonstrating that integrating non-linear chaotic physics into neural networks yields superior yet compact inductive biases for real-time ETS synthesis.

Figures & tables

Figure 1: Detailed architecture of CGS-ETS with chaos-driven LyRIC activation and GLARE attention.

Figure 2: Architecture of GLARE attention.

Figure 3: (Left) Comparing different activation functions (Eqn. 2 ). (Right) Effect of $\alpha$ on log-divergence.

Figure 4: LyRIC activation with $\alpha\in\{-1,-1.5\}$ .

	Function	FLOPs/element $\downarrow$
$P_{0}$	$\alpha=0.5$	11
$P_{1}$	$\alpha=1$	1
$P_{2}$	$\alpha=1.5$	12
$P_{3}$	$\alpha=2$	2
$P_{4}$	$\alpha=2.5$	13
$P_{5}$	$\alpha=3$	3

Table 1: FLOPs footprint analysis of hyperparameter

\alpha

Figure 5: (Left) Comparison of different activation functions. (Right) Effect of $\alpha$ on LyRIC activation.

	Model	Cr	L $\downarrow$	ST $\uparrow$	P $\uparrow$	SD $\uparrow$	N $\uparrow$	W ${}^{*}\downarrow$	C $\downarrow$	Pr $\downarrow$
$P_{0}$	Baseline 1	EN	3.23	0.04	1.17	-52.5	3.28	68.00	38.2	60.21
$P_{1}$	Baseline 1	ZH	3.50	0.03	1.05	-58.1	1.31	$\times$	59.1	60.21
$P_{2}$	Baseline 2	EN	2.25	0.13	1.18	-42.0	3.30	42.20	23.7	54.10
$P_{3}$	Baseline 2	ZH	2.67	0.10	1.08	-39.5	1.84	$\times$	39.8	54.10
$P_{4}$	Baseline 3	EN	$\times$	$\times$	$\times$	$\times$	$\times$	46.14	$\times$	$\times$
$P_{5}$	Baseline 4	ZH	$\times$	$\times$	$\times$	$\times$	$\times$	$\times$	38.0	$\times$

Table 2: Comparison against SOTA methods. Here, Cr=Corpus, EN=English, ZH=Mandarin, L=LSD, ST=STOI, P=PESQ, SD=SI-SDR, N=NISQA-MOS, W=WER %, C=CER %, Pr=Parameters in Millions. ∗ As Mandarin text lacks spaces, corpora rely on CER rather than WER.

P_{4}

and

P_{5}

codebases are not public.

Model	CFE $\downarrow$	Enc $\downarrow$	Total $\downarrow$	IT $\downarrow$	Fs $\downarrow$	RTF $\downarrow$
Gaddy and Klein (2021)	10.17	44.03	54.10	5.97	2400	0.0057
Proposed CGS-ETS	4.49	9.85	14.34	5.61	926.6	0.0057

Table 3: Computational efficiency. Here, Enc=Encoder Size, Total = Total Parameters in Millions, ITs = Inference Time in Milliseconds, and Fs = FLOPs in Millions.

	Model Config.	L $\downarrow$	ST $\uparrow$	P $\uparrow$	SD $\uparrow$	N $\uparrow$	W $\downarrow$	Pr $\downarrow$
$P_{1}$	w/o LER+MSDFA	1.14	0.60	1.12	-35.5	3.25	51.56	14.34
$P_{2}$	w LER w/o MSDFA	1.10	0.60	1.18	-33.7	3.29	48.34	14.34
$P_{3}$	w MSDFA w/o LER	1.09	0.60	1.19	-32.6	3.31	45.65	14.34
$P_{4}$	w LER+MSDFA	1.08	0.61	1.19	-32.6	3.33	41.36	14.34

Table 4: Ablation study on chaotic losses. Here, metrics acronyms are provided in Tables 2 and 3 .

	CFE	Mam.	FFN	SD $\uparrow$	N $\uparrow$	W $\downarrow$	IT $\downarrow$	Fs $\downarrow$	RTF $\downarrow$
$P_{0}$	ReLU	SiLU	SwiGLU	-31.5	3.25	51.16	7.12	1038	0.0075
$P_{1}$	ReLU	SiLU	GeLU	-31.3	3.28	47.06	5.92	929.8	0.0059
$P_{2}$	LyRIC	SiLU	GeLU	-33.2	2.90	71.86	5.92	929.8	0.0059
$P_{3}$	ReLU	SiLU	LyRIC	-31.9	3.23	52.63	5.70	928.4	0.0057
$P_{4}$	ReLU	LyRIC	SwiGLU	-32.6	3.30	45.71	6.21	1035	0.0062
$P_{5}$	ReLU	LyRIC	GeLU	-32.6	3.33	41.36	5.61	926.6	0.0057

Table 5: Ablation on activations. Here, metrics acronyms are provided in Tables 2 and 3 .

	Layers	SD $\uparrow$	N $\uparrow$	W $\downarrow$	Pr $\downarrow$	IT $\downarrow$	Fs $\downarrow$	RTF $\downarrow$
$P_{0}$	None	-34.4	2.91	73.22	12.68	4.23	848.3	0.0046
$P_{1}$	$L=1,2$	-32.4	3.30	46.14	14.34	5.91	926.6	0.0059
$P_{2}$	$L=3,4$	-33.0	3.25	50.25	14.34	5.97	926.6	0.0059
$P_{3}$	$L=1,4$	-33.5	3.30	49.01	14.34	5.91	926.6	0.0061
$P_{4}$	$L=1,2,3$	-33.3	3.26	46.38	15.05	6.86	966.5	0.0068
$P_{5}$	$L=2,3,4$	-32.8	3.28	44.91	15.05	7.11	966.5	0.0071

Table 6: Ablation study on GLARE attention on different layer depths. Metrics LSD, STOI, and PESQ showed negligible variance, hence are omitted here. Metrics acronyms are provided in Tables 2 and 3 .

	$\alpha$	L $\downarrow$	ST $\uparrow$	P $\uparrow$	SD $\uparrow$	N $\uparrow$	W $\downarrow$	IT $\downarrow$	Fs $\downarrow$	RTF $\downarrow$
$P_{0}$	$0$	1.09	0.60	1.18	-34.1	3.30	48.22	5.98	927.0	0.0058
$P_{1}$	$1.5$	1.09	0.61	1.18	-30.8	3.26	44.73	5.95	929.9	0.0060
$P_{2}$	$2$	1.08	0.60	1.18	-32.3	3.30	45.40	5.95	927.2	0.0059
$P_{3}$	$3$	1.09	0.60	1.18	-33.0	3.30	49.26	6.00	927.3	0.0059
$P_{4}$	$1$	1.08	0.61	1.19	-32.6	3.33	41.36	5.61	926.6	0.0057

Table 7: Ablation study on hyperparameter

\alpha

of LyRIC activation. Acronyms are provided in Tables 2 and 3 .

	Attention Type	SD $\uparrow$	N $\uparrow$	W $\downarrow$	Enc $\downarrow$	IT $\downarrow$	Fs $\downarrow$	RTF $\downarrow$
$P_{0}$	MHA, All Layers	-32.4	3.30	43.32	14.49	7.42	1166	0.0074
$P_{1}$	MHA, $L=1,3$	-32.4	3.27	44.73	12.39	5.92	1061	0.0059
$P_{2}$	MQA, All Layers	-31.7	3.33	44.85	10.56	7.10	966.5	0.0071
$P_{3}$	MQA, $L=1,3$	-31.8	3.31	44.90	9.38	5.69	907.4	0.0058
$P_{4}$	GLARE, $L=1,3$	-32.6	3.33	41.36	9.85	5.61	926.6	0.0057

Table 8: Ablation study on different attention mechanisms. Here, Enc=Encoder Size in Millions. Other metrics acronyms are provided in Tables 2 and 3 .

Agg.	Model	$n$	Mean $\uparrow$	SDv	SEM	95% CI $\uparrow$
Utter.	Gaddy 2021	99	3.301	0.593	0.060	[3.193, 3.409]
Utter.	CGS-ETS	99	3.329	0.560	0.056	[3.217, 3.440]
Sess.	Gaddy 2021	7	3.303	0.195	0.074	[3.132, 3.474]
Sess.	CGS-ETS	7	3.328	0.059	0.022	[3.273, 3.383]

Table 9: MOS (NISQA) descriptive statistics.

Agg.	$n$	$\overline{\textbf{d}}$	Median(d)	$W^{+}$	$W^{-}$	T	p
Utter.	99	0.028	-0.064	2405.0	2545.0	2405.0	0.807
Sess.	7	0.025	-0.008	13.0	15.0	13.0	0.938

Table 10: Paired Wilcoxon signed-rank test results.

	Lyapunov (LER)			Fractal (MSDFA)
Phase	MACs	FLOPs	Lat.	MACs	FLOPs	Lat.
Training	31.81M	63.62M	1.28ms	0.358M	0.716M	0.16ms
Inference	0	0	0	0	0	0

Table 11: Code-derived computational complexity for deterministic chaotic objectives per 200-frame utterance. These modules are exclusively active during the training phase. Here, MACs, FLOPs are in Millions and Lat. = Latency in Milliseconds.

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

	CFE	Mam.	FFN	L $\downarrow$	ST $\uparrow$	P $\uparrow$	SD $\uparrow$	N $\uparrow$	W $\downarrow$	IT $\downarrow$	FLOPs $\downarrow$	RTF $\downarrow$
$P_{0}$	ReLU	SiLU	SwiGLU	1.10	0.59	1.16	-31.47	3.25	51.16%	7.12ms	1.038G	0.0075
$P_{1}$	ReLU	SiLU	GeLU	1.09	0.60	1.18	-31.30	3.28	47.06%	5.92ms	929.76M	0.0059
$P_{2}$	LyRIC	SiLU	GeLU	1.16	0.54	1.13	-33.22	2.90	71.86%	5.92ms	929.76M	0.0059
$P_{3}$	ReLU	SiLU	LyRIC	1.10	0.59	1.17	-31.85	3.23	52.63%	5.70ms	928.43M	0.0057
$P_{4}$	ReLU	LyRIC	SwiGLU	1.08	0.61	1.19	-32.63	3.30	45.71%	6.21ms	1.035G	0.0062
$P_{5}$	ReLU	LyRIC	GeLU	1.08	0.61	1.19	-32.61	3.33	41.36%	5.61ms	926.55M	0.0057

Appendix

Table 12: Ablation Study on Activation Functions.

	Layers	L $\downarrow$	ST $\uparrow$	P $\uparrow$	SD $\uparrow$	N $\uparrow$	WER $\downarrow$	Para. $\downarrow$	IT $\downarrow$	FLOPs $\downarrow$	RTF $\downarrow$
$P_{0}$	No Attention	1.15	0.53	1.14	-34.42	2.91	73.22%	12.68M	4.23ms	848.33M	0.0046
$P_{1}$	$L=1,2$	1.08	0.60	1.18	-32.41	3.30	46.14%	14.34M	5.91ms	926.55M	0.0059
$P_{2}$	$L=3,4$	1.10	0.59	1.17	-31.96	3.25	50.25%	14.34M	5.97ms	926.55M	0.0059
$P_{3}$	$L=1,4$	1.10	0.59	1.17	-33.54	3.30	49.01%	14.34M	5.91ms	926.55M	0.0061
$P_{4}$	$L=1,2,3$	1.08	0.61	1.19	-33.31	3.26	46.38%	15.05M	6.86ms	966.45M	0.0068
$P_{5}$	$L=2,3,4$	1.09	0.60	1.19	-32.81	3.28	44.91%	15.05M	7.11ms	966.45M	0.0071

Appendix

Table 13: Ablation Study on GLARE Attention.

	Attention Type	L $\downarrow$	ST $\uparrow$	P $\uparrow$	SD $\uparrow$	N $\uparrow$	W $\downarrow$	Enc. $\downarrow$	IT $\downarrow$	FLOPs $\downarrow$	RTF $\downarrow$
$P_{0}$	MHA (All Layers)	1.08	0.61	1.19	-32.43	3.30	43.32%	14.49M	7.42ms	1.166G	0.0074
$P_{1}$	MHA ( $L=1,3$ )	1.08	0.61	1.18	-32.36	3.27	44.73%	12.39M	5.92ms	1.061G	0.0059
$P_{2}$	MQA (All Layers)	1.07	0.60	1.18	-31.69	3.33	44.85%	10.56M	7.10ms	966.50M	0.0071
$P_{3}$	MQA ( $L=1,3$ )	1.08	0.60	1.18	-31.81	3.31	44.90%	9.38M	5.69ms	907.41M	0.0058
$P_{4}$	GLARE ( $L=1,3$ )	1.08	0.61	1.19	-32.61	3.33	41.36%	9.85M	5.61ms	926.55M	0.0057

Appendix

Table 14: Ablation Study on Different Attentions

	Dimension	L $\downarrow$	ST $\uparrow$	P $\uparrow$	SD $\uparrow$	N $\uparrow$	W $\downarrow$	Pr $\downarrow$	IT $\downarrow$	FLOPs $\downarrow$	RTF $\downarrow$
$P_{0}$	$C_{D}=128$	1.13	0.57	1.15	-34.35	3.09	58.88%	0.91M	5.53ms	59.64M	0.0055
$P_{1}$	$C_{D}=256$	1.11	0.59	1.16	-33.09	3.20	52.14%	3.59M	5.59ms	234.030M	0.0056
$P_{2}$	$C_{D}=1024$	1.08	0.61	1.19	-32.67	3.34	45.10%	56.82M	15.72ms	3.690G	0.0088
$P_{3}$	$C_{D}=512$	1.08	0.61	1.19	-32.61	3.33	41.36%	14.34M	5.61ms	926.55M	0.0057

Appendix

Table 15: Ablation Study on Channel Dimension

	Count	L $\downarrow$	ST $\uparrow$	P $\uparrow$	SD $\uparrow$	N $\uparrow$	W $\downarrow$	Enc. $\downarrow$	IT $\downarrow$	FLOPs $\downarrow$	RTF $\downarrow$
$P_{0}$	$L_{c}=2$	1.10	0.58	1.16	-32.75	3.20	55.94%	5.67M	4.52ms	721.48M	0.0045
$P_{1}$	$L_{c}=3$	1.08	0.60	1.18	-31.45	3.33	45.18%	8.51M	5.37ms	863.65M	0.0057
$P_{2}$	$L_{c}=5$	1.08	0.61	1.19	-33.06	3.25	41.91%	14.18M	8.50ms	1.148G	0.0091
$P_{3}$	$L_{c}=4$	1.08	0.61	1.19	-32.61	3.33	41.36%	9.85M	5.61ms	926.55M	0.0057

Appendix

Table 16: Ablation Study on Layer Count of GLAME

Component	Ref.	Bottleneck	Without Component	With Proposed Component	Efficiency Gain
GLAME	Tab. 3	Macro	Gaddy and Klein (2021) Encoder	GLAME	-34.18M Params
(Encoder)	Tab. 3	Architectural Bloat	(Enc: 44.03M, FLOPs: 2400M)	(Enc: 9.85M, FLOPs: 926.6M)	-1473.4M FLOPs
Chaos Losses	Tab. 4	Acoustic Fidelity,	w/o LER+MSDFA ( $P_{1}$ )	w/ LER+MSDFA ( $P_{4}$ )	N/A
(LER + MSDFA)	Tab. 4	Phonetic Accuracy	(WER: 51.56%, LSD: 1.10)	(WER: 41.36%, LSD: 1.08)	N/A
LyRIC Activation	Tab. 5	Computational	SiLU + SwiGLU ( $P_{0}$ )	LyRIC + GeLU ( $P_{5}$ )	-111.4M FLOPs
(in Mamba block)	Tab. 5	Cost, Latency	(WER: 51.16%, FLOPs: 1038M)	(WER: 41.36%, FLOPs: 926.6M)	-1.51ms Latency

Appendix

Table 17: Consolidated Summary of Individual Component Contributions. This table highlights the isolated impact of each proposed mechanism compared to its standard counterpart.

Figure 6: Output Density Distributions of ReLU, GELU, SiLU against Log-divergence Equation (Equation 6 )

	Function	FLOPs/element $\downarrow$
$P_{0}$	ReLU	1
$P_{1}$	GeLU	14
$P_{2}$	SiLU	22
$P_{3}$	Log-divergence	47

Appendix

Table 18: Comparison of Computational Profiling among ReLU, GeLU, SiLU, and Log-divergence Equation (see Equation 6 )

Figure 7: Topological Sensitivity Analysis of the LyRIC Activation Surface ( $f(x,\alpha)=x|x|^{\alpha}$ ).

Figure 8: Geometric Representation of the LyRIC Activation Function at the Optimal Expansion Coefficient $\alpha=1.0$ .

Figure 9: Gradient Landscape Analysis of ReLU, GeLU, SiLU, and LyRIC ( $\alpha=1$ ).

Figure 10: Parametric Influence of the Expansion Coefficient ( $\alpha$ ) on the Gradient Landscape of the LyRIC Activation.

Figure 11: The Software Interface Used in Subjective Tests.

Hyperparameter	Value	Use Case & Rationale
Optimization & Training Dynamics
Max epochs	80	Provide sufficient gradient updates for convergence while preventing catastrophic representational over-fitting.
Batch size	32	Mathematically balance gradient variance stabilization with strict GPU VRAM (OOM) constraints.
Initial learning rate ( $\eta$ )	$1\times 10^{-3}$	Ensure robust initial gradient descents across the highly non-convex objective manifold.
Learning rate warmup	500 steps	Strictly prevent early gradient spikes and stabilize initial optimization dynamics.
Weight decay	$1\times 10^{-7}$	Subtly regularize network weights to prevent over-fitting on specific real-world EMG physiological artifacts.

Appendix

Table 19: Comprehensive Summary of Critical Hyperparameters, Architectural Configurations, and Their Theoretical Justifications within the Proposed CGS-ETS Framework.

Module	Stage	Layer Type	Input→Output	Kernel	Stride	Padding	Params
CFE Block	Block 1	Conv1d (Main)	8→512	3	2	1	12 800
		BatchNorm1d + ReLU	512→512	–	–	–	1 024
		Conv1d (Main)	512→512	3	1	1	786 944
		BatchNorm1d	512→512	–	–	–	1 024
		Conv1d (Residual)	8→512	1	2	0	4 608
		BatchNorm1d + ReLU	512→512	–	–	–	1 024

Appendix

Table 20: Comprehensive Layer-wise Parameter Breakdown of the Proposed CGS-ETS Architecture. The summary block demonstrates the strict architectural compression achieved by our GLAME and its selective application of GLARE attention modules.

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