Power-of-Two Leaky Integrate-and-Fire Neurons for Event-Driven Vision-Language-Action Inference

Rui Liu; He Lv; Ziyao Zhang; Rui Ma; Rongxiang Nie

cs.AIOct 24, 2026

Power-of-Two Leaky Integrate-and-Fire Neurons for Event-Driven Vision-Language-Action Inference

Authors: Rui Liu, He Lv, Ziyao Zhang, Rui Ma, Rongxiang Nie

Organizations: Sivy Limited, Hangzhou, China

Abstract

Vision-language-action (VLA) models have demonstrated strong capabilities in robotic manipulation, yet their reliance on dense, continuous-valued computation presents a fundamental challenge for energy-constrained deployment. Inspired by the sparse, event-driven signaling and temporal integration mechanisms of biological neurons, a promising alternative is to introduce spiking computation into VLA models. However, enabling such computation without restructuring pretrained policies or compromising closed-loop control remains an open challenge. To address this challenge, we introduce the Power-of-Two Leaky Integrate-and-Fire (PoT-LIF) neuron, which emits signed spikes with power-of-two amplitudes. By combining magnitude-coded spike events with residual-preserving membrane dynamics, PoT-LIF enables continuous information to be progressively represented through discrete spikes. The Heartbeat formulation further localizes this process within weighted projections, bridging biologically inspired spiking computation and pretrained VLA architectures without modifying their external inference interfaces. We integrate PoT-LIF into the vision projection, vision-language projection, and action projection of $π_{0.5}$ and evaluate both operating modes over 2,000 paired closed-loop LIBERO episodes per configuration. Standard-mode PoT-LIF VLA achieves success rates of 96.90% and 96.35% at $T = 1$ and $T = 2$ , respectively, while Heartbeat mode achieves 97.25% and 96.90% at $T = 2$ and $T = 4$ , compared with 96.70% for the original continuous-activation $π_{0.5}$ baseline. At $T = 1$ with a 60.01% firing rate, PoT-LIF uses approximately 1/7.67 of the dense-reference arithmetic energy, corresponding to a modeled reduction of 86.95%.

Figures & tables

Figure 1: PoT-LIF dynamics and power-of-two event encoding. (a) Standard mode: presynaptic events arrive through weighted synapses and are integrated into the membrane state. Each emitted event carries a sign and an integer exponent specifying its amplitude. The residual remains in the membrane state across successive input calls. (b) Heartbeat mode: a scalar input is injected once and decomposed into a bounded event sequence using the same recurrence with $\lambda=1$ . The residual is retained between internal extraction steps, and the local state is reset at the end of the projection invocation.

Figure 2: (a) PoT-LIF integration into $\pi_{0.5}$ . Heartbeat encoders supply signed power-of-two events to selected weighted projections in the vision encoder, vision–language backbone, and action expert. Event contributions are evaluated through scaling–accumulation (SAC) within each projection. Attention computation, the blockwise mask, KV-cache structure, residual paths, and action interfaces retain their original organization. Dashed boxes indicate the three module groups; (b) shows the event–projection pairs within a block. Abbreviations: RGB, red–green–blue; ViT, vision transformer; LM, language model; FFN, feed-forward network; RMSNorm, root mean square normalization; adaRMSNorm, adaptive RMSNorm; GELU, Gaussian error linear unit; bbox, bounding box; proprio., proprioceptive state; MatMul, matrix multiplication.

Configuration	Spatial	Object	Goal	Long-H.	Overall	$\Delta$
Continuous activation	98.8	98.6	97.0	92.4	96.70	–
Continuous, matched budget	98.0	97.6	97.8	91.6	96.25	$-$ 0.45
Standard mode $T=1$	99.2	98.4	97.6	92.4	96.90	$+$ 0.20
Standard mode $T=2$	98.2	97.8	97.4	92.0	96.35	$-$ 0.35
Heartbeat $T=2$	99.2	97.4	98.2	94.2	97.25	$+$ 0.55
Heartbeat $T=4$	99.2	98.0	97.8	92.6	96.90	$+$ 0.20

Table 1: Main LIBERO results (success rate per suite over 500 episodes; 2,000 per configuration).

\Delta

is the overall percentage-point difference from the continuous-activation control.

Figure 3: Average arithmetic energy per reference product with matched FP32 accumulation. One FP32 MAC costs 4.6 pJ. At

T=1

and a 60.01% firing rate, the PoT-LIF SAC path averages 0.6001 pJ: 0.06001 pJ for exponent scaling and 0.54009 pJ for accumulation. The reference-to-SAC energy ratio is 7.67, corresponding to a modeled reduction of 86.95%. Other power terms are excluded.

Figure 4: Modeled projection arithmetic energy relative to an FP8 E4M3 baseline. Both methods use FP8 weights and FP32 accumulation. Energy is normalized per original dense projection product using sampled fanout-weighted activity: $0.6001$ and $1.0565$ SAC contributions for $T=1$ and $T=2$ , respectively, with $k=4$ . Green denotes multiplication or exponent scaling and control; gray denotes FP32 accumulation. PoT-LIF reduces modeled projection arithmetic energy by $59.54\%$ and $28.77\%$ . These estimates conditionally transfer BF16-derived activity to FP8 weights and exclude neuron encoding, shared computation, and data movement.

Figure 5: Modeled dynamic energy per policy inference with a matched fixed data-movement budget. Each inference includes ten denoising steps; all configurations use FP8 weights and FP32 accumulation. Green denotes projection arithmetic, gold denotes neuron encoding and other modeled computation, and light gray denotes the identical $2.518$ J data-movement budget. With $k=4$ , the modeled subtotal decreases from $6.038$ J to $4.058$ J for $T=1$ and $5.082$ J for $T=2$ , corresponding to savings of $32.79\%$ and $15.83\%$ . Results are conditional on BF16-derived activity and represent partial energy estimates, not hardware measurements or complete system energy.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Configuration	Surrogate setting	Success (%)
Heartbeat $T=4$ , identity STE	identity surrogate	96.90
Heartbeat $T=4$ , magnitude STE	magnitude surrogate	96.90

Appendix

Table 2: STE training ablation over 2,000 paired LIBERO episodes per configuration. Both runs start from the same pretrained checkpoint and are fine-tuned separately with the indicated surrogate.

Method	Parameters	Implementation	LIBERO mean
Spike-driven VLA [ 8 ]	0.15B	fully spiking, direct training	92.4%
DS-VLA [ 9 ]	—	dendritic spiking action control	91.6%
PoT-LIF on $\pi_{0.5}$	3.3B	Heartbeat $T=2$ projections	97.25%

Appendix

Table 3: Reported nominal LIBERO success of spiking VLA models. Results use each study’s architecture and training protocol; — indicates an unlisted parameter count. The PoT-LIF row repeats the Heartbeat

T=2

result in Table 1 .

Model	Event representation	Integration strategy
Spike-driven VLA [ 8 ]	Binary spikes	Spiking perception, fusion, and action modules
DS-VLA [ 9 ]	Spiking dynamics	Dendritic-inspired architecture for action control
PoT-LIF standard mode	Signed power-of-two events; residual retention	Temporal sequence across layers
PoT-LIF Heartbeat	Signed power-of-two events; residual retention	Event generation and accumulation within each projection

Appendix

Table 4: Event representations and integration strategies. Entries summarize the cited models; the PoT-LIF rows refer to the

\pi_{0.5}

implementation evaluated here.

Parameter	Standard mode	Heartbeat
Input flow	one current per tick	single injection ${I}_{1}=x$
Decay $\lambda$	configurable (main runs: 1)	1
Emission threshold $\theta$	Two-sided; main runs: ${2}^{-16}$	two-sided, code floor ${2}^{{e}_{\operatorname{min}}}={2}^{-16}$
State initialization	${r}_{0}=0$ for each image-and-prompt input	${r}_{0}=0$ per projection invocation; ${u}_{1}=x$
Residual update and reset	Subtractive update each internal step; reset at next image-and-prompt input	Subtractive update; reset after $T$ steps or early termination
Event application	events propagate downstream	applied inside the projection

Appendix

Table 5: Operating-mode parameters. Both modes use the integration and residual balance in Eq. ( 10 ) and the emission rule in Eq. ( 7 ); the evaluated policies use ten external flow-matching solver steps, distinct from the internal event budget.

Parameter	Setting
Decay $\lambda$	1 (no leakage during local decomposition)
Emission threshold $\theta$	two-sided code floor ${2}^{{e}_{\operatorname{min}}}={2}^{-16}$ ; extracts nonzero powers of the input significand
Primary Heartbeat and $T=1$ surrogate	magnitude STE on the reconstructed sum, ${g}_{T}(x)={q}_{T}(x)/x$ for $x\neq 0$
Surrogate at $x=0$	magnitude: $0$ at full strength, $1-\alpha$ during insertion; identity: $1$
Standard-mode surrogate at $T=2$	constant 0.5 including at zero membrane potential, with cross-tick backpropagation
FP8 weights	E4M3FN, static power-of-two per-tensor scale

Appendix

Table 6: Training parameters and numerical formats. FP8 weights and A24 accumulation are supplementary configurations; the main table uses BF16 weights.

Path	Multiplication / scaling (pJ)	FP32 accumulation (pJ)	Total (pJ)
FP32 MAC	$1\times 3.7=3.7$	$1\times 0.9=0.9$	4.6
PoT-LIF $T=1$	$0.6001\times 0.1$ $=0.06001$	$0.6001\times 0.9$ $=0.54009$	0.6001

Appendix

Table 7: Average arithmetic energy per dense reference product with matched FP32 accumulation; the

T=1

PoT-LIF row uses a 60.01% firing rate. All other power terms are excluded.

Fam.	Configuration B / reference A	A (%)	B (%)	$\Delta$	$b$	$c$	$p$	$p_{\mathrm{Holm}}$
F1	Heartbeat $T=4$ , identity STE	96.70	96.90	+0.20	38	42	0.738	1.000
F1	Heartbeat $T=4$ , magnitude STE	96.70	96.90	+0.20	38	42	0.738	1.000
E	Heartbeat $T=4$ FP8/FP32 (archived)	96.70	97.00	+0.30	40	46	0.590	—
F1	Heartbeat $T=4$ FP8/A24	96.70	97.50	+0.80	38	54	0.117	0.704
F1	Standard mode $T=2$	96.70	96.35	$-$ 0.35	62	55	0.579	1.000
F1	Heartbeat $T=2$ main	96.70	97.25	+0.55	40	51	0.294	1.000

Appendix

Table 8: Paired statistical comparisons. A and B are success rates (%);

\Delta=B-A

is in percentage points. For F1 and the first nine E rows, A is the 96.70% continuous control; for F2, A is the 96.25% matched-budget control. Other E rows name their reference configuration.

p

is the unadjusted exact value;

p_{\mathrm{Holm}}

is reported only for F1 and F2. The two STE rows correspond to separately fine-tuned final checkpoints. “BF16 membrane” distinguishes the precision sweeps from the main configurations with FP32 membrane state.

$T$	$\theta$	Spatial	Object	Goal	Long-H.	Overall	$\Delta$
2	${2}^{-16}$	99.4	98.8	97.6	92.8	97.15	$-$ 0.10
2	${2}^{-8}$	98.2	98.6	98.4	93.0	97.05	$-$ 0.20
4	${2}^{-16}$	99.4	97.6	98.8	93.0	97.20	$+$ 0.30
4	${2}^{-8}$	98.8	98.2	99.0	92.8	97.20	$+$ 0.30

Appendix

Table 9: Heartbeat with BF16 membrane state and explicit thresholds, using fixed checkpoints and BF16 weights without further fine-tuning. The implementation’s four-bit threshold-selection index maps

c=15

\theta={2}^{-16}

and

c=7

\theta={2}^{-8}

; it is not the event-exponent field.

\Delta

is relative to the main Heartbeat configuration at the same

T

, which uses FP32 membrane state and

\theta={2}^{-16}

. Rates are percentages; differences are percentage points.

$\theta$	Spatial	Object	Goal	Long-H.	Overall	$\Delta$
${2}^{-16}$	98.8	98.6	98.0	93.6	97.25	$+$ 0.35
${2}^{-8}$	98.2	98.0	97.6	91.6	96.35	$-$ 0.55
${2}^{-4}$	98.6	97.6	97.8	94.2	97.05	$+$ 0.15

Appendix

Table 10: Standard mode at

T=1

with FP8 E4M3FN weights and three explicit thresholds, using the final

T=1

checkpoint without further fine-tuning and a static power-of-two scale per weight tensor.

\Delta

is relative to the 96.90% BF16-weight

T=1

result. Rates are percentages; differences are percentage points.

Efficient VLA Model Inference

Efficient vision-language-action (VLA) model inference reduces robot-control latency, memory use, and energy while preserving task performance.

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Vision-Language-Action (VLA) models have become a dominant paradigm for embodied intelligence. However, most existing approaches are built on large-scale transformers, resulting in substantial inference latency and energy consumption that limit their practical deployment in low-power, real-time scenarios. We propose SpikeVLA, a spiking VLA architecture for embodied navigation with energy-efficient inference, consisting of three key components. (i) A spiking vision encoder, Spike-V, that replaces dense continuous layers with event-driven spiking layers to reduce the energy consumption of visual representation learning. (ii) A multi-modal spiking large language model, Spike-L, that reformulates cross-modal reasoning with spiking dynamics and token-level event-driven sparsity to further lower computational cost. (iii) A spiking action policy network, Spike-A employs Laplacian-kernel population coding with a multi-layer fully connected SNN, and decodes spiking activities into stable and robust continuous control with energy-efficient inference under low-power constraints. Experiments on navigation and robotic control tasks show that SpikeVLA significantly reduces energy consumption and computational cost while maintaining competitive performance, highlighting its potential for low-power, real-time embodied intelligence.

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