Otters: An Energy-Efficient Spiking Transformer via Optical Time-to-First-Spike Encoding
Authors: Zhanglu Yan
Jiayi Mao
Qianhui Liu
Fanfan Li
Tao Luo
Gang Pan
Bowen Zhu
Weng-Fai Wong
Venue: ICLR 2026 Poster (2026)
Keywords: Spiking neural network
Energy efficient
Time-to-First-Spike Encoding
Optoelectronic Synapse
Primary area: other topics in machine learning (i.e., none of the above)

Abstract: Spiking neural networks (SNNs) promise high energy efficiency, particularly with time-to-first-spike (TTFS) encoding, which maximizes sparsity by emitting at most one spike per neuron. However, this energy advantage is often unrealized because inference requires evaluating a temporal decay function and then multiplying the result by the synaptic weights. 
This paper challenges this costly approach by repurposing a physical hardware `bug', namely, the natural signal decay in optoelectronic devices, as the core computation of TTFS. We fabricated a custom indium oxide optoelectronic synapse that demonstrates how its intrinsic physical decay directly implements the required temporal function. By treating the device's analog output as the fused product of the synaptic weight and temporal decay, optoelectronic synaptic TTFS (named Otters) eliminates these expensive digital operations. 
To use the Otters' paradigm in complex architectures such as the transformer, which are challenging to train directly due to sparsity, we introduce a novel quantized neural network-to-SNN conversion algorithm. 
This complete hardware-software co-design enables our model to achieve state-of-the-art accuracy across seven GLUE benchmark datasets and demonstrates a 1.77$\times$ improvement in energy efficiency over previous leading SNNs, based on a comprehensive analysis of compute, data movement, and memory access costs using energy measurements from a commercial 22nm process. 
Our work thus establishes a new paradigm for energy-efficient SNNs that translates fundamental device physics directly into powerful computational primitives. All codes and data are open source.

Published as a conference paper at ICLR 2026
OTTERS: AN ENERGY-EFFICIENT SPIKING TRANSFORMER VIA OPTICAL ENCODING
Zhanglu Vant Mao Qianhui Liu Fanfan Li", Gang Pan', Tao Luo", Bowen Zhu?, Weng-Fai Wong!
DDpartment of Computer Science, National University of Singapore, "School of Engineering, Westlake University,
Schoool of Artificial Intelligence, Shandong University,
*College of Computer Science and Technology, Zhejiang University,
5 Aggeny for Science, Research and Technology. Singapore.
ABSTRACT
Spiking neural networks (SNNs) promise high energy efficiency, particularly with toee----irtt-ppike (TTFS) encoding, which maximizes sparsity by emitting most one spike per neuron. However, this energy advantage is often unrealized because inference requires evaluating temporal decay function and then multi- plying the result by the synaptic weights. This paper challenges this costly ap- proach by repurposing a physical hardware 'bug', namely, the natural signal de- cay in optoelectronic devices, as the core computation of TTFS, We fabricated a custom indium oxide optoelectronic synapse that demonstrates how its intrinsic physical decay directly implements the required temporal function. By treating the device's analog output as the fused product of the synaptic weight and tem- poral decay, optoelectronic synaptic TTFS (named Otters) eliminates these ex- pensive digital operations. To use the Otters' paradigm in complex architectures such as the transformer, which are challenging to train directly due to sparsity, we introduce a novel quantized neural network-to-SNN conversion algorithm. This complete hardware-softwaal co-design enables our model to achieve state-of-the- art accuracy across seven GLUE benchmark datasets and demonstrates 1.77 improvement in energy efficiency over previous leading SNNs, based on com- prehensive analysis of compute, data movement, and memory access costs using energy measurements from a commercial 22nm process. Our work thus estab- lishes paradígm for energy-efficient SNNs that translates fundamental de- vice physics directly into powerful computational primitives. All codes and data are open souree")
INTRODUCTION
Large language models (LLMs) have demonstrated remarkable capabilities, yet their immense computational and energy costs hinder deployment resource-constrained edge devices (Lin) et aL. 2023: Jegham et al. 2025). This critical challenge has spurred research on more efficient, brain-inspired architectures, with spiking neural networks (SNNs) emerging as promising candi- date (Xing et al. 2024a Tang et al. 2025 Liu et al.) 2025). SNNs are known for their potential energy efficiency, arising from sparse, event-driven computations that use addition rather than expen- sive multiplications. However, realizing this efficiency in practice is complex and depends heavily on the encoding scheme used (Yan et al., 2024). In conventional rate-coded SNNs, information encoded in the number of spikes in a fixed time window. This approach necessitates multiple mem- ory accesses for weights and frequent data movement on each spikes, which may negate the benefits of the sparse computation. Temporal coding schemes, specifically. time-to-fire fo-ist---i--- (TTFS), offer
*Correspondence Zhanglu Yan. Email: zlyan Syan@nuse @du..euu.sg * Equal contribution.

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Published as a conference paper at ICLR 2026
potentially more efficient alternative. By encoding information in the precise timing of a single spike, TTFS-SNN neuron fires at most once per activation cycle. This maximizes sparsity, dramat- ically reducing spike count and the associated data movement costs, making TTFS theoretically optimal encoding for energy efficiency (Yu et al. 2023
Zhao et al. 2025).
Exput
Input spike train 00000700
spike 00100110
Enerey potential
most one spike Fower colcullnionss
Esput spike triin
Input spike train
11100110 Σ Euye
11100011
00010000 (
00000100 Ooiput spikk triis
Qusput
Ingus Eu
spiko
Input spilke train 00010000
20
11100119-
Multiple weight cocess
Nox consyy efficim!
Addiiional fonction Roquiree MAC operation
Warning
Multiple ACC
a) Rate-encoding
by TTFS encudligg
Figure I: Rate encoding vs TTFS encoding
However, there are hidden costs behind this theoretical efficiency. In TTFS, information is encoded by mapping spike timing to importance; typically, the earlier a spike arrives, the larger the numerical value it represents. To implement this principle, the network typically requires an additional compu- tational step to convert each spike's s raw arrival time into a corresponding value. This done using a decay function (e.g.. <(t) e-t or T () whose output is then multiplied by the synaptic weight (w- e(t)) (Wei et al., 2023 Che et al. 2024b). This conversion process requires energy to compute the decay function, and it reintroduces multiplication operations that SNNs are designed to avoid. This practical drawback negates the energy savings from sparsity, thereby raising critical question: how can we exploit the sparsity of TTFS while avoiding the costly computation? Recognizing that the costly term w - <(t) is a quantity that decreases predictably over time, our answer lies not in optimizing the digital computation but in finding physical analog simulate this process. This approach leads us to optoelectronic synapses, which are attractive for their fJ-level energy consump- tion and high resistance to electromagnetic interference (Li et al., 2024b). Notably, while this field has traditionally focused on suppressing their natural signal decay (volatility) to create stable mem- ories (Alqahtani et al., 2025), we embrace this decay. We recognize it not as a bug but as the exact physical implementation of the temporal decay function required by TTFS. To implement this prin- ciple, we fabricated a custom In203 optoelectronic synapse. Our method, Otters, uses the natural decay of this device's 's optical signal to perform the required computation. This approach integrates storage and computation into a single physical step, thereby addressing the overhead of traditional TTFS.
While our Otters hardware mitigates the computational overhead of TTFS, a second major barrier remains: the inherent difficulty of training such networks, especially for complex architectures such as transformers. Directly training SNNs is challenging. In event-driven learning, error backprop- agation depends on spike timing; if neuron fires too sparsely or not at all, it fails learn. This "over-sparsity" problem can severely limit the model's performance and even lead to training fail- (Wei al., (202)). To sidestep this issue, we employ a quantized neural conversion methodology. We first train QNN and then convert its weights to our Otters SNN, thereby avoiding the pitfalls of direct spiking-domanl -omain training. To further maximize efficiency, we use knowledge distillation to train a highly compressed model with 1-bit weights and 1-bit key/value (KV) projections. Our complete hardware- software co-design, combining the Otters synapse with our QNN-to-SNN conversion pipeline, establishes a new state of the art for spiking language models. Evaluated on the GLUE benchmark, Otters achieves average accuracy of 3% higher than previous leading SNNs while demonstrating 1.77-3.04 x improvement in energy efficiency compared to baselines like Sorbet and SpikingLM (Tang et al., 2025 Xing et al. 2024b). Notably, this energy- efficiency gain is validated by rigorous and comprehensive analysis that goes beyond the simplistic metrics commonly used in prior SNN research. While previous work often only counted compute operations (e.g., additions vs. multiplications), our analysis provides more realistic estimate. It
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is grounded in measurements from commercial 22nm process and provides full accounting of compute, data movement, and memory access costs, making our efficiency claims robust.
We also investigate the Otters paradigm's 's sensitivity to the hardware noise inherent in analog de- vices. Our initial amalysis shows that, on the SST-2 benchmark, the baseline model's performance begins to degrade when key physical parameters vary by around 5%. To improve robustness, propose Hardware-Awan Training, a method that introduces different levels of simulated Gaussian noise during training. This approach enhances the model's resilience, enabling maintain robust performance under noisy conditions and providing a practical path toward real-world deployment.
2
PRELIMINARY
2.1
OPTOELECTRONIC SYNAPSE
An optoelectronic synapse is a neuromorphic device that emulates biological synaptic functions by using optical signals modulate its electrical conductance. These devices are renowned for their potential for extreme energy efficiency, broader bandwidth and faster signal transmission in neu- romorphic computing, which are key advantages over purely electronic counterparts (Xie et al. 2024 Wang et al. 2023). Recent studies have reported energy consumption reaching the femtojoule (fJ)/siie level, comparable that of biological synapses and substantially lower than that of con- ventional CMOS neuron devices (Shi et al. [022, Wang et al.) 2024). Among various implementa- tions, oxide thin-film transistors (TFT) are regarded as viable candidates for optoelectronic synapses due to their low Icakage current and capability for large-area, flexible fabrication. colution-bases fabrication further offers the advantages of low cost, simplified processing, and facile compositional control. Previous reports have shown that solution-processee operational stability, and low energy consumption (Li et al. 2025). Building upon these advances, this work employs the mature and reliable oxide-TFF platform develop the Otters spiking neuron.
devices exhibit uniform performance,
2.2 TIME-TO-FIRSTT-PIIE SNN
In contrast to rate-based encoding, which uses the frequency of spikes to represent information, TTFS encoding leverages the precise timing of a single spike. The core principle is that stronger input stimulus causes a neuron's 's membrane potential to rise faster, reaching its firing threshold sooner. Thus, the information is encoded in the arrival time of the first- and only spike within given time window, T. This approach maximizes temporal sparsity and highly efficient, as each neuron fires most once (Che et al. 2024a).
The operation of a standard TTFS neuron involves two phases. First, the neuron integrates incom- ing spikes, updating its membrane potential (t). Second, it compares this potential firing threshold e (t).. A spike is generated at the first time step t where the potential meets or exceeds the threshold:
11 if V)(() (1)
st(()
0, otherwise
However, the asynchronous nature of SNNs, combined with the "fire-as-earlyas--ooiiii objectivee of TTFS, can lead to another problem. If a presynaptic neuron fires after postsynaptic neuron has already fired, its spike becomes invalid for membrane potential accummalation. To solve this, we employ Dynamic Firing Threshold (DFT) model that enforces synchronous, layer-by-layer processing schedule (Wei et al. 2023). The threshold for any neuron in layer 1 is set to infinity outside of a designated time window, effectively ensuring that layer is only active from time T
to T (1 (1+1) 1):
Olynamic (4), IT..ISIST ((+1)) +00,
('(1)
otherwise
This scheduling guarantees that all spikes from a preceding layer are processed before the current layer can fire, thus preserving the valid causal relationship.
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3 METHODS
This section details the methodology behind Otters. We first describe the core of our model: the optoelectronic synapse and the neuron model that performs the TTFS computation (Sectionn..1] We then explain how these components are assembled into the complete optimized spiking transformer architecture (Section 3.2), and then, we outline the QNN-10-SNN conversion pipeline used to build the Otters model (Section 3.3 Finally, we present the framework for the comprehensive energy analysis used validate our model's 's efficiency (Section 3.4.
* Jepar gakr Dell
Hondease printte
Seysair (hessal Sigusir
Figes
Figure 2:
Device and workflow: (a) the custom-fabricated InzOg thin-film transistor (TFT); (b) measured decay curve of the device response: (c) Otters neuron workflow.
3.1 OTTERS SPIKING NEURON
The core of our method is the Otters optoelectronic synapse, a hardware element that physically implements the modulated synaptic dynamics required for TTFS computation. Each synapse is composed of two main parts: custom- fabricataere Indium Oxide Thin-Film Transistor that provides a physical signal decay, and an amalog-to-digita. converter (ADC) that map and scale the analog signal to digital. Fabrication details for the device in Fig. 2 a) are provided in Appendix [ To ensure a deterministic response, the TFT is operated with a fixed light intensity, yielding a consistent
non-linear decay curve, modeled by the function (t)) To e (t/rr² + Tottses (Li et al. 2024a Liang et al. 2022) We fit the model parameters by minimizing the sum of squared residuals using the differential evolution algorithm, yielding: 1o 110.989, = 1.3425, 3 = 0.495, and
Toliset = - 109.989, showing in Figure Thus, the TFT's current decay over time naturally forms the temporal component of the post-synaptic potential (PSP).
However, the device's 's physical nonlinearity poses a critical design challenge. For our QNN-to- SNN conversion to be lossless, the information encoded by spike's ' timing must map set of uniformly spaced logical values. Specifically, a spike occurring at physical time &ę must represent the quantized value (T' A)/T. The device's 's non-linear decay, Ott), means that the physical times t at which the device output naturally equals these target values are themselves non-uniformly spaced. A naive approach using constant threshold and uniform time sampling would therefore fail to establish the required functional equivalence.
Therefore, our solution to reconcile the non-lineat device physics with the linear encoding require- ment. Instead of implementing a complex, non- con-uniform clock, we engineer dynamic, wiie decreasing firing threshold, 0l (t), while operating the system on a standard, uniform physical clock. This threshold is designed to change its value only at the pre-calculated time points (t&) which are derived from the inverse of the physical decay function. This design ensures that the firing condition where the membrane potential exceeding the threshold can only be met at one of these discrete mo- ments tg. The neuron fires at the first such time point where its accumulated potential is sufficient. Consequently, the output spike time tj encode the intended quantized value (T k)/T. Be- cause this encoding scheme is applied consistently throughout the network, the output spike of one layer provides correctly timed and valued input the next, ensuring the integrity of information
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propagation across the entire architecture. The full mathematical formulation of this threshold will be defined in our conversion methodology in Section 3.3
The ADC implements a % times scaling mapping from the physical decay to digital post-synaptic potential (PSP). Thus, the full PSP c' generated by presynaptic spike is therefore the direct analog output of the synapse at the time arrival:
(t)) 10-- O(t)
The membrane potential (t) of neuron accumulates these PSPs. At each discrete physical time step t, the potential is updated based on incoming spikes:
(t() (t +)+
Σ
(t)
(4)
(1)=1
neuron fires when its membrane potential first meets or exceeds the dynamic threshold. This spike time, spike. corresponds to the first logical timestep k where the condition is met:
& Spike. min(44/V 2 0' (1x4)
In adherence with the TTFS paradigm, the neuron is deactivated after firing ensure most one spike per inference cycle. Algorithm in appendix formally describes this forward pass.
3.2 NETWORK STRUCTURE
A primary challenge in creating a spiking transformer is the matrix multiplication required for self- attention score calculation (Q K"). While some rate-coded SNNs can simplify this by treating one matrix binary spike train (turning multiplication into selective addition), this approach is incompatible with TTFS encoding, which requires decoding spikes into non-binary values. To overcome the problem, quantize the key (K) and value (V) projections Consequently, the dot product with TTFS-encoded query (Q) is computed using only selective, additions and subtractions. This allows us eliminate the multiplication bottleneck while still benefiting from the high sparsity of TTFS. To implement this 1-bit attention mechanism efficiently, designed a supporting dataflow architecture inspired by the Canon architecture (Bai al., 2025). as illustrated in Figure 3 During inference, the binary K (or V) vectors are pre-loaded into the local memory of a Processing Element (PE) array. The
single bit, (+1.
input stream (representing
Q) is broadcast to the PEs. As shown, each PE computes partial sum by accumulating its local K values only at the time steps corresponding to incoming spikes. These partial sums are then passed between PEs for final accumulation. This architecture minimizes data movement and leverages the spatio-temporal sparsity of the TTFS input for energy efficiency.
ACCUMILATION
Nerto
Biroey Errieciling
Spitz Xeansx
Spike Masson
Sprie Aewmer
S80 EELL SE9S KYGE SVIA
Binary weight Ontn-FC
kvis
Savs kvia
Binury weialr Opto FC
Binary weighn Outo-CC
Binary weight Opto PC
64
ROGEE BAR WASAER Soees kva.. Seves kY
Sptte Asaane
Nawson
weght
Xpier
Nevera
ACTIVATIOON
Figure Scores calculations
Figure 4: Oaters-based transformer structure
This self-attention module, along with feed-forward layers built from our Opto-FC and spiking neuron primitives, forms the complete Otters transformer architecture shown in Figure
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3.3 QNN-TO-SNT CONVERSION
To overcome the challenges of direct SNN training, we employ a QNN-to SONN-o--NNN-A conversion method- ology. We first train a QNN and then map its learned parameters to an equivalent Otters SNN, ensuring the two networks are functionally identical. To formalize this relationship, we first de- fine the specific QNN layer architecture that enables this equivalence. A compatible QNN layer computes its output 4. for neuron j as follows:
df = Σ
1 b
(6)
A/1 = Q(d,) = Clip(1 a - -
(7)
where af is the pre-activation, wi are the weights, b' is the bias, and a' is the quantization scaling factor for layer With this structure established, we can now state the proposition that governs the exact conversion from the trained QNN to the Otters SNN:
Proposition 1. An Otters SNN layer (as defined in Section Sy. is functionally equivalent to trained n-bit QNN layer (as defined above) if its parameters are constructed as follows:
1. The number of discrete time steps in the SNN simulation window, is set to match the number of positive quantization levels of the n-bit QNN: T = =2" 1
2. The mapping from logical time step k (0.1...., T 1} physical spike time tu is defined such that the device's output at that instant, Ottx). is linearly proportional to the T-
remaining time in the window: O(tx)= T
3. The SNN's physical scaling factor for the synapse connecting neuron i in layer I - 1 to neuron j in layer I, Ti is set based on the corresponding QNN weight and the quantization scale of the previous layer: Thi = w/g ---1... .T
4. The SNN's s firing threshold for neuron in layer I is step-wise decreasing function of time, defined as: 6¹ (t) a' -T for tt S tk-1-
The proof proceeds in two steps. First, during integration, we show that the accumulated membrane potential V in an SNN neuron is numerically identical to the corresponding QNN neuron's 's pre- activation value a/. We binarize weights w/y to reduce energy and increase the reuse of factor 7/y- Second, during firing, we show that the engineered, time-dependent threshold 6) (t) compensates for the device's s intrinsic non-linee con-linearity by permitting firing only al pre-calculated time points, 4x. derived from the inverse of the physical decay function. This mechanism ensures the SNN neuron fires at time e s that precisely encodes the QNN's quantized output x/yj- A detailed proof is provided in the Appendix A.2
3.4 ENERGY ANALYSTS
To evaluate the efficiency of our approach, we formulate an analytical energy model. The total inference energy (E) is decomposed into three primary components: computation energy (ECompute). data movement energy (Epaa), and analog energy (EAnalog) Yan et al. 2024 Dampthotfer et al.) 2022]. The computation energy, Ecompute. accounts for arithmetic operations of additions. The data movement energy, EDau. encompasses the energy for transferring data, including both dynamic and statie power consumption. The final component, Exnaloy, includes the energy to power the TFT, the sampling energy, and ADC energy required to converted the analog signal to scaled digital value, collectively represented as EReal Analog Thus, we have = ECompute + EData + Emnalog. For our energy calculation, we consider a spatial dataflow architecture where information (e.g., spike packets) is communicated over Network-on-Chinn (NoC) (Yan et al.] 2024). This architecture is representative of modern specialized hardware such as neuromorphic chips like Loihi (Lines et al. 2018) and dataflow AI accelerators like Tenstorrent (Vasiljevic et al. 2021) and Sambanova (Prabhakar al. 2022]. We consider the control logic energy to be negligible as our analysis focuses on specialized accelerator designs where such overhead is minimal Yann al. 2024

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Thus, model the energy consumption of our Otters-based linear projections and attention op- erations. We disregard the computational cost of certain operations, such as Softmax and Layer Normalization, as their contribution to the total compute is negligible compared large-scale ma- trix multiplications. The energy to perform a linear projection, FO is modeled by Equation 8 The calculation is performed channels, The total energy is the sum of the following components per output element:
batch of size B, sequence of length S, and for C. output
EOptoFFC = B.
C. CT (sp (EACe +
ReRc Analog
E move
Total Outputs
Spike Processing
+ Eicakage
+ T (ECMP +
Read ihresholal
E Write
binaryky
Thresholding
K/V Write
Computation Energy: This includes the energy for sparse accumulations. The total number active accumulate operations is the workload (C,) scaled by the average number of spikes (T 8p), with each operation costing Eace. Additionally, each of the C, output neurons performs T comparisons against its threshold, costing FCMP per comparison.
Data Movement Energy: This is composed of dynamic and static costs. Dynamic energy (Fmgure) consumed to move spike data and is proportional to the spike rate (s,)) Otters paradigm requires a dynamic, step-wice wise decreasing threshold, which introduces additional dynamic energy of reading operations ExReal Eihreshold which is need for spiking neurons. Static energy (Ereakage) accounts for constant leakage power the time window T. After the computation completes, additional energy cost, W is incurred to write the gener- ated binary Key and Value vectors to SRAM, as described in Section 3.2
Analog Energy: Each incoming spike initiates two analog operations: first, the optoelec- tronic synapse emits light, and second, the decay function is sampled at a specific time la- The energy for both the light emission and the sampling event calculated by integrating the instantaneous power (P V over the duration of each respective operation. For the readout circuitry, including the amplifier and the look-up-table, we adopt the energy values of successive approximation register-assisted pipelined ADC (Su et al. 2023 The total energy consumed in this process is denoted E/Read "Amlog per spike.
The energy model for attention score calculation, Eopto-score analogous to the linear projection, with two key differences which lies in the outer dimensions and an additional data movement cost for reading the binary Key (or Value) vector from SRAM determine whether the sampled membrane potential should be added to or subtracted from the accumulator, showing in Appendix A.3 A.3
RESULTS
In this section, we evaluate Otters on seven datasets from the GLUE benchmark. We compare its performance against both standard QNN and SNN baselines, using BERT base as the teacher model for knowledge distillation. We further provide detailed analysis of the model's energy efficiency and robustness. All experiments were conducted simulation window size recommended by Sorbet (Tang et al., 2025) (In our setting, it is equal to timestep T 15). The training process of Otters is shown in Appendix A.5 dataset we adapted is shown in Appendix A.6
three NVIDIA A100 GPUs with fixed 4-bit
A.5 and the description of
4.1 GLUE BENCHMARK PERFORMANCE
As shown in Table 1 Otters achieves SOTA results among SNNs across all seven evaluated GLUE tasks, consistently outperforms larger and more complex SNN models like SpikingBERT and SpikeLM. For example, Otters surpasses existing SNNs and achieve accuracy of 68.95% on RTE and 91.28% on SST-2. The average accuracy for Otters is 83.22%, which 3.42% and 2.98% higher than Sorbet and Spikel.M, respectively.
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Table 1: Performance comparison on the GLUE benchmark. All scores are accuracy, except for STS-B (Pearson correlation). "e" indicates that the model size was not reported in the original paper. Bold indicates the best performance among SNN models. Only Otters quantizes KV bit.
Model
Size
QQP
MNLI-m
SST-2
QNLI
RTE
MRPC
STS-B
Average
BERT DDelin et al.
2019
418M
91.3
84.7
93.3
91.7
72.6
88.2
89.4
87.31
DistilBERT (Sanh et
2020
207M
88.5
82.2
89.2
59.9
87.5
86.9
83,64
ThnyBRTT
207M
84.6
93.1
90.4
70.0
87.3
83.7
84.85
Q2BERT (Zane al
2020
43.0M
67.0
47.2
80.6
61.3
52.7
68.4
4.4
54.51
BiT (Liu el al. 2022
13.4M
82.9
77.1
87.7
85.7
58.8
79.7
71.1
77.57
SpikingFrmas Zini al.
2023
83.8
67.8
74.6
74.0
72.3
73.43
SpikingBH:RI (Bal Sengupla 2024
50M
86.8
78.1
88 22
85.2
66.1
79.2
82.2
80.83
SpikeLM King et al. 2024b
87.9
76.0
86.5
84.9
65.3
78.7
84.3
80.51
1-bit Spikel M Xing et al. 2024b
87.2
74.9
86.6
84.5
65.7
78.9
83.9
80.24
1-bit Sorbet (Tang el al. 2025
13.4M
86.5
77.3
90.4
86.
60.3
79.9
78.1
79.80
Otters (Ours)
87.67
86.42
84.56
85.19
83.22
4.2 ENERGY EFFICIENCY
We analyzed the energy consumption of Otters on the SST-2 dataset, comparing against full- precision and quantized BERT models we converted from, well as SOTA 1-bit SNNs. The 1 1-bit quantized BERT is the QNN Otters converted from which sharing the same structure and parame- ters. As detailed in Table 2 Otters consumes only 4.06 mJ inference for one attention block. This represents a 41.36x x energy saving compared to the full BERT base model and a 2.72 efficient compared the 1-bit quantized BERT. Otters is also more efficient than previous SNNs, taking 3.04x energy saving of Sorbet and 1.77x SpikingLM.
Appendix A.3 provides the full energy equation, detailed measurements for all compared models, and an ablation study comparing traditional TTFS with Otters. All energy figures include com- pute, data movement, and static components. In the same appendix section, provide detailed breakdown of the energy consumption in Otters to clarify the contribution of each component.
Table 2: Energy consumption analysis on the SST-2 dataset. Energy is reported for each FC layer (QKV linear projections), each QKV V self-attention score calculation, and the total sum per inference. The Energy Ratio is Energy(Full BERT) EMergy(Model) (f higher is better).
Model
FC (mJ)
QKV (mJ)
Total (mJ)
Energy Ratio(1)
Full BERT DDelin et al. 2019
50.35
8.41
167.92
1.00x
Quanlized BERT
3.31
11.03
15.2x
Sorhet (Tang et 2025
3.39
1.08
12.34
13.61x
Spi [Bat & Sengupta. 2024
6.37
2.05
23.22
7.23x
SpikingLM (Xing et al. 202440
2.09
0.46
7.2
23,32x
Otters (4bit kV)
1.14
0.53
4.49
37.40x
Otters (1bit kv)
1.14
0.33
4.06
41.36x
4.3 EFFECT OF KV CACHE QUANTIZATION
To further optimize energy, we explored the impact of quantizing the Key and Value projections in the self-attention mechanism. Table 3 shows that reducing the KV precision from 4-bit to 1- bit (Otters-Ibitky yields 10% reduction in total energy consumption (from 4.49 mJ to 4.06 mJ). This energy saving comes at the cost of 0.23% drop in accuracy on SST-2, demonstrating highly favorable off between efficiency and performance.
Table 3: Impact of KV quantization energy and accuracy SST-2.
Energy (mJ)
Model
FC
QKY
Total
Accuracy (%)
Otters-4bitky
1.14
0.53
4.49
91.51
Otters- 1biik
1.14
0.33
4.06
91.28
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4.4 ROBUSTNESS DISCUSSION TO HARDWARE PARAMETER VARIATIONS
The practical deployment of the Otters paradigm hinges on the assumption that the physical decay characteristics of all optoelectronic synapses are uniform. However, analog hardware inevitably subject to device-to-deviee variability from the fabrication process, which is significant challenge for large-scale integration (Garg et al., 2022). Such inherent hardware noise can corrupt the precise time-to-valie mapping that underpins our conversion method. To evaluate robustness against hard- ware variability (Faghohungbe Qian (02T]Xuan & Narayanan, [022 [Su et al. 2024), we injected zero-mean standard deviation Gaussian noise, which is commonly used to simulate and represent hardware noise, into the physical decay function, Ott), and its parameters, T and B. The injected noise is proportional to parameter magnitude: at level each parameter is scaled as p <- (1 A)) As shown in Table 4 the baseline Otters model can tolerate about 5% total output O(t) difference with minimal accuracy impact and remains robust.
To keep improving the robustness, we propose Hardware-Aware Training (HAT), a method that builds robustness by simulating hardware non-idealities during training. We introduce two vari- ants, HAT and HAT?, by injecting 10% and 20% Gaussian noise, respectively, into the QNN's activations (see Eq. 7). As shown in Table 4. both HAT settings improve noise resilience. The HAT model maintains a stable accuracy of 80.8% even under a 20% noise level. HAT trained with more noise, excels high-noist noise regimes, whereas HAT achieves higher accuracy in low-noise conditions while still substantially outperforming the baseline (e.g., 11.5% accuracy gain with 12% noise in O())). Thus,
models trade a minor drop peak accuracy for significant increase in resilience against hardware noise. This demonstrates that the model can be regularized to generalize across a range hardware imperfections. Consequently, the HAT noise level can be tuned to the manufacturing tolerances of specific hardware platform, ensuring reliable real-world performance and validating the Otters paradigm as a robust and practical approach.
Table 4: Noise Robustness in Physical Decay Function. The best performance per noise level within each component group in boldface. Results: mean + std dev over runs.
Method
Gaussian Noise Level
Full Function O(t) Experiments
O(t)
0.04
0.08
0.12
0.16
0.20
Otters
89,9 + 0.8
86.1 0.8
73.8 = 0.9
58.0 =
53.3 0.4
OUrrs+HAT
89.3 1 0.5
89.0 1 0.6
85.3
1 0.6
76.5 1 0.4
61.0 0.8
Oltrs+lAAT
87.4 1 0.5
87.2 1 0.7
85.9 1 0.7
85.2 1 0.7
80.8 0.3
Parameter / Experiments
B
0.01
0.02
0.03
0.04
0.05
Otters
90.2 + 0.1
89.5
87.5 1.8
79.2 +
72.5 1.4
Otters+HAT'
89.6 + 0.1
89.2 - 0.3
89.1 - 0.4
87.7 =
80.6 2.8
Otters+HAT
87.8 + 0.7
88.1 +
87.4 = 1.0
85.5 = 1.1
83,8 0.5
Parameters T Experiments
0.10
0.20
0,30
0.40
0.50
Otters
90.3 + 0.1
90.1 0.5
87.0 1.7
75.0 + 4.1
67.5 4.8
OutrrsHHTT
89.6 + 0.5
89.3 1.2
88.2 0.7
88,2 +
76.1 2.8
Ouers+HATT
87.8 + 0.6
87.7
87.1 0.6
87.2
83.0 1.4
DISCUSSION AND FUTURE WORKS
To make SNNs more energy-efficient Otters focuses on hardware-softwan co-design to optimize a core computing operation. We replace the temporal decay function and its following multiplication by sampling the natural decay of an oxide optoelectronic synapse. This shifts the computation from digital to analog for a more energy-efficient computing method. However, at the same time, many related works are also working toward better energy efficiency for SNNs, but from another direction, such algorithmic and architectural improvements. These methods, including QKFormer, SSSA, and A OSSS"A A. optimize the spiking attention mechanism from ( to linear complexity (linear-
attention SNNs) (Zhou al. 2024 Wang et al., 2025b: Guo al. 2025 These two directions

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Published as a conference paper at ICLR 2026
not in conflict. They complementary and solve different parts of the problem. Future work includes designing a linear attention mechanism based on the Otters spiking neuron to make energy even more efficient.
We further discuss the hardware scale. The InzO; optoelectronic synapse in our prototype has an effective area of about 0.012 mm? with channel length of 30 jam. This size is mainly due to the precision limits our fabrication equipment and does not represent the scaling limits of InyO3 technology. Since the goal of this paper is validate the optoelectronic TTFS mechanism, we did not focus on device size optimization. However, recent work has demonstrated InzO3 transistors with channel lengths down 40 nm (Si al. 202I). showing that the device area can be reduced by nearly three orders of magnitude. Additionally, several studies show that oxide devices can be integrated in 3D stacked layers, providing another path to further reduce the effective area per synapse (Tang et al. 2022 Yuvaraja et al., 2024, Kwak et al., 2024). With the TTFS mechanism verified, we plan to focus on device scaling in future work. We also note that the device count can be reduced by device sharing. For example, consider a Q-projection layer with input channels C; and output channels C., If every weight required one device, the layer would need O(C₂ C.) devices. In the Otters setting, this number would reach 10--107, which is clearly not practical. However, in our setting (introduced in Section 3.3), all weights are quantized to 1-bit. This means the decay function is identical for the entire layer, making it possible to share the In3O3 device. In the best case, one FC layer can reuse just one physical device. Thus, single BERT block would require about 8 devices, resulting in a total area of 0.096 mm3: 6 for the self-attention module (projections of Q. K. V, their multiplication and output) and 2 for the feed-forward module. (In real systems, the number of devices might be higher, and sharing may be limited by architecture and compiler constraints.) The next step of this work is to design an architecture that increases this device reuse further reduce the chip area.
CONCLUSION
This paper introduces Otters, a new paradigm for energy-efficient neuromorphic computing that challenges this digital-centric approach. Through hardware-software co-design, we repurpose the natural signal decay custom-fabricated optoelectronic synapse, transforming this physical phe- nomenon into computational method. This allows to eliminate the costly evaluation of the decay function inherent in traditional TTFS, thereby fusing computation and memory into the phys- ical process. To deploy this paradigm in complex architectures such transformers, a QNN-to-SNN conversion algorithm that circumvents the challenges of direct SNN training. The Otters model achieves satee-of-the-att accuracy among SNNs on seven GLUE benchmark datasets, while simultaneously delivering a 1.77x improvement in energy efficiency over previous leading spiking models. By directly harnessing fundamental device physics for computation, this work demonstrates a new path to a more energy energy-efficient neuromorphic computing design.
developed
7
ACKNOWLEDGEMENT
This research is partially supported by the Ministry of Education, Singapore, under the Academic Research Fund Tier (FY2024).
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A APPENDIX
A.1 FABRICATED IN203 TFTS
To prepare the indium oxide thin-film transistors (IngO; TFTs), indium nitrate was first dissolved in mixed solvent of 2-methoxycthanol (2-ME), acetylacetone (AcAc), and ammonium hydroxide (NH3-H2O to form precursor solution, which stirred overnight to ensure complete dissolu- tion and coordination. Subsequently, gate electrodes were fabricated on a silicon substrate coated with 2iO₂ insulating layer, followed by sequential deposition of 8 nm chromium and 50 nm gold via electron-beam evaporation. A 30 nm-thick Al2O3 dielectric layer was then uniformly deposited the substrate using atomic layer deposition (ALD). The In,O3 precursor solution spin- coated onto the dielectric surface, after which the channel regions were defined through standard photolithography, and the unprotected areas were removed by hydrochloric acid etching. The films were annealed in air at 300 "C for 1 hour to enhance crystallinity and improve film quality. Portions of the Al2O3 layer were subsequently etched to expose selected regions of the gate elec- trodes. Finally, source and drain electrodes, along with interconnects, were patterned and metallized with an additional 8 nm chromium and 50 nm gold layer via electron-beam evaporation. The indium oxide thin-file film transistor 405 nm laser illumination, oxygen vacancies in the channel layer were photoionized, generating free electrons and thereby enhancing the channel conductivity.
characterized under gate bias of 0 V and drain bias of 5 m.V. Upon
500
Gate
Drain
Source
(a) Optical microscope
(b) Otters under optical microscope
Figure 5: Details design of Otters
Regarding integration with state-of-the-as art digital hardware, recent studies show that InşO3 TFTs are compatible with 3D stacking on CMOS chips. This is because they have low thermal budget (S 300 *C) and good uniformity (Tang et al. (022). This provides a practical path for vertical integration. However, several challenges remain, such as managing wire density in stacked layers, aligning the photodetectors/TFF layers with metal layers, and handling device variability large arrays.
A.2 PROOF FOR PROPOSITION
A.2.1 INTEGRATION PIASE EQUIVALENCE
The foundation of the proof lies in the relationship between the QNN's discrete value and the SNN's spike time. From Section 3.3 know that the QNN output activation from the previous layer is [-1
9.6 a 1-1 o. where 9, is the integer value:
1-1
d Clip Clip
O,
We define the TTFS encoding scheme such that this integer value of is represented by single spike from neuron at the discrete time step k:
k 13
1-1
(10)
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This encoding adheres to the TTFS principle: a larger integer value of results in smaller time step k signifying an earlier spike. A value of corresponds to no spike within the active window, and the maximum value T corresponds to spike at k = 0.
When a presynaptic neuron fires at time step k, its contribution to the postsynaptic potential of neuron j is given by the Otters PSP function, c'(.). Using the conditions specified in Proposition 1, the normalized value produced by the decay function (tt) at time step ty. is:
O(tx) = T
(11)
T
Substituting the encoding relationship from Step =
qi 1):
((++) T - (T 1-1
4 1-1
(12)
T
T
Thus find that the normalized output of the physical decay process the spike time is directly proportional the integer value q it is meant encode.
The full PSP contribution from the synapse connecting to is the product of this normalized value and the scaling factor vly. Using the definition of from Proposition 1:
7/ w a T
(13)
The PSP is therefore:
(x) 1//- .((x)
9, J-1
= -ulj .1-1.T)
T
(14)
T
= w (at 11
Recognizing that g. al -- we find:
e'(wly, (x) = why 1-1 9,a
(15)
This shows that the contribution of a single spike in the SNN is exactly equal to the weighted input term in the QNN.
The final membrane potential V is the sum of all such PSPs from incoming spikes, plus the bias term:
Vj Σ e'(wyg ( + bJ E(uly ) +b
(16)
By comparing this with the definition of the QNN pre-activation from Section 1.2,
d = Σ wly +b2
(17)
we arrive at the desired equality:
V o
(18)
A.2.2 FIRING PHASE EQUIVALENCE,
In this section, prove that the integer value encoded by the SNN's output spike time, U is equal to the integer value of the QNN's output, of. That is, if oi spike,j corresponds to time step knne
we have:
a. a
T kire of = Clip
,,
(19)
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According to the SNN model definition, the neuron fires at the earliest discrete time step &s for which its potential V meets or exceeds the threshold 0 (tx).
V (tx)
(20)
Substituting the result from Part I (V) = d)) and the definition of the time-varying threshold from Proposition (0' (1x) = a² (7 k))); the firing condition becomes:
df 2 a' (T k)
(21)
Assuming a' > 0, we can rearrange the inequality to solve for the term (T - k), which represents the integer value that would be encoded by a spike at time step k:
d a
T
(22)
The threshold (tx, aT - k)) is monotonically decreasing function of the time step k. For fixed membrane potential aj. this means that if the firing condition is met for a certain time step k", it will also be met for all subsequent time steps k" The TTFS firing rule dictates that the neuron fires at the first time step that satisfies the condition. This corresponds to finding the smallest integer k that satisfies the inequality (largest T ). By the definition of the floor function, the integer value encoded by the output spike, which is defined by our encoding scheme as Youi, = T knne is:
a a
of =
(23)
The derivation above assumes the result of the floor function falls within the valid range of encodable integers. We now analyze the boundary conditions imposed by the finite simulation window.
Upper Bound (Clipping at T) If the pre-activation a' is very large such that [a5/aa|] > T, the condition /t//a' > T - k will be satisfied for all k E T. The neuron will fire at the earliest possible time step, which is = O. The value encoded by a spike at k = is T - 0 = T. This naturally implements the upper bound of the clipping function, mapping any integer value greater than T to T.
Lower Bound (Clipping at 0). If the pre-activation a' is such that [a//a'] 0, then the term a/ aa' is negative. Thus, the firing condition a.//a 2 T k can never be satisfied. The neuron will not fire within the time window. The absence of spike is interpreted as encoding the integer value 0. This naturally implements the lower bound of the clipping function.
Combining these cases, the integer value encoded by the SNN's firing mechanism, Vout,3 is:
Lout,
Clip
0,T
(24)
This is identical to the definition of the QNN's integer output, d/.
A.3
ENERGY ANALYSIS
A.3.1 ENERGY COMPARISON WITH RELATED WORKS
For the energy calculation in Table 2, did not use the numbers reported in the original papers. Since energy depends heavily on batch size and sequence length, a direct comparison is often unfair. Furthermore, most related work does not account for hardware overhead, which dominates the total energy. Therefore, we re-calculated their energy to ensure a fair comparison. We assumed the same model size, batch size, sequence length and weight quantization level for all works.
For transformer baselines, the energy consumption of full precision BERT (FP32) is dominated by expensive 32- multiply-accumulan (MAC) operations and data movement, We also compared
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it to quantized BERT (INT4), which uses the architectural settings Otter, including 1-bit weight, 4-bit activations and 1-bit Key-Value (KV) cache.
For SNNs, used the energy equations built for them, which depend the spike rate (s,) and the number of timesteps (2)) To match Otters' performance, we selected the most optimized settings for the baselines (Sorbet, SpikingBERT, and SpikingLMM) This resulted in spike rates of 13% for Sorbet, 25% for SPiKingBERT,, and 33% for SpikingLM. We used the timestep values (T) directly from their original papers: 16, 16, and respectively.
Full BERT (FP32)
EFC = S. Co (7- C. (EMAC + ERend + 32 Em + C₁- Eicakage + 2 Eelamp + Exgele (25)
EFc- sccore = h. S (dy
y ( (Ekr + +EMAC + 32 Empore + dx Ereakage + 2 Eclampp
(26)
Quantized BERT
EFC, B.S-C. - (7-CC, (FMac Feweight +log2 (T+1) Move ) Ci Fieekage + +2 E.wrle
(27)
EFC,-son = B-h 1-hh-S 52 (d +lgg
Enoee - +. Erenkage + Exelump) (28)
Typical SNNs
+ ESNN.FC BB-.Co-(CC-8., T.AcCC Beed + Eaporrs
) C.TT -.TTT-eeaageee +T TT (ECMP+ + ESUR Egy Write)
(29)
ESNN-scoe B-h- s, s. T. EACC E + -T TEeakage + (ECMP -ESBB)
Rend
(30)
Otters
FO B.
C T. (or (Frace +
ReRad AAnalog
Exppare
Outpuis
Spike Processing
(31)
Fieekage)
T (ECMP
F Read (hreshold
Write F binuryky
Thresholding
K/V Write
( (de .T T (sp -EscC +
Eopto-score = B- BB
Rend Analog
Expore +
Read binaryky)
Total Scores
Spike Processing
(32)
Freakage)
T (FEMP +
Read Frthresoold
Thresholding
Key differences between Otters and other typical SNNs include replacing digital weight reads with lower-energy analog reads from the TFT (Eaeau Analog) and, for the QKV calculation, using an energy- efficient binary KV read (FRead (mmaayyy)) The energy model is configured for a BERT-base architecture with a batch size (B) of 64, a sequence length (S) of 128, and input/output channel dimensions (C,, C.) of 768. The model features 12 attention heads (h), with per-head dimension (d&) of 64. Energy costs are derived from established models. For FP32 operations, we assume that a multiply-accumulate (MAC) consumes 4.6 pJ and clamp operation consumes 0.9 pJ which is from (Horowitz 2014) cause our platform doesn't it support FP calculations. For our INT4 models, we differentiate between 4-4-16bits MAC (0.0848 pJ) and a 1-4-16bits MAC (0.0663 pJ). The costs for 4-16-16bins 16biss 2-16- 16bis and 1-16-16bits ACC are 0.0502 pJ. 0.0477 pJ and 0.0429 pJ, respectively. SNN-specific operations, such as comparison and subtraction, are each modeled at 0.0502 pJ. The total energy for an analog read operation is 0.0246 pJ (0.00875p) for power the TFT, 1.33e-6pJ for sampling, 0.0053pJ for ADC including the amplifier and 0.010505 for the 4bits LUT). The model accounts for static leakage energy Eleaugee of 0.002 pJ per cycle, weight activation (read/write) cost of 0.0985 pJ/bit, and a sparse data movement cost of 0.18 pJ per bit. All integer compute, data movement, and memory access costs based measurements from commercial 22mm process, while the floating floating-point point compute energy (Horowitz) 2014) and ADC values (Su et al. 2023) taken from existing literature.
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A.3.2 DETAILED ENERGY BREAKDOWN
Table 3 and Figure 6 detail the energy breakdown of Otters-lbitkv. Spike movement is the main energy consumer, accounting for approximately 55% of the total. The next largest contributor is membrane potential accumulation (Mem. ACC), while K/V read/write (K/V R/W) consumes the least energy.
Table 5: Energy breakdown of the Otters self-attention block (in mJ), "Mem. membrane-potential accumulation; "K/V R/W" denotes key/value read/write.
ACC" denotes
Compute
Data movement
Block
Read analog
Leakage
Total
Mem. ACC
Thresh.
Spike movement
K/V R/W
Opto-FC
0.5611
0.1257
2.0117
0,0012
0.2744 0.0305
0.4349
3,4091
Opto-qkv
0.0623
0.1676
0.2235
0,1223
0.0483
0.6546
Total
0.6235
0.2933
2.2352
0.1235
0.3049
0.4832
4.0637
7.5%
Spicz Movement
Menthrase Potentia (15
11.9%
(1.9%,044 0.4 mi)
55.0%
(3.5% 0.30 al)
Thouhslding (7,7%, 0.79 mu)
Wente (30% 8.12 au))
15.3%
Figure 6: Proportional Energy Breakdown of Otters-1bitke
A.3.3 ABLATION STUDY OF SOFTMAX AND LAYER NORMALIZATION
We initially omitted Softmax and Layer Normalization from energy analysis, their consump- tion negligible compared to the matrix multiplication operations. In this section, we present an ablation study that accounts for these operations. We adopt the energy models from Sorbet (Tang et al. 2025). which define the costs for Softmax as ((d) ACC, O(d) division, and ((d) exponential operations. The same model defines LayerNorm costs O(5d) ACC. O(3d) MAC, (d) division. and ((1) exponential operations. We calculated the total energy for one complete transformer block in Figure including QKV projections, attention score calculations, the attention output projection, Softmax, Layer Normalization, and the feedforward layers (intermediate size of 3072). The results show that Softmax and LayerNorm account for only 0.32% of the energy in the Otters block. Also, Otters remains the most efficient method compared to related works.
A.3.4 ABLATION STUDY OF USING OTTERS AND TRADITIONAL TTFS METHODS
We can group TTFS encoding into two main classes: continuous TTFS and quantized-timg TTFS. In other work, like TTFSFormer (Zhao al. 2025). the time domain is continuous. This means they pass the time-to-first-ppiee between layers using floating-pons (FP32) values. This high- precision FP32 number helps keep the SNN accurate after the ANN-SNN conversion. However, comparing the energy of these continuous-time methods with our approach, which uses quantized time, is not fair. In TTFSFormer, their main math unit (e.g., the accumulator, ACC) is FP32 and costs about 0.9 pJ per operation, while our INT4 ACC only costs 0.05 pJ. Also, the data movement cost grows with bittwidth. This means continuous time TTES designs use much more memory and movement energy than low-bit designs.
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Energy Consumption (mJ))
60
40.85
42.04
40
14.21
Quanlized BERT
SpiingBERT
Sorbet
SpikingLM
Ofters (Ours)
Madel
Figure 7: Energy Consumption per Transformer Block with softmax and layerNorm.
To make fair comparison, we re-evaluated the continuous-ting TTFS method in the same quantized time domain Otters. We did this by quantizing the spike times while keeping the weights, network structure, and all other hyperparameters the same. This lets us clearly see the benefit of Otters' analog-basee -baoo computing. Traditional quantized-tinn -imm TTFS requires digital encoding, additional MAC operations (Eencoding + EMAC), and extra weight accesses. With T=15 using the simplest --t encoding (4---4-bit ACC, 0.0163 pJ), traditional TTFS attention block consumes 5. 12 mJ, 26. 1% more energy than 1bit Otters.
A.4 FORWARD PROCESS OF OTTERS
The forward process is shown in Algorithm
Algorithm Otters Neuron Forward Pass (TTFS)
1: Inputs: Presynaptic spikes (t)) weights {nty Nin. bias 6'; threshold function ('(;;;
total time steps T.
2: Output: Postsynaptic spike train (s)()))
3: Vi + b/ (Initialize membrane potential with bias}
4: : + (Initialize output spike train to zeros] false
5: has-fired
6: fort= 10t==12,.... 1,2 T do
7: for 1,2, .., Nin do
8:
if (t))
(t) then
9:
Vi M O(t) (Compute PSP using the physical decay function (
10:
V; V, U2 (Aceumulate potential}
11:
end if
12:
end for
13:
if Vi 2 (t( and not has fi red then
14:
(t) + FFire a spike at the current time step)
15:
has iis_fired- true
16:
break (TTFS constraint: emit at most one spike and stop)
17:
end if
18:
end for
return s)
A.5 QNN TRAINING ALGORITHM
To mitigate the accuracy degradation from quantization, we employ a knowledge distillation (KD)
framework for quantization-aware training (Liu al. 2022 Tang al. 2025). This approach
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Table Task-specific training hyperparameters.
Task
Max. Seq. Length
Batch Size
Learning Rate
MNLI
128
80
2 x
MRPC
128
80
5 x 10-5
SST-2
64
80
1 10
STS-B
128
80
x 10-5
QQP
128
80
2 10-5
QNLI
128
80
2 10-4
RTE
128
80
5 X 10-6
transfers inductive biases from a pre-trained, full-precision teacher model the quantized student network. Our training objective is hybrid loss function that aligns both the output distributions and the intermediate representations of the student with those of the teacher. The total distillation
loss LTD is a weighted combination of two components: logits distillation loss Logiis and representation distillation loss Tepps
LKD Ligits ALreps
(33)
where À is hyperparameter that balances the two terms.
The first component, Logits is the Kullback-Leible (KL) divergence between the teacher's soft target distribution and the student's output distribution This loss encourages the student to learn the teacher's s predictions and understanding of inter-class similarities.
Logits (L(pl)9)
(34)
The second component, /reps- minimizes the Mean Squared Error (MSE) between the intermediate feature representations from corresponding transformer blocks of the teacher (r() and the student (r?). This forces the student to mimic the teacher's ' internal representation structure.
Lreps Σ || 1
(35)
The student model trained end-to-end by minimizing LKD using the Adam optimizer, while the teacher model's weights remain frozen. We use task-specific hyperparameters for training, which are detailed in T All models are trained on A100 GPUs.
A.6 EVALUATION BENCHMARK
We evaluated our model, Otters, on seven datasets from the GLUE benchmark:
MNLI (Multi-Genre Natural Language Inference): A large-scale, crowdsoureed collection of sentence pairs annotated for textual entailment across multiple genres.
QQP (Quora Question Pairs): A paraphrase identification task to determine if two questions from Quora are semantically equivalent.
QNLI (Question-Answeringg NLJ): A natural language inference task converted from the Stanford Question Answering Dataset (SQuAD), where the goal is natural language infer- ence
SST-2 (Stanford Sentiment Treebank); A single-sentence classification task for sentiment analysis (positive negative) on movie reviews.
STS-B (Semantic Textual Similarity Benchmark): regression task to predict the degree of similarity (on 1-5 scale) between sentence pairs drawn from news headlines, video titles, and image captions.
RTE (Recognizing Textual Entailment): A compilation of data from several textual entail- ment challenges, using text from news articles and Wikipedia.
MRPC (Microsoft Research Paraphrase Corpus): paraphrase detection task using sen- tence pairs from online news sources. The dataset is imbalanced, with 68% of pairs being paraphrases.
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A.7 INFERENCE TIME ANALYSIS
In Otters. the inference latency is mainly determined by the duration of the optical decay function (Figure 2b in the revised manuscript). Within this time window, the SNN neuron compares its accumulated membrane potential with the dynamic threshold at each time step 44. If the membrane potential is larger than the threshold, the neuron fires. It then samples the value from the thin-film transistor and adds it to the next neuron's membrane potential. Once the decay period finishes, the next layer ready to start. Thus, in theory, the computation for one layer is completed within a single time window. Taking transformer block optical cycles: 6 cycles for the Self-Attention module (projections of Q, K, V, their multiplication and output) and 2 cycles for the Feedforward module.
example, the calculation requires roughly 8
In our current measurements, the transient optoelectronic response was recorded using a source- measure unit (SMU), whose minimum integration time is the order of tens of microseconds. To ensure a window that can reliably acquire complete attenuation and fit parameters, we used a conservative sampling configuration, which resulted in a coding window of about 100 jas. This results in a total latency of 0.8 ms for one block. Further, in theory, the window can be compressed by faster readout and higher light intensity.
A.8 ACCURACY GAP ANALYSIS
In this section, we show an analysis to separate the two sources of accuracy loss: the Quantization step (Full BERT to QNN) and the Otters implementation step (QNN Otters). As the Table7 the main drop in accuracy occurs during the first step which is the expected performance loss from quantizing the model's 's weights and activations. We then measured second, much smaller accuracy drop when converting from the QNN to our Otters SNN. The average drop is 0.59%, which mainly comes from sampling errors (the exact physical time E needed for value O(ts) might fall between two sampling points, causing a representation error). We believe this small accuracy trade-off is highly favorable, as the Otters implementation achieves this performance while consuming only 36.8% of the QNN energy.
Table 7: Accuracy gap analysis on the GLUE benchmark, where all scores are accuracy except for STS-B (Pearson correlation).
Model
QQP
MNLI-m
SST-2
QNLI
RTE
MRPC
STS-B
Avg
Full BERT
91.3
84.7
93.3
91.7
72.6
88.2
89.4
87.31
QNN
87.81
78.40
91.28
86.80
70.03
86.51
85.87
83.81
Otters
87.67
78.50
91.28
86.42
68.95
84.56
85.19
83.22
A.9 GENERALIZABILITY OF OTTERS
Otters is proposed to optimize the temporal decay function and its subsequent multiplication by sampling the natural decay of an oxide optoelectronic synapse. In other words, Otters provides an analog alternative to digital matrix multiplication, which is basic and commonly used unit in most models. Therefore, Otters has the potential be applied most network structures (or least optimize parts of them) since it is optimization for base units. In Table we provide VGG/ResNet on CIFAR-10 with different time window size as an example to demonstrate the generalizability.
Table 8: Top-1 accuracy (%) of SNNs converted from ResNet18 and VGG16 across different time steps The time steps T 2n (for n 2,3, 4, 5) are selected based on the n-bit QNN conversion discussed in Proposition 1.
Time steps T
Model
3
7
15
31
Nestr1
89.27
89.31
92.02
92.05
OGGel--VGG16
87.38
89.42
91.62
91.49
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A.10 1-BIT KV ENERGY ABLATION STUDY
In this section, we recalculate the energy of other SNN methods, assuming all K/V projections are quantized 1-bit for fair comparison with our Otters-Ibitky model. The spike rates and time window sizes are set to be consistent with those in Appendix A.3.1. As shown in Table Otters still achieves the best energy efficiency within this 1-bit KV setting,
Table 9: Energy consumption analysis on the SST-2 dataset. The Energy Ratio is Energy(Otters) / Energy(Model).
Model
FC (mJJ
QKV (mnJ
Total (mJ)
Energy Ratio
Sorbet (1bit kv) (Tang et al. 2025
3.39
0.58
11.32
2.79x
SpikingBERT (1 (V Sehgupta. 2024
6.37
1.07
21.27
5.24x
SpikingLM (1bit (ing et 20248
2.09
0.35
6.97
1.72x
Otters (lbit kv)
1.14
0.33
4,06
1x
A.11 QNN-TO-SNN CONVERSION DISCUSSION
Direct training of SNNs is challenging because the binary spike activation is non-differentiable. Instead of using approximate gradients, QNN-to-SNN conversion trains a functionally equivalent QNN first and transfers the weights the SNN. This approach often yields higher accuracy for deep networks. Many related works have implemented this. For example, in language tasks, Sor- bet achieves 79.80% accuracy on GLUE using an average spike generation method (Tang et al., 2025]; for vision tasks, Wang et al. reach 85.31% % on ImageNet using a Multi-basis Exponential Decay (MBE) neuron (Wang al. 2025a). Liu et (Liu Liu 2018) propose quantization aware DNNs using neuron convergence and weight clustering, and deploy the resulting 4-bit networks on memristor-based Spiking neuromorphic computing systems, achieving 90.33% for CIFAR-10. Be- yond these, Ajay et al. (Ajay et al. 2024) introduce MC-QDSNN, quantized deep evolutionary SNN that uses Multi-Compartmenn Leaky (MCLeaky) neurons for hetter and more efficient model- ing of time-series data. However, most prior works rely rate encoding and do not target optical hardware. contrast, Otters focuses on TTFS-based SNNs using optical spiking neurons. To adapt QNNs to our InzO, devices, we propose specific conversion techniques, including dynamic thresh- olding and mapping quantization bits to the natural decay. This allows us to replace expensive digital matrix multiplication with energy energy-efficient analog sampling.
A.12 THE USE OF LARGE LANGUAGE MODELS
We use LLMs to aid or polish writing.
23


Reviews:
[{"review_id": "4eLj6m3jbK", "reviewer": "Reviewer_8Ccw", "summary": "This paper propose to transform the intrinsic “signal decay” of optoelectronic synapses into a computational resource, thereby achieving TTFS coding in SNNs with extremely low energy consumption. Specifically, it uses the physical decay curve of customized indium oxide transistors to replace digital computation, and then proposes a novel QNN-to-SNN conversion algorithm that maps a trained quantized Transformer into an equivalent spiking network. Finally, this paper adds 1-bit KV projection to further reduce energy consumption.", "questions": "check the weakness", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1. It proposes a new “physical computation” paradigm that achieves in-memory computation by integrating synaptic weight multiplication and temporal decay into a single optoelectronic physical process, thereby improving energy efficiency from the ground up.\n\n2. It achieves the highest accuracy among SNNs on the GLUE benchmark and demonstrates a 1.77x energy-efficiency improvement over the previous SOTA model, which validate the effectiveness of the proposed framework.", "weaknesses": "1. Since the paper’s contributions involve algorithm–hardware co-design, it should provide a more detailed breakdown of energy consumption to clarify the contribution of each component, such as $(E_{\\text{analog}})$.\n\n2. The results are presented only for the BERT-Base model, which raises concerns about the generalizability of the proposed method.\n\n3. For a fairer comparison, the paper should include both performance and energy consumption results of other models with 1-bit KV to more clearly demonstrate the energy savings achieved by the new hardware paradigm.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "AkAaSrctRu", "reviewer": "Reviewer_CymU", "summary": "This paper introduces a hardware–software co-design framework named Otters, which leverages the natural signal decay in indium oxide optoelectronic transistors to physically implement TTFS computation. By interpreting the analog output as a fused representation of synaptic weight and temporal decay, the system eliminates costly digital multiplications. Furthermore, the authors propose a QNN-to-SNN conversion algorithm, integrating it into Transformer architectures. Experimental results on the GLUE benchmark demonstrate SOTA accuracy and a 1.77× improvement in energy efficiency compared to previous SNNs, validated through comprehensive measurements on a 22nm commercial process.", "questions": "1. The reported energy analysis omits Softmax operation and Layer Normalization [3], both essential operations in Transformer computation. Incorporating these operations would provide a more comprehensive and realistic assessment of the total energy consumption.\n\n2. Since the paper emphasizes energy efficiency, providing inference latency results is necessary to validate the method’s real-time performance and practicality. \n\n3. It remains unclear whether the proposed Otters-based TTFS framework generalizes to other datasets or CNN-based architectures. Demonstrating such experiments would enhance the paper’s impact and generality. \n\n[3] Spatio-temporal approximation: A training-free snn conversion for transformers. ICLR 2025.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 1, "contribution": 2, "strengths": "1. This paper presents a novel physical computing paradigm that leverages the inherent signal decay of optoelectronic devices as the temporal decay mechanism for TTFS computation, thereby eliminating the need for energy-intensive digital multiplications.\n\n2. It introduces a theoretically grounded QNN-to-SNN conversion framework, establishing the functional equivalence between quantized neural representations and spike-based computation, which is significant for bridging conventional deep learning and neuromorphic systems.\n\n3. The proposed Otters architecture, validated through a hardware–software co-design, achieves state-of-the-art performance on GLUE and demonstrates energy efficiency advantages.", "weaknesses": "1. The experimental evaluation is limited to Transformer architectures, which are not the primary application domain for SNNs. Since SNNs are particularly suited for edge computing and low-power vision tasks, extending the analysis or providing validation on CNN-based models [1] would substantially strengthen the work.\n\n2. The proposed QNN–SNN mapping depends on a pre-trained quantized model, which introduces additional training overhead. The authors should clarify whether this preprocessing step yields tangible performance benefits and discuss whether the Otters framework provides practical deployment advantages over conventional QNNs on real hardware.\n\n3. The experimental comparison is limited. Including results against other TTFS-based conversion methods [2] would better substantiate the claimed efficiency gains.\n\n4. The mathematical expressions lack consistency in formatting and punctuation. All equations should be standardized, properly numbered, and punctuated to ensure clarity and formal correctness.\n\n[1] Deep residual learning for image recognition. CVPR 2016.\n\n[2] TTFSFormer: A TTFS-based Lossless Conversion of Spiking Transformer. ICML 2025.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "VmZuc52bA8", "reviewer": "Reviewer_Ei9k", "summary": "This paper proposes to use opto-electrical neurons for low-power SNN acceleration using time to first spike encoding that naturally aligns with the opto electrical neuron's characteristics.  The energy analysis and accuracy analysis is quite reasonable.  The conversion approach and quantization techniques as well as the noise-aware training all appear well explained and reasonable.", "questions": "Please see weaknesses. \n\nI also heard of other SOTA SNNs such as QKFormer. Can you comment on how this work relates to yours? See https://arxiv.org/abs/2403.16552.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "I think the novelty of the approach and the write-up and analysis are solid. Well explained paper and concept.  I was very happy to see the energy analysis use estimates from Horowitz which are realistic and capture the cost of ADCs and data movement.", "weaknesses": "It seems the opt-electrical device is not small compared to a digital SNN accumulator.  It seems to me that the scale of the hardware may be the biggest challenge in making such an approach practical and yet there seems to be no description of this challenge in the paper, even in the future work. \n\nI think even for a conference like ICLR and perhaps especially for a conference like ICLR where the audience may not realize the fundamental difference in hardware scale, this should be mentioned and scaling efforts for this technology should be at least outlined.  Otherwise, this is yet another pipedream in the field of energy-efficient SNN hardware. More specifically, how many such devices might be needed to have the same order of magnitude in compute latency and what, with current technology, would the size of such a chip be.  What are the challenges of heterogeneously integrating such devices with SOTA digital hardware?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "jddxnwvf5Y", "reviewer": "Reviewer_AM8c", "summary": "This submission implements spiking neural networks (SNNs) on optoelectronic devices to mitigate the high computational cost associated with evaluating temporal decay functions and their subsequent multiplications with synaptic weights. Specifically, the authors fabricate a custom indium oxide–based optoelectronic synapse capable of directly realizing the required temporal function. Furthermore, they introduce a quantized neural network–to–SNN conversion algorithm to enhance the efficiency and practicality of the proposed system.", "questions": "1. Since the experiments are conducted through simulation rather than on real optoelectronic hardware, it remains unclear how much of the performance degradation shown in Table 1 originates from the Otters implementation itself, as opposed to the quantization step during the QNN-to-SNN conversion. A clearer analysis quantifying the accuracy gap relative to standard BERT, after isolating the impact of quantization, would help clarify the true effect of the proposed Otters mechanism on model accuracy.\n\n\n2. Can you provide the reference to the cost computation functions in A 3.1. Without proper references, these cost formulations appear insufficiently justified, as they seem to assume idealized conditions rather than reflecting the complexities of realistic hardware environments.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "The work elegantly bridges neuromorphic hardware and algorithmic innovation by exploiting the intrinsic physical decay of optoelectronic devices to implement TTFS encoding. This approach offers a conceptually novel solution to the costly digital decay function in TTFS.\n\nThe authors provide a rigorous and realistic energy model covering compute, data movement, and analog operation costs, grounded in commercial 22nm process measurements.\n\nThe paper contributes a tangible step toward neuromorphic computation for language models, merging physical device dynamics with algorithmic efficiency, an area of high impact given the growing energy concerns of LLMs.", "weaknesses": "**i**. While the concept is elegant, it remains unclear how scalable the proposed In₂O₃ optoelectronic synapses are for large-scale deployment or integration into full neuromorphic hardware systems. For instance, what is the device size of otters for BERT?\n\n**ii**. The transition from quantized neural networks (QNNs) to spiking neural networks (SNNs) is not a new research question, as several prior works have explored QNN-to-SNN conversion frameworks. However, this submission does not provide a sufficient comparative analysis with existing methods, like [1][2]. A more detailed discussion is needed to highlight the unique technical contributions, methodological distinctions, and advantages of the proposed conversion algorithm over established approaches. \n\n**iii**. The experiments are conducted only using BERT as the base architecture. It remains unclear whether the proposed Otters framework can generalize to other Transformer variants or model families.\n\n**iv**. The reported energy savings appear to stem primarily from quantization effects rather than the proposed optoelectronic TTFS mechanism itself. In particular, the ablation study compares a 4-bit SNN with a 1-bit Otters, which inherently favors the latter due to lower bit precision. This comparison seems unfair and may overstate the true contribution of the proposed hardware-software co-design. A more controlled comparison at equal bit-widths would provide a clearer and more convincing evaluation of Otters’ energy efficiency.\n\n[1] Liu, Fuqiang, and Chenchen Liu. \"Towards accurate and high-speed spiking neuromorphic systems with data quantization-aware deep networks.\" Proceedings of the 55th Annual Design Automation Conference. 2018.\n\n[2] Ajay, B. S., and Madhav Rao. \"MC-QDSNN: Quantized Deep evolutionary SNN with Multi-Dendritic Compartment Neurons for Stress Detection using Physiological Signals.\" IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (2024).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "XuKdJqW4OB", "reviewer": "Reviewer_YQwJ", "summary": "The paper presents an interesting hardware-software co-design for ultra-low-energy Spiking Neural Networks (SNNs). The core innovation is the OTTERS optoelectronic synapse, which repurposes the natural signal decay of a custom-fabricated Indium Oxide (In2O3) thin-film transistor (TFT) to physically implement the temporal decay function required by Time-to-First-Spike (TTFS) encoding. This strategy eliminates the costly digital computation that has plagued traditional TTFS approaches.", "questions": "In the energy estimations, which terms dominate (analog read, ADC, spike movement, threshold reads, K/V write)? Provide a breakdown per term with uncertainties and explicitly list all constants used and their sources.\n\nIn the baseline comparisons, clarify experimental protocol and, where feasible, re-evaluate key baselines under the same measurement assumptions or provide scripts to reproduce the energy comparison.\n\nMinor:\n- In Table 2, for the last column Energy Ratio, I suggest using an upward arrow (or statement in the caption) to clearly indicate that the higher is better.\n\n- Please add the date for the ICML paper of Xing et al. line 588 (2024), and clarify which paper by Xingrun Xing is referred to by \"Xing et al.\" since you cite two papers in the same year with same first author.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Repurposing the natural decay of a fabricated In2O3 optoelectronic TFT to implement TTFS temporal decay is original and elegant, it turns a device “bug” into a computational primitive.\n\nPractical engineering choices are well motivated to avoid run-time multiplications and to exploit sparsity in TTFS.\n\nThe work is novel, impactful, and supported by extensive experiments and a rigorous analytical model.", "weaknesses": "The energy numbers rely on an analytical model mixing measured device values (ADC, TFT) with literature energy numbers for ACC/NoC/etc. However, the headline claims (Otters 4.06 mJ per attention block, etc.) would require clearer provenance.\n\nTable 1 and Table 2 compare to SNN and QNN baselines, but it is unclear whether baselines were re-run (or taken from the original work) with identical data preprocessing, same batch length/sequence length, or whether SOP/spike rates were taken from original papers.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)