Antiferroelectric polarization enabling physical activation in CuBiP_2Se_6 for medical image processing

Domain: biology
Published: 2026-04-03
Editorial outcome: major_revision

Abstract
Antiferroelectric materials, featuring field controllable antipolar ordering and reversible polarization switching, offer a promising platform for hardware efficient neuromorphic computing. The tunable polarization dynamics and layered van der Waals structure enable the multifunctional integration of sensing, learning, and computation within a single device architecture. Here, we demonstrate an antiferroelectric polarization driven diode exhibiting an extended linear operating region, which simultaneously enables physical activation and computing-in-memory. Building on the device capability, we construct an in-sensor computing system that achieves over 95% accuracy in medical image classification. We further integrate the devices to demonstrate a hardware-based activation function, attaining accuracy and training loss comparable to an ideal activation function. To enhance adaptability, we further propose a tunable activation circuit that enables linear modulation of the reverse bias slope via gain control. Overall, this work establishes a dual-functional antiferroelectric heterojunction, highlighting its strong potential for constructing optically triggered, compact, and low-power perception–computation-integrated neuromorphic systems for medical image processing.

Introduction
Against the backdrop of rapid advances in artificial intelligence, deep learning has emerged as a core technology and has been extensively applied across diverse fields, including autonomous driving1, 2, 3, 4, computer vision5, 6, 7, and natural language processing8, 9, 10, 11. With the continuous evolution of visual models12, 13, 14, large language models15, 16, multimodal large language models17, 18, 19, deep neural networks are reshaping human society at an unprecedented scale and complexity. However, conventional von Neumann architectures20, 21, 22, which physically separate memory and computation, suffer from increasingly high energy consumption and latency 22, 23, 24. As indispensable components in deep neural networks,25 activation functions further exacerbate the burden of data processing and data transfer26, intensifying the computational and communication overhead between computing and memory units.

Antiferroelectric materials, distinguished by their reversible antipolar ordering and tunable phase transitions, provide a materials-based route toward adaptive computing paradigms. Their field responsive polarization behavior enables efficient in-memory processing, thereby overcoming the inherent data transfer bottlenecks of von Neumann architectures. In contrast to conventional ferroelectrics, antiferroelectric materials exhibit reversible and energy-efficient polarization switching, supporting repeatedly executable analog computing operations27, 28. These properties naturally map onto the continuous and plastic behaviors required for synaptic weight modulation in neuromorphic systems. Moreover, their layered van der Waals structure facilitates scalable integration with 2D semiconductors, enabling the synergistic realization of sensory perception, synaptic plasticity, and in-memory computing within a unified device framework. Most current implementations of activation functions still rely on external processors for computation29 or CMOS-based activation functions. This decoupling not only increases system complexity but also limits the potential for monolithic, compact, and energy-efficient neuromorphic platforms. This leads to high interconnect energy consumption and necessitates large area analog to digital converters, posing major challenges for hardware efficiency in edge computing systems30, 31. Therefore, achieving seamless integration of activation functionality within memristive devices is a potential solution. In addition to activation function integration, another critical challenge in in-sensor computing lies in maintaining high signal fidelity during large scale data processing, particularly in noisy or resource constrained edge environments. Ultraviolet (UV) light, with its inherently high signal to noise (SNR) ratio, is particularly advantageous for maintaining signal fidelity under such demanding conditions32, which is of paramount importance for ensuring reliable feature extraction and diagnostic accuracy in medical image processing applications addressed in this work. Although few studies have attempted to implement activation functions using CMOS based circuits or hybrid materials33, 34, These solutions often suffer from increased circuit complexity, limited scalability, and incompatibility with emerging material platforms. However, the lack of seamless integration35, 36 between activation and sensing components, prevents true in-situ data processing, thereby undermining the potential of monolithic neuromorphic architectures.

In this study, we present an antiferroelectric heterojunction integrating CuBiP₂Se₆ (CBPS) and MoS₂ that unifies sensing, computation, and activation. The device exhibits an extended linear operating region under forward bias driven by antiferroelectric polarization, together with a finite reverse-bias slope (α ≈ 0.02), resulting in a nonlinear transfer characteristic. This nonlinear mapping, intrinsically generated by the device physics and resembling the commonly used activation functions in neural networks, is defined as physical activation. Under UV stimulation, the heterojunction exhibits synaptic characteristics, enabling its direct implementation in an in-sensor computing architecture where it simultaneously functions as a reservoir and a nonlinear activation unit. This enables an energy-efficient perception–computation pipeline for three dimensional medical image classification, achieving an accuracy over 95%. We further integrate the device into a vision transformer as a physical activation function, attaining accuracy comparable to the ideal activation function while reducing training loss during backpropagation. The designed antiferroelectric polarization enabling physical activation for tunable activation circuit offers task adaptive, circuit level configurability for neuromorphic network design.

Results
2.1. Antiferroelectric Heterojunction Characterization and Electrical Volatile Switching Behavior
To realize a dual functional device, two key criteria must be satisfied, volatile behavior with diode like rectification under electrical stimulation, and synaptic behavior under optical stimulation. CBPS, a two dimensional antiferroelectric material, exhibits rapid polarization recovery and abrupt current switching under bias, making it suitable for fast and volatile electrical operation. In contrast, MoS₂ is a well established 2D semiconductor with excellent photoresponse, capable of generating strong and persistent photocurrents. When integrated into a heterostructure, the resulting CBPS/MoS₂ device exhibits both rapid electrical recovery and prominent optically induced synaptic characteristics, such as light triggered synaptic potentiation and short-term memory behavior. This enables the seamless integration of nonlinear electrical activation and optoelectronic synaptic responses within a single device. Figure 1 illustrates the design of this dual functional heterojunction device, which supports both in-sensor computing and neuron activation, serving as a key element for low -power and highly integrated neuromorphic systems.

Convolutional neural networks require nonlinear activation functions following convolution and weighted summation operations to enhance feature extraction and model expressiveness. However, in conventional architectures, activation functions are typically computed by separate processors, leading to frequent data transfer between sensing and computing units. This results in increased energy consumption and latency, posing a major bottleneck for in-sensor computing systems. Figure 1a presents the envisioned application of the CBPS/MoS₂ heterojunction device within a neural network framework. The device can directly sense optical input and generate photocurrent responses, enabling integrated "sense compute" functionality. Simultaneously, its asymmetric I–V characteristics emulate a LeakyReLU activation function, allowing the device to replace traditional processor based activation units and act as a hardware level physical activation function. An optical micrograph of the fabricated device and a 1×5 array are provided in Figure S1 and S2 (see Supporting Information), showing the heterojunction layout on a SiO₂/p++ Si substrate (with 300 nm SiO₂). To further confirm the thickness of the CBPS/MoS₂ heterostructure, atomic force microscopy (AFM) is performed to examine the topography and profile of the device, as shown in Figure S3. The height profile measured along the path indicated in the inset reveals that the MoS₂ flake has a thickness of approximately 3.8 nm, while the CBPS layer measures around 13.4 nm. The optical absorption of MoS₂ and CBPS is low at small thicknesses and saturates as thickness increases37, 38. Consequently, a moderate thickness is preferred to balance the requirements for high mobility and sufficient absorption. The room temperature polarization-electric hysteresis loop (P-E loop) of CBPS is measured to confirm its antiferroelectric behavior, as presented in Figure 1b. It is observed that an external electric field induces a polarized state in CBPS (also referred to as field induced ferroelectric state). As shown in Figure 1b, when the electric field returns to zero, the remanent polarization is −0.86 μC/cm², indicating that the polarization is close to zero, which is consistent with the spontaneous depolarization behavior characteristic of antiferroelectric materials. By extracting the first derivative of the P-E loop (Figure S4), a pronounced discontinuity is observed at approximately 50 kV cm⁻¹, indicating a rapid polarization switching process occurring at this field. To quantitatively evaluate the loop symmetry, we extract two parameters. The polarization values at +200 kV/cm and −200 kV/cm are +9 μC/cm² and −9 μC/cm², respectively. In addition, the loop areas obtained during forward and reverse scans are 171.04 and 138.36, respectively. We measure the P-E loop hysteresis loops of CBPS at various thicknesses (Figure S5). The loops consistently exhibit antiferroelectric characteristics across all measured thicknesses. To investigate the polarization direction, we perform piezoresponse force microscopy (PFM) measurements. The cyclic PFM amplitude and phase images obtained from multiple cycle PFM measurements with continuous voltage scanning, as shown in Figure S6, reveal significant domain evolution. During a +4 V voltage scan, a clear phase shift appears, indicating the occurrence of domain switching. Transmission electron microscopy (TEM) and energy dispersive spectrometry (EDS) are employed to confirm a clean interface and homogenous elemental distribution of the device. TEM images demonstrate that our fabricated vdW heterojunction has clean interfaces between the 2D materials.

Raman spectroscopy is employed to identify the constituent van der Waals (vdW) nanoflakes, as shown in Figure S7. The Raman spectrum of CBPS exhibits five characteristic peaks located at 111.7 cm⁻¹ (E1g), 135.3 cm⁻¹ (E2g), 207.5 cm⁻¹ (A1g), 431.9 cm⁻¹ (A2g), and 465.9 cm⁻¹ (A3g), which are consistent with previous reports38. Additionally, the frequency difference of 24.5 cm⁻¹ between the E12g (383.3 cm⁻¹) and A1g (407.8 cm⁻¹) modes confirms the multilayer structure of MoS₂39. A detailed schematic of the device structure employed in Figure 1a is presented in Figure 2a. The device consists of vertically stacked p-type antiferroelectric CBPS and n-type two dimensional semiconductor MoS₂, with an in plane electrode configuration. Under DC voltage sweeps from –3 V to 3 V (Figure 1d), the device exhibits a pronounced asymmetric current–voltage (I–V) response, with a sharp increase in current observed under forward bias, while conduction under reverse bias is suppressed. This behavior closely resembles the LeakyReLU activation function, indicating the device’s suitability for hardware level nonlinear activation in neural networks. The inset in Figure 1d presents the linear fitting of the DC I–V curves in both the forward and reverse regions, revealing high linearity. The piecewise-linear function (PWLF) method was employed for the fitting (see Supplementary Note 1). The calculated coefficient of determination (R²) is 0.999, with a normalized root mean square error (NRMSE) of 0.0098, which demonstrates a high degree of linearity. Figures 1e presents the mechanism of the heterostructure under voltage sweeping. The nonlinear behavior arises from the combined action of the built-in electric field and the ferroelectric polarization, which are formed at the interface between n-type MoS₂ and p-type CBPS. In the unbiased state, the dipoles within CBPS are oppositely oriented, leading to mutual cancellation of the overall polarization and thus exhibiting a neutral polarization state. When a forward bias is applied, the external electric field partially compensates the CBPS/MoS built-in field and drives the dipoles to realign along the field direction, resulting in a polarization orientation inside the material. During the reverse voltage sweep, the relaxor antiferroelectric nature of CBPS induces an ordered polarization state, resulting in high conductance. As the voltage is withdrawn, the remnant polarization field rapidly dissipates, accompanied by rapid restoration of antiferroelectric domains, leading to a narrow and volatile memory window under forward bias. In contrast, under reverse bias, the built-in electric field aligns with the external field at the heterointerface impedes Cu-ion migration in CBPS, suppressing the formation of ordered polarization states and consequently erasing the memory notch. This unique volatile behavior exhibited by the heterostructure is particularly suitable for iterative computing applications.

Figure 2 illustrates the nonlinear and volatile electrical conductance behavior of the CBPS/MoS₂ heterojunction device under electrical stimulation, highlighting its potential as a physical activation function. Bidirectional DC voltage sweeps (-3 V to +3 V to -3 V) at different sweeping rates are further performed, as illustrated in the inset of Figure 2b. The results show negligible conductance hysteresis in the reverse sweep, indicating a near zero memory window, while only a very small memory window is observed in the forward direction. These findings confirm the highly volatile nature of the device. Moreover, the memory window of the device shows negligible dependence on the scan rate. Figures 2c to 2f further investigate the device’s conductance dynamics under pulsed electrical stimuli. Figures 2c and 2d demonstrate that, under varying pulse amplitudes (with a fixed pulse width of 100 ms) and varying pulse widths (at a constant 5 V amplitude), the device exhibits a rapid increase in current that quickly saturates, with a read voltage fixed at 0.1 V. The extracted current responses at different pulse amplitudes (inset in Figure 2c) show a consistent linear dependence on the applied voltage, indicating stable and predictable electrical behavior. According to the Shockley diode equation (see Supplementary Note 2), the current exhibits an exponential increase as the applied voltage gradually raised. However, the extracted linear response demonstrates that in CBPS, the polarization-induced electric field counteracts the applied electric field, resulting in a highly linear process with a NRMSE of 0.0722. Subsequently, we tested the device’s response to successive pulsed stimuli. Figure 2e, 2f and S8 show the current response under 1 to 20 electrical pulses with amplitudes of ±3 V and ±5 V. The current reaches a steady state after approximately five pulses and remains stable thereafter, demonstrating the device’s robustness and reliability as a physical activation unit. Inset of Figure 2e shows a magnified view of the region highlighted in red, where the channel conductance trend clearly stabilizes. To evaluate the cycling stability and device uniformity, the cycle-to-cycle and device-to-device variability are presented in Figure S9. The devices exhibit quantitatively similar responses, indicating good uniformity, with a cycle-to-cycle mean standard deviation (STD) of 0.014 and a device-to-device mean STD of 0.023. We apply an electrical pulse with a width of 500 µs and amplitude of 1 V to estimate the energy consumption, yielding an energy consumption per computation event of 95.5 pJ (Figure S10a). We compare the computation time and power consumption of CBPS/MoS with other device based activation functions in Table S1. The results demonstrate that the proposed device achieves superior energy efficiency. Figures 2g and 2h schematically depict the band alignments before and after the formation of the CBPS/MoS₂ heterojunction. Specifically, the work function of MoS₂ is approximately 4.5 eV with an electron affinity of ~4.0 eV and a bandgap of ~1.3 eV40, 41, while CBPS exhibits a larger work function of ~5.26 eV and a bandgap of ~1.27 eV38. A type-II band alignment is established, with the built-in electric field oriented from CBPS to MoS₂. This built-in field, in combination with an external bias, modulates the depletion region width, thereby controlling the turn on and turn off states of the channel, which explains the observed asymmetric I–V characteristics and supports the emulation of an activation function like behavior. Under forward bias (Figure 2i), the depletion width narrows and the diffusion current increases, further enhancing the device’s forward conduction. The CBPS/MoS₂ heterojunction exhibits asymmetric I–V characteristics, making it a promising candidate for use as a physical activation function in neuromorphic computing systems, particularly in compact, low-power, in-sensor computing neural nodes.

2.2. Optoelectronic Synaptic Plasticity in CBPS/MoS₂ Heterojunction Devices
To evaluate the potential of the device as a photonic synaptic element for optical in-sensor computing architectures, Figure 3 presents the synaptic behavior of the CBPS/MoS₂ heterojunction device under laser illumination. As shown in Figure 3a, the device generates a photocurrent response upon exposure to pulsed light (365 nm). Figure 3b shows a typical EPSC response to a single 500 ms light pulse (with a constant forward bias of 0.1 V). After the pulse terminates, the current gradually decays, demonstrating short-term plasticity (STP) akin to biological synapses. Figure 3c further investigates the EPSC amplitudes under various power densities. The EPSC amplitude increases with light intensity, indicating high sensitivity to the illumination strength. Figure 3d explores the influence of pulse width (ranging from 1 ms to 50 ms) on EPSC amplitude, showing that longer pulses induce stronger synaptic responses. We employed a 1 ms pulse to estimate the computational energy consumption (Figure S10b). The resulting energy per computation is estimated to be approximately 3.6 pJ. Subsequently, we varied the number of light pulses to evaluate multi pulse responses. Upon applying 5, 10, 20, and 100 stimulation pulses, the corresponding relaxation behaviors were recorded, as shown in Figure S11a. The relaxation time is extracted and fitted using the stretched-exponential function42, which is expressed as,
ϕ(𝑡) = I0∗e−(𝑡/𝜏)𝛽 (1)
Here, ϕ(𝑡) is the relaxation function, τ is the characteristic relaxation time, I0 is the prefactor, and β is the stretch index ranging between 0 and 1. The obtained fitting results are summarized in Figure S12. After a single pulse, the extracted τ is approximately 1 s, indicative of STP. With increasing pulse number, τ increases and reaches nearly 1 minutes at 100 pulses, demonstrating a transition from STP to long-term plasticity (LTP) under repeated stimulation. In Figure S11b, application of 100 successive light pulses leads to a gradual increase in device conductance, confirming the emergence of long-term memory behavior. Figures 3e and 3f validate the self-driven operation of the device under zero bias. Responses are recorded under varying power densities (ranging from 3 mW/cm2 to 15 mW/cm2, Figure 3e) and pulse widths (ranging from 2 ms to 1 s, Figure 3f), confirming stable self-driven current without external bias. The extracted current responses under different UV power densities are plotted in Figure 3g, and fitting to the power-law relation I~kPα yields an exponent of 𝛼 ≈ 0.935 (NRMSE = 0.014), further confirming a highly linear photocurrent response to power density and indicating drift dominated current transport43. To further assess stability, we applied 10 consecutive light pulses, and as shown in Figure S13, the device exhibits consistent photocurrent responses across all pulses, reinforcing its reliability in self-driven mode. Figures 3h and 3i illustrate the carrier transport mechanism of the device under optical illumination. Incident photons are absorbed by the MoS₂ layer, generating electron–hole pairs. These photogenerated carriers are then separated and transported under the combined influence of the built-in electric field at the heterojunction interface and any applied external bias, resulting in a measurable photocurrent. Under forward bias conditions (Figure 3i), carrier injection is enhanced, leading to an increased photoresponse. Even under zero or weak bias (Figure 3h), the built-in field is sufficient to drive carrier separation and transport, enabling self-driven operation through the photovoltaic effect. We also performed a paired pulse facilitation (PPF) test to quantify the short-term synaptic enhancement behavior. As shown in Figure S14a, two consecutive light pulses with a time interval Δt (under a constant bias of –0.1 V) are applied. The second pulse induces a larger EPSC (ΔA₂) compared to the first (ΔA₁), confirming the presence of typical PPF behavior. The PPF index is calculated using the formula PPF = ΔA₂ / ΔA₁ × 100%, quantifying the facilitation effect. The dependence of the PPF index on Δt is summarized in Figure S14b. The data are well fitted using a double exponential decay model,
PPF = C0 +C1e−∆t/τ1 +C2e−∆t/τ2 (2)
Here, the time constants τ₁ and τ₂ correspond to different temporal scales of decay, reflecting the device’s ability to respond across multiple memory timescales. The pronounced synaptic responses observed under optical stimulation indicate that the CBPS/MoS₂ heterojunction device holds strong potential as an optoelectronic synaptic node for integration into in-sensor computing architectures.

2.3. In-Sensor Computing Based on the Dual Functional Device
Employing the dual functional properties of the CBPS/MoS₂ heterojunction device, we experimentally implemented a 4 × 5 letter image recognition task, as illustrated in Supplementary Note 3 and Figure S15. Experimental results demonstrate close agreement with simulation in weight programming, network outputs, and final classification tasks, validating the CBPS/MoS₂-based in-sensor system reliably accomplishes the intended letter recognition tasks. To further extend this validation to a more complex and practical task, we constructed an in-sensor computing system simulation for three-dimensional medical image classification. The overall architecture and performance evaluation of the system are presented in Figure 4. As shown in Figure 4a, the OrganMNIST3D dataset44 is used as the input, which contains 3D CT images of multiple organs and serves as time sequence data. In this study, five organ categories are selected, including liver, heart, left lung, right lung, and spleen (the specific 3D image categories are presented in the Supplementary Video 1). Each 3D image consists of 64 frames with a resolution of 64 × 64 pixels per frame. Each image is fed into the reservoir frame by frame, and features are extracted every four time steps to generate the corresponding feature maps. Figure 4b illustrates the core architecture of the neural network. The 3D image sequence are transformed into a temporal evolution vector, which is then processed by the reservoir acting as the perception unit. The output signals from the reservoir are sampled and fed into a readout layer for classification. In this architecture, the CBPS/MoS₂ device functions as a physical activation function in the readout stage, utilizing its nonlinear I–V characteristics to perform hardware level activation, thereby enabling a fully integrated data flow from acquisition to computation and decision. To visualize the separability of the extracted features, linear discriminant analysis (LDA) is employed to reduce the dimensionality of the reservoir output. As shown in Figure 4c, the resulting 2D projections of the feature points form clearly separable clusters corresponding to different organ classes, indicating the strong discriminative capability of CBPS/MoS₂ based reservoir. Figure 4d shows the test accuracy over training epochs. After approximately 20 epochs, the test accuracy rapidly increases and stabilizes above 95%, while the training loss continues to decrease. This demonstrates that the neuromorphic computing system based on the dual functional device is capable of efficient feature extraction and classification for complex spatiotemporal image sequences. Figure 4e presents the confusion matrix of the classification results, showing that the recognition accuracy for organs such as the liver, heart, lung, and spleen exceeds 97%, with some categories approaching 100%, further validating the robustness and reliability of the proposed system.

2.4. Generalization Capability of the CBPS/MoS₂ Based Activation Function and Circuit Design
To further evaluate the generalizability of the proposed CBPS/MoS₂ heterojunction device as a physical activation function, we embedded it into mainstream neural network architectures by replacing the conventional LeakyReLU function in image classification tasks. As shown in Figure S16, the CBPS/MoS₂ based activation function is integrated into the multilayer perceptron (MLP) modules of the vision transformer architecture, forming a “physical activation layer”. Input images are divided into patches, embedded with positional encodings, and processed through the transformer encoder. Then, the CBPS/MoS₂ device is used to emulate the LeakyReLU activation behavior. Figure S17 shows examples of the eight class BloodMNIST dataset44 used for training, including the following cell types, basophil, eosinophil, erythroblast, immature granulocytes (myelocytes, metamyelocytes and promyelocytes), lymphocyte, monocyte, neutrophil, and platelet (arranged from top-left to bottom-right). Figures 4f and 4g compare the test accuracy and training loss curves obtained using the CBPS/MoS₂ activation function versus the ideal LeakyReLU. In both cases, the models achieved nearly identical convergence rates and final loss values, demonstrating the functional equivalence and training stability of the device based activation function. The classification results are summarized in the confusion matrix shown in Supplementary Figure S18, where diagonal elements represent correct predictions and other elements indicate misclassifications. Figure 4h presents saliency heatmaps of Figure S17 obtained using the Grad-CAM++ method45, which visualizes the regions on which the model focuses during prediction (see Supplementary Note 4). As shown, the model incorporating the CBPS/MoS₂ activation function effectively concentrates on discriminative cellular features, indicating preserved semantic attention capability. To further validate cross task generalization, we applied the CBPS/MoS₂ activation function in vision transformer models trained on multiple diverse datasets, including CIFAR1046, Oxford-IIIT Pets47, and Food10148 (Figure S19a), as well as across various neural network architectures (LeNet49 and fully connected ANN) trained on the same dataset (MNIST, Figure S19b). We summarize the training loss and accuracy of different models and datasets using both the device based activation function and the ideal LeakyReLU in Table S2. The results demonstrate that the device physics-based activation function proposed in this work can closely approximate the performance of the ideal activation function. The detailed architectures of LeNet and the ANN are shown in Figure S20. In all cases, the CBPS/MoS₂ activation function achieved consistently high accuracy and enabled effective loss minimization during backpropagation, confirming its strong nonlinear expressiveness and adaptability across diverse networks and tasks. To account for the impact of device variability, the Gaussian noise with different STD is introduced after the activation in each model, and its effect on classification performance is investigated (Figure S21). Classification accuracy remains robust against an increasing STD values up to 0.1, with no observable performance drop. Since the maximum standard deviation of the experimentally measured cycle-to-cycle variability in this device is only 0.018, we conclude that the intrinsic device variability has a negligible impact on classification accuracy in the demonstrated tasks.

To further enhance the generalizability and task adaptability of the device based activation function, we designed a tunable activation circuit capable of adjusting the negative slope of the response curve. Simulations are conducted using the LTspice platform, and the results are shown in Figure S22-S26. As illustrated in Figure S22, the circuit incorporates a nonlinear activation unit based on the CBPS/MoS₂ heterojunction device as the input element. A multistage operational amplifier structure is employed to form a variable gain path. Under negative input conditions, the circuit allows modulation of the response slope in the negative region by adjusting the feedback resistor network (R₅ and R₆), which controls the overall gain factor (Av). By comparing a reference voltage (Vref) with the input voltage (Vin), a multiplexer is used to select the appropriate output signal, enabling compatibility with neural networks that require different levels of nonlinear sensitivity to negative inputs. To better illustrate the working principle of the tunable activation circuit, Figure S23 presents a logic flow diagram that outlines the signal selection process. The input voltage Vin is continuously compared with a reference voltage Vref. When Vin > Vref, the circuit enables the default amplification path with a unit slope (slope = 1). Otherwise, a reduced amplification path is activated, and the output follows a weaker slope (α) tunable through the gain configuration. This decision making mechanism is implemented via the analog multiplexer controlled by the enable signal Ven. Figure S24 shows the simulated voltage transfer curve of the circuit, highlighting the coordination between the input voltage, the enable signal Ven (magenta), and the output voltage Vout (orange). As the input voltage rises and crosses the threshold defined by Vref, Ven switches from low to high. This transition triggers the multiplexer to select between the two output branches, thereby controlling the slope of Vout. In the weaker slope region, a shallow output slope α is maintained, while in the positive input region, a unit slope amplification is activated. This selective response demonstrates how the circuit achieves programmable, asymmetric activation characteristics. Figure S25 presents simulated I–V curves of the activation circuit under various gain settings (Av = 0.1–1.75). While the forward bias region maintains the original activation characteristics of the device, the slope of the reverse bias region increases linearly with Av, demonstrating continuous and controllable slope tuning. Figure S26 further analyzes and fits the relationship between the slope coefficient (α) and the gain factor (Av), confirming a well defined linear correlation.

Methods
Heterostructure Preparation and Device Fabrication
Atomically thin CuBiP₂Se₆ and MoS₂ are mechanically exfoliated from bulk crystals and transferred to a silicon substrate with a 300 nm thick SiO₂ layer via the dry transfer method using polydimethylsiloxane (PDMS). Subsequently, the device is coated with polymethyl methacrylate (PMMA 950 A4) by spin-coating, with an initial speed of 500 rpm for the first 10 s, followed by 4000 rpm for 60 s. After baking the sample on a hot plate at 180 °C for 2 min, electron beam lithography (EBL) is used to develop and fix the electrode patterns for the source and drain. Finally, 5 nm/50 nm Cr/Au electrodes are deposited using thermal evaporation, and acetone is used to remove the unexposed PMMA and excess metal.

Device Characterizations
The electrical behavior of the device under various optoelectronic pulse conditions is investigated using a Keithley B1500A semiconductor parameter analyzer and a Lakeshore CRX-VF probe station. The optical microscope image of the device is captured with an optical microscope, and the height profile of the 2D thin films within the heterostructures is characterized using atomic force microscopy (AFM). Raman spectra are recorded with a confocal Raman spectrometer, employing an excitation wavelength of 532 nm. The ferroelectric measurement was performed by ferroelectric analyzer (Huace FE-2000 Analyzer) in a probe station (CRX-6.5, LakeShore).

Simulation of the In-Sensor Computing System with the CBPS/MoS₂ heterojunction
Firstly, the heterojunction serves as the reservoir mode in simulated in-sensor computing system. The readout layer consists of a two layer multilayer perceptron (MLP) with 500 hidden neurons, where the heterojunction device is employed as the activation function following the first linear layer. The learning is carried out by minimizing the categorical cross entropy loss using a minibatch (batch size = 8) gradient descent with the Stochastic Gradient Descent (SGD) optimizer (initial learning rate = 0.001, momentum = 0.9, weight decay = 5 × 10-5, the learning rate is multiplied by a factor of 0.95 every 10 epochs).

Simulation of the Vision Transformer with the CBPS/MoS₂ heterojunction
The vision transformer model used in this task is ViT-B/16, which refers to the “Base” variant with 16 × 16 input patch size. During training, the pretrained weights of ViT-Base-Patch-224-in21k are first loaded. These weights are pretrained on the ImageNet-21k dataset, enabling improved model performance. the learning is carried out by minimizing the categorical cross-entropy loss using a minibatch (batch size = 8) gradient descent with the Stochastic Gradient Descent (SGD) optimizer (initial learning rate = 0.001, momentum = 0.9, weight decay = 1 × 10-4, the learning rate is multiplied by a factor of 0.9 every 20 epochs).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors present a compelling study demonstrating antiferroelectric polarization–induced physical activation in CBPS heterostructures, integrating materials physics, optoelectronic characterization, and neuromorphic computing demonstrations. The work leverages AFE polarization dynamics to achieve a diode-like response with a tunable reverse bias slope, applied to medical image classification. The manuscript is well-written, however, the current version lacks quantitative rigor, deeper physical interpretation, and consistent data presentation. Below are comments for the authors’ reference:\n1. The novelty relative to other AFE materials (e.g., CCPS, HZO ) used in neuromorphic applications is not sufficiently discussed. A short discussion or a table summarizing their switching energy, coercive field, accuracy and scalability would enhance context.\n2. The paper asserts low power operation, but quantitative data such as energy per switching or per recognition task would provide a clearer perspective on practical benefits.\n3. The term “physical activation” appears repeatedly throughout the manuscript but is not clearly defined. The authors should explicitly clarify the physical basis of this concept—whether it denotes carrier activation, polarization-modulated charge transport, or another field-driven mechanism. Furthermore, it should be stated whether “physical activation” directly corresponds to the activation functon(e.g., LeakyReLU) in neural networks or instead represents a broader physical phenomenon with analogous behavior. A detailed definition would significantly improve conceptual clarity and help readers understand its physical and computational significance.\n4. In Figure 1b, the polarization-electric field loops are shown, but the coercive fields, remnant polarization, and any asymmetry should be quantified. This data is critical to understand switching behavior.\nIn Figure 1d, the I–V curves suggest linearity, but more detailed fitting parameters and the Taylor series expansion or model used should be provided to substantiate the claims of high linearity.\nFigures should be redrawn in vector format (SVG/EPS) for publication quality. And ensure consistent font styles and line thicknesses.\n5. The statement on lines 232-233 mentions that the device exhibits a highly linear photocurrent response to power density, indicating a drift-dominated current transport mechanism. Please explain how drift transport leads to this linearity and what evidence confirms drift, rather than diffusion or trap-related processes.\n6. Details regarding the implementation of the device as an activation function within the neural network are sparse. Including a schematic of the circuit, the training process, and comparison metrics with existing activation functions would clarify the advantages.", "reviewer_2": "In the work “Antiferroelectric Polarization Enabling Physical Activation in CuBiP2Se6,” the authors demonstrate CBPS-MoS2 heterostructure capable of both reservoir computing and physical implementation of a LeakyReLU function. The dual functionality is promising for in-sensor computing architectures, especially for optically driven information processing.\nThe authors successfully present the material, electrical, and optical characterizations of a single device. However, most of the following figures are based on simulations, which limit the impact of the study. The simulated results alone are not convincing, as the claimed energy advantages are not quantitatively supported, and the implications of Fig. 4 and Fig. 5 overlap considerably. Further clarification and experimental validation—preferably through small-scale array implementation (or multiple devices acting as multiple neurons)—are required to substantiate the claims regarding the benefits of CBPS-based neural networks. I would not recommend publication in Nature Communications without substantial improvements.\n1. The manuscript lacks quantitative data highlighting the energy efficiency of the proposed CBPS device. A direct comparison of energy consumption between neural networks using the device and those using conventional electronic activation elements would strengthen the work.\n2. The proposed CBPS device uses a heterostructure of relatively thick MoS₂ and CBPS flakes (more than five layers). The relationship between antiferroelectricity, optical absorption, and the thickness of both materials should be clarified. Please explain how the specific number of layers is advantageous.\n3. Since the LTP behavior is not shown under self-powered operation, the authors should further clarify how LTP and STP responses can be selectively achieved through the applied voltage and pulse parameters under both electrical and optical stimulation.\n4. For Fig. 4b, please provide the corresponding circuit diagram. According to the Methods section, the results in Fig. 4 appear to be fully simulated. Please specify whether any experimental data are included. Fabricating and testing a small device array would help bridge the simulation results with experiments rather than relying solely on single-device characteristics.\n5. Similarly, for Fig. 5, please clarify how the simulations are based on experimental results. The activation function represents only a small portion of a transformer architecture, and it is not evident how the simulated CBPS-based activation offers tangible energy efficiency advantages. The demonstration of physical LeakyReLU activation in Fig. 5 appears somewhat redundant, as Fig. 4 already discusses both reservoir computing and activation functionality. These results could be merged for clarity.\n6. There are other studies of physical activation based on neuromorphic devices1-3. Please specify the advantages of the proposed devices over these studies.\nRef. 1) Oh, Sangheon, et al. \"Energy-efficient Mott activation neuron for full-hardware implementation of neural networks.\" Nature nanotechnology 16.6 (2021): 680-687.\nRef. 2) Li, Kun, et al. \"Configurable activation function realized by non-linear memristor for neural network.\" AIP Advances 10.8 (2020).\nRef. 3) Chen, Ziqi, et al. \"Full-analog implementation of activation function based on phase-change memory for artificial neural networks.\" IEEE Transactions on Industrial Electronics 71.8 (2023): 9914-9922.\nMinor comments\n1. Include a quantitative metric (e.g., RMSE) to evaluate the linearity of experimental data in Fig. 1d, Fig. 2b, and Fig. 3g.\n2. In line 164, the role of MoS₂ is unclear. Please elaborate.\n3. The description of the device structure and type (line 176) should precede the discussion of the electrical response (line 161), which could then be linked to Fig. 1a.\n4. The caption of Fig. 2e is incorrect ((h) → (d)). Fig. 2e could also be included as an inset of Fig. 2d.\n5. Indicate the bias polarity in Fig. 2i.", "reviewer_3": "The authors report the fabrication, structural and opto-electrical characterization, as well as selected proof of concept neural network applications of layered van der Waals heterostructure devices. The subjects of the reported work, i.e., the hardware-realization of customizable activation functions and the exploitation of short-term / long-term memory effects as a computational resource are highly timely. The experimental and simulation-based study is overall properly carried out, however, some important aspects require more detailed discussion. I am pleased to recommend the manuscript for publication in Nature Communications, provided that the following points are satisfactorily addressed either in the main article or in the Supporting Information.\n1. Please include data showing the device-to-device and cycle-to-cycle variability.\n2. Please discuss their effect on the accuracy of the outlined proof-of-concept classification tasks.\n3. Short-term and long-term memory is presented in Fig.S7. However, the data does not show any qualitative change in the current slow decay. Please clarify your quantitative criteria of STP / LTP behavior.\n4. The range of conductance relaxation seems moderate and the rate of relaxation is second-scale. Please discuss how many conductance states a single device can access when you employ it as an RC node. Also, what is the optimum frequency and affordable length of the temporal signal which is fed into such a node?\n5. Is the second-scale relaxation not a problem in the ReLU application?\n6. Please state/assess the computational time and energy in the outlined proof-of-concept classification tasks and compare them to the SoA.\n7. Figs 2&3 exhibit very different current scales from uA’s to 100’s of pA. Please discuss.\n8. Fig.S5: Is there a sweep-rate dependence?\n9. Please add references to line 67.\n10. Line 227 and further on: I find the term ‘self-powered’ misleading. Although the externally applied voltage bias is zero here, the device is still exposed to considerable optical power.\n11. The manuscript needs a thorough English proof-reading."}, "author_response": "Point-by-Point Response to Reviewers’ Comments\nWe sincerely thank the Editor and the reviewers for their careful evaluation of our manuscript and\nfor the constructive and insightful comments. These comments have helped us significantly improve\nthe clarity, quality, and scientific rigor of the manuscript. We have carefully addressed all comments\nand revised the manuscript accordingly. All changes are highlighted in the revised version.\nReviewer #1:\nThe authors present a compelling study demonstrating antiferroelectric polarization–induced\nphysical activation in CBPS heterostructures, integrating materials physics, optoelectronic\ncharacterization, and neuromorphic computing demonstrations. The work leverages AFE\npolarization dynamics to achieve a diode-like response with a tunable reverse bias slope, applied to\nmedical image classification. The manuscript is well-written, however, the current version lacks\nquantitative rigor, deeper physical interpretation, and consistent data presentation. Below are\ncomments for the authors’ reference:\nRe: We sincerely appreciate the reviewer for the positive evaluation of our work. Meanwhile, the\nreviewer has provided detailed and constructive comments, which have greatly helped improve the\nquality and readability of the manuscript. With these valuable suggestions, the manuscript has been\nsignificantly improved. Below, we respond to all comments point by point and revise the manuscript\naccordingly. We hope that the revised manuscript will address all the concerns from the reviewer.\nComment 1:\nThe novelty relative to other AFE materials (e.g., CCPS, HZO ) used in neuromorphic applications\nis not sufficiently discussed. A short discussion or a table summarizing their switching energy,\ncoercive field, accuracy and scalability would enhance context.\nRe: We sincerely thank you for raising this insightful comment. We surveyed the currently\nprominent antiferroelectric materials. We conducted a comprehensive comparison of their device\nstructures, application in neural networks, switching energy, and accuracy in relevant classification\ntasks, as summarized in Table R1. The comparison highlights that our work is the first to exploit the\npolarization characteristics of an antiferroelectric material for implementing the activation function\nin neuromorphic computing. Compared with conventional CMOS-based implementations of\nactivation functions, the proposed device exhibits reduced power consumption. We compare our\ndevice with representative devices that have been reported for hardware activation functions in\nterms of energy consumption, pulse width, and functional characteristics. The comparison results\nare summarized in Table R2. The results demonstrate that our device achieves superior performance\nin energy consumption. Our approach not only ensures low power consumption but also achieves\ndual-functional device that integrates electrical activation and optical synaptic behavior.\nWe have added the summary and comparative table at line 426 with highlight in revised manuscript,\nas well as the table in Supporting information Table S1 and S3.\nTable R1 Comparison of device structure, application in neural networks, switching energy, and\nclassification accuracy\nAFE Device structure Application Switching Classification\nmaterial energy accuracy (dataset)\nHZO W/TiN/HZO/TiN1 Spiking Neurons 37 fJ 96.8% (MNIST)\nHZO W/HZO/W2 Artificial Neurons 1.36 fJ >90% (MNIST)\nAu/Ti/HZO/W2 Synaptic weights 245 aJ\nHZO W/HZO/W/Al O /MoS 3 Spiking Neurons 0.1 pJ 97.8% (MNIST)\n2 3 2\nHZO W/HZO/Al O /MoS 4 Reservoir - 88.6% (NIST\n2 3 2\nTI467)\nHZO TiN/HZO/TiN5 Spiking Neurons - >90% (MNIST)\nSynaptic weights - 92.7% (Heart\nMRI8)\nCuCrP S CuCrP S /h-BN/SnS 6 Reservoir 0.3 pJ 97.7% (MNIST)\n2 6 2 6 2\nSynaptic weights 94.7% (decision\nmaking)\nCuBiP Se CuBiP Se /MoS (this Reservoir 3.6 pJ >95%\n2 6 2 6 2\nwork) Activation 95.5 pJ (OrganMNIST3D)\nTable R2 The computation time and power consumption among devices based activation function\nActivation Energy Power\nDevices Pulse width\nfunction consumption consumption\nPt/VO /Pt 9 Sigmoid - 0.3-2.38 nJ 11.9 µW\n2 3 2\nNIs/Pt 10 LeakyReLU 5 ms 33 nJ-1.42 µJ 1.65-71 µW\nMott device 11 ReLU 65 ns 199.5 pJ ~11 mW\nCBPS/MoS (This\nwork)\n1. Cao R, et al. Compact artificial neuron based on anti-ferroelectric transistor. Nat Commun 13,\n7018 (2022).\n2. Xu K, et al. Novel Two-Terminal Synapse/Neuron Based on an Antiferroelectric Hafnium\nZirconium Oxide Device for Neuromorphic Computing. Nano Lett 24, 11170-11178 (2024).\n3. Gao J, et al. Reconfigurable neuromorphic functions in antiferroelectric transistors through\ncoupled polarization switching and charge trapping dynamics. Nat Commun 16, 4368 (2025).\n4. Shi Y, et al. Switching Dynamics in Anti‐Ferroelectric Transistor for Multimodal Reservoir\nComputing. Advanced Functional Materials 34, (2024).\n5. Zhang J, et al. Ferroelectric/Antiferroelectric HfZrO(x) Artificial Synapses/Neurons for\nConvolutional Neural Network-Spiking Neural Network Neuromorphic Computing. Nano Lett 25,\n13739-13747 (2025).\n6. Yu Z, et al. Van der Waals Antiferroelectric CuCrP(2)S(6)-Based Artificial Synapse for High-\nPrecision Neuromorphic Computation. Small 21, e2502676 (2025).\n7. Liberman, Mark, et al. TI 46-Word LDC93S9. Web Download. Philadelphia: Linguistic Data\nConsortium, 1993.\n8. Antonelli M, et al. The Medical Segmentation Decathlon. Nature Communications 13, 4128\n(2022).\n9. Jerry M, Parihar A, Grisafe B, Raychowdhury A, Datta S. Ultra-low power probabilistic IMT\nneurons for stochastic sampling machines. In: 2017 Symposium on VLSI Technology) (2017).\n10. Liang H, et al. Artificial Neurons Based on a Threshold Switching Memristor with Ultralow\nThreshold Voltage. ACS Applied Electronic Materials 7, 3019-3029 (2025).\n11. Oh S, et al. Energy-efficient Mott activation neuron for full-hardware implementation of neural\nnetworks. Nat Nanotechnol 16, 680-687 (2021).\nComment 2:\nThe paper asserts low power operation, but quantitative data such as energy per switching or per\nrecognition task would provide a clearer perspective on practical benefits.\nRe: Thank you for the insightful comments. We have calculated the energy consumption of the\ndevice operating as both an electrical activation unit and an optical synapse. The results are\nsummarized in Figure R1. Under an electrical pulse with a width of 500 µs and an amplitude of 1\nV, the energy consumption per computation event is 95.5 pJ. For optical synaptic operation, under\na light pulse with a width of 1 ms and using a read voltage of 0.1 V, the corresponding energy\nconsumption per synaptic event is 3.6 pJ. These results demonstrate that the device exhibits energy\nefficiency in both optical and electrical operating modes.\nThe relevant content has been added to line 226 and line 255 of the revised manuscript.\nFigure R1 The energy consumption when applied a) an electrical pulse with a width of 500 µs and\nan amplitude of 1 V and b) an optical pulse with a width of 1 ms and a bias of 0.1 V.\nComment 3:\nThe term “physical activation” appears repeatedly throughout the manuscript but is not clearly\ndefined. The authors should explicitly clarify the physical basis of this concept—whether it denotes\ncarrier activation, polarization-modulated charge transport, or another field-driven mechanism.\nFurthermore, it should be stated whether “physical activation” directly corresponds to the activation\nfuncton(e.g., LeakyReLU) in neural networks or instead represents a broader physical phenomenon\nwith analogous behavior. A detailed definition would significantly improve conceptual clarity and\nhelp readers understand its physical and computational significance.\nRe: We sincerely thank the reviewer for highlighting the ambiguity of the term “physical activation”.\nWe agree that a clearer and more rigorous definition is essential.\nIn this work, physical activation refers to a field-driven, polarization-modulated charge‐transport\nprocess arising from the antiferroelectric polarization switching in CuBiP Se (CBPS). Under the\n2 6\ncombined influence of antiferroelectric polarization and the built-in electric field, a nonlinear\nmodulation of carrier drift is induced. This physical nonlinearity produces an input–output\ncharacteristic that mathematically resembles a neural‐network activation function. Importantly,\nphysical activation does not denote semiconductor carrier activation (e.g., thermal excitation), but\nrather a device-intrinsic nonlinear mapping. In our system, this mapping naturally produces a\nLeakyReLU-like asymmetric response, providing a direct physical realization of an activation\nfunction without additional CMOS circuits.\nThus, physical activation represents a broader physical phenomenon: A nonlinear mapping\ndirectly arising from the device physics, which resembles the commonly used activation\nfunctions in neural networks. The LeakyReLU implementation shown in the manuscript is a\nnonlinear mapping of the CBPS/MoS device.\nComment 4:\nIn Figure 1b, the polarization-electric field loops are shown, but the coercive fields, remnant\npolarization, and any asymmetry should be quantified. This data is critical to understand switching\nbehavior.\nIn Figure 1d, the I–V curves suggest linearity, but more detailed fitting parameters and the Taylor\nseries expansion or model used should be provided to substantiate the claims of high linearity.\nFigures should be redrawn in vector format (SVG/EPS) for publication quality. And ensure\nconsistent font styles and line thicknesses.\nRe: We sincerely thanks for the professional comments. As shown in Fig. R2a, when the electric\nfield returns to zero, the remanent polarization is −0.86 μC/cm², indicating that the polarization is\nvery close to zero, which is consistent with the spontaneous depolarization behavior characteristic\nof antiferroelectric materials. Unlike ferroelectric materials, for which the coercive field is well\ndefined, antiferroelectric materials do not yet have a universally accepted definition of coercive field\nin current studies. However, by extracting the first derivative of the polarization–electric field\nhysteresis loop (Fig. R2b), a pronounced discontinuity is observed at approximately 50 kV cm⁻¹,\nindicating a rapid polarization switching process occurring at this field. To quantitatively evaluate\nthe loop symmetry, we extracted two parameters. The polarization values at +200 kV/cm and −200\nkV/cm are +9 μC/cm² and −9 μC/cm², respectively. In addition, the loop areas obtained during\nforward and reverse scans are 171.04 and 138.36, respectively.\nThe quantified coercive fields, remnant polarization, and any asymmetry have been added in revised\nmanuscript (line 149 to line 157).\nFigure R2 a Polarization–electric hysteresis loops measured on CBPS antiferroelectric capacitor. b\nThe derivative of the polarization–electric hysteresis loops\nWe model the measured – characteristics using a continuous piecewise-linear function (PWLF)\nconsisting of segments. The domain is partitioned by breakpoints:\n𝐼 𝑉\n𝑛𝑠𝑒𝑔 [𝑥min,𝑥max]\nwhere and .\nseg 𝑏 ={b0,b1,…,b𝑛𝑠𝑒𝑔}\nEach segment is linear:\n𝑏0 =𝑥min 𝑏𝑛 =𝑥max\nContinuity is enforced through:\n𝑓(𝑥)=𝑎𝑘𝑥+𝑐𝑘,𝑏𝑘 ≤𝑥 ≤𝑏𝑘+1\nThe locations of the internal breakpoints are not assigned manually but are automatically determined\n𝑎𝑘𝑏𝑘+1+𝑐𝑘 =𝑎𝑘+1𝑏𝑘+1+𝑐𝑘+1\nthrough a global optimization process. Specifically, the internal breakpoints\nseg\n𝑛seg −1\nare treated as free variables to be optimized within the domain .To determine the\n𝐛int ={𝑏1,𝑏2,…,𝑏𝑛 −1}\noptimal breakpoint set, we minimize the sum of squared residuals (SSR):\n[𝑥min,𝑥max]\n𝑁\n∗ 2\n𝐛 =arg m𝐛iinnt ∑[𝑓(𝑥𝑖;𝐛int)−𝑦𝑖]\nBecause the SSR landscape is non-convex 𝑖=a1nd contains multiple local minima due to the\ndiscontinuous dependence of the regression matrix on , we employ the differential evolution\nalgorithm for robust global optimization. In differential evolution, a population of candidate\n𝐛int\nbreakpoint vectors is evolved through mutation, crossover, and selection. For each generation , a\nmutant vector is generated as:\n𝑔\n(𝑔) (𝑔) (𝑔) (𝑔)\nWhere is the mutation factor (𝐯0.5–1=.0𝐱 i𝑟n1 o+ur 𝐹im(𝐱p𝑟l2em−en𝐱t𝑟a3tio)n, , each iteration randomly takes a\nvalue within this range), are distinct random individuals from the population. A trial\n𝐹\nvector is formed via binomial crossover:\n𝐱𝑟1,𝐱𝑟2,𝐱𝑟3\n(𝑔)\n𝐮 if\n(𝑔)\n(𝑔) 𝑣𝑗 , ra o n t d h ( e 0 rw ,1 i ) se <𝐶𝑟,\n𝑢𝑗 ={ (𝑔)\n𝑥𝑗 , ,\nwhere is the crossover probability (0.7 in our implementation). The trial vector replaces the\nparent if it yields a lower SSR. After convergence, the differential evolution algorithm outputs the\n𝐶𝑟\noptimal breakpoints . For fixed breakpoints , the slopes and intercepts are obtained.\n∗ ∗\n𝐛 𝐛\nCoefficient of determination ( ) is established upon the decomposition of the total sum of squares,\nserving as a measure to indicate2 the goodness of fit of a regression equation to the observed data. A\n𝑅\ncloser alignment of the observed data points around the regression line signifies a better fit of the\nmodel, resulting in a higher . Conversely, a poorer fit is indicated by a lower value. Ideally, a\nvalue of 1 for the R² correspon2ds to a perfect fit, where all data points are accurately predicted by\n𝑅\nthe model. Consequently, an R² value closer to 1 indicates a better fit of the model to the data. To\nquantitatively evaluate the goodness of fit of our piecewise-linear model, we compute the as:\n2\n𝑅\n𝑁 2\n2\n∑𝑖=1(𝑦𝑖−𝑦̂𝑖)\n𝑅 =1− 𝑁 2\nwhere is the fitted value and is the mean ∑of 𝑖t=h1e( m𝑦𝑖e−as𝑦u¯r)ed data. Our model exhibits an almost\nperfect fit, with a calculated R² value of approximately 0.999. Furthermore, the Root Mean Square\n𝑦̂𝑖 𝑦¯\nError (RMSE) and the Normalized Root Mean Square Error (NRMSE) were calculated to quantify\nthe high linearity using the following equations:\n𝑁\n1 2\n𝑅𝑀𝑆𝐸 =√ ∑(𝑦𝑖−𝑦̂𝚤)\n𝑁𝑖=1\n1 𝑁 2\n√ ∑𝑖=1(𝑦𝑖−𝑦̂𝚤)\n𝑁\nwhere is the fitted value, the c𝑁al𝑅cu𝑀la𝑆te𝐸d= results for RMSE and NRMSE were 0.0534 and 0.0098,\nmax (𝑦𝑖)−min (𝑦𝑖)\nrespectively.\n𝑦̂𝑖\nBased on the comprehensive analysis, these findings demonstrate that our model is highly linear.\nThe model used for fitting is added in line 181 of revised manuscript and supplementary text 1 of\nsupporting information.\nAll figures in the manuscript and supplementary materials are exported in the vector format (SVG)\nand reformatted in Adobe Illustrator to ensure consistent font styles and line thicknesses.\nComment 5:\nThe statement on lines 232-233 mentions that the device exhibits a highly linear photocurrent\nresponse to power density, indicating a drift-dominated current transport mechanism. Please explain\nhow drift transport leads to this linearity and what evidence confirms drift, rather than diffusion or\ntrap-related processes.\nRe: We appreciate for your professional comments. In the field of photodetectors, it is common\npractice to fit the photocurrent power relationship using a power-law dependence1,2,3,4,5,6, which can\nbe expressed as follows：\nph\nwhere α is the dimensionless exponent of the pow𝛼er law and b is a parameter related to the\n𝐼 ∝𝑏𝑃\nphotodetector responsivity. The exponent α reflects the influence of trap states within the\nphotodetecting system1. In an ideal trap free photodetector, α equals 1, indicating that the\nphotocurrent increases linearly with incident power and that the responsivity remains constant\nacross different power levels. However, in low dimensional photodetectors, it is typical to observe\na nonunity exponent (0 < α < 1), which results from coupled processes of photocarrier generation,\ntrapping dynamics, and recombination within the semiconductor2. A smaller exponent indicates\nlarger effective trap density and dominance of photogating over photoconductive3. In our device,\nthe extracted exponent α is 0.935, which is very close to 1, indicating that the photoconductive\nprocess dominates over photogating effect.\nThis also suggests that trap-related mechanisms are not the primary contributors to the photocurrent.\nUnder illumination, the photogenerated carriers are efficiently separated by the built-in electric field,\nsuppressing recombination and resulting in a drift-dominated rather than diffusion-dominated\ntransport4.\n1. Zhao Q, et al. The role of traps in the photocurrent generation mechanism in thin InSe\nphotodetectors. Materials Horizons 7, 252-262 (2020).\n2. Fang H, Hu W. Photogating in Low Dimensional Photodetectors. Adv Sci (Weinh) 4, 1700323\n(2017).\n3. Thakar K, Mukherjee B, Grover S, Kaushik N, Deshmukh M, Lodha S. Multilayer ReS\nAppl Mater Interfaces 10, 36512-36522 (2018).\n4. Tamalampudi SR, Dushaq G, Rasras MS. An ultra-high-speed vertically illuminated self-driven\nlateral asymmetric InSe photodetector. Nanoscale 17, 14206-14214 (2025).\n5. Liu M, et al. Photogating-assisted tunneling boosts the responsivity and speed of heterogeneous\nWSe /Ta NiSe photodetectors. Nat Commun 15, 141 (2024).\n2 2 5\n6. Ghosh S, Varghese A, Thakar K, Dhara S, Lodha S. Enhanced responsivity and detectivity of fast\nWSe phototransistor using electrostatically tunable in-plane lateral p-n homojunction. Nat\nComment 6:\nDetails regarding the implementation of the device as an activation function within the neural\nnetwork are sparse. Including a schematic of the circuit, the training process, and comparison\nmetrics with existing activation functions would clarify the advantages.\nRe: Thank you for the insightful comment. As illustrated in Figure R3, the dual-functional device\nproposed in Figure 4 follows the general architecture of in-sensor reservoir computing demonstrated in\nrecent studies. First, the input optical signal is transduced into an electrical signal by the\nCBPS/MoS₂ device and subsequently converted into a voltage signal through an operational\namplifier for computation. After the matrix multiplication operation in the RRAM array, the\nprocessed signal is routed through the processor and a multiplexer, and then fed back to the device\nalong the red path for activation. The physically activated output is again converted into a voltage\nsignal and input into the array for the next matrix-multiplication stage, completing one forward\ncomputation cycle. For in-situ training, after each forward pass, the processor calculates the updated\nweights. The multiplexer then switches to the black path to program the synaptic weights in the\narray, enabling on-chip learning.\nTo validate the performance gap between the device implemented physical activation and the ideal\nLeakyReLU function, we performed neural network inference on multiple benchmarks. Specifically,\nwe validated small-scale ANN and CNN models on the MNIST and CIFAR-10 datasets, while larger\ntransformer-based ViT architectures were evaluated using CIFAR-10, Oxford-IIIT Pets, and Food-\n101 datasets. As summarized in Table R3, the networks employing our device-based activation\nexhibit training loss and test accuracy highly comparable to those using the ideal LeakyReLU\nactivation function, across different models and datasets. The results demonstrate that the device\nphysics-based activation function proposed in this work can closely approximate the performance\nof the ideal activation function.\nThe relevant content, figure and table have been added and highlighted in line 317 to 326 of the\nmanuscript, the figure and table in Supplementary Figure S15 and Table S2.\nFigure R3 Schematic of the circuit\nTable R3 Device based activate function compare with ideal LeakyReLU\nModel Dataset Train loss Test accuracy\nIdeal 0.0018 90.1%\nFashionMNIST\nANN Device 0.0062 89.7%\nMNIST Ideal 0.001 98.2%\nDevice 0.0008 98.32%\nIdeal 0.0213 89.8%\nFashionMNIST\nDevice 0.012 89.9%\nLeNet\nIdeal 0.0001 99.1%\nMNIST\nDevice 0.0001 99.25%\nIdeal 0.101 98.3%\nCIFAR10\nDevice 0.100 98.4%\nOxford-IIIT Ideal 0.062 89.9%\nViT\nPets Device 0.072 87.5%\nIdeal 0.103 89.7%\nFood 101\nDevice 0.125 88.5%\nReviewer #2:\nIn the work “Antiferroelectric Polarization Enabling Physical Activation in CuBiP2Se6,” the\nauthors demonstrate CBPS-MoS2 heterostructure capable of both reservoir computing and physical\nimplementation of a LeakyReLU function. The dual functionality is promising for in-sensor\ncomputing architectures, especially for optically driven information processing.\nThe authors successfully present the material, electrical, and optical characterizations of a single\ndevice. However, most of the following figures are based on simulations, which limit the impact of\nthe study. The simulated results alone are not convincing, as the claimed energy advantages are not\nquantitatively supported, and the implications of Fig. 4 and Fig. 5 overlap considerably. Further\nclarification and experimental validation—preferably through small-scale array implementation (or\nmultiple devices acting as multiple neurons)—are required to substantiate the claims regarding the\nbenefits of CBPS-based neural networks. I would not recommend publication in Nature\nCommunications without substantial improvements.\nRe: We sincerely thank the reviewer for the thorough assessment of our manuscript and for the\nconstructive comments. While appreciating the acknowledgment of the potential relevance of our\nwork, we fully recognize the reviewer’s concerns and suggestions. These comments have been\ninstrumental in guiding substantial revisions to the manuscript. Below, we respond to all comments\nin detail and revise the manuscript accordingly. We hope that the revised version satisfactorily\naddresses the reviewer’s concerns and improves the overall quality and impact of the work.\nComment 1:\nThe manuscript lacks quantitative data highlighting the energy efficiency of the proposed CBPS\ndevice. A direct comparison of energy consumption between neural networks using the device and\nthose using conventional electronic activation elements would strengthen the work.\nRe: Thank you for the insightful comments. We have calculated the energy consumption of the\ndevice operating as both an electrical activation unit and an optical synapse. The results are\nsummarized in Figure R4. Under an electrical pulse with a width of 500 µs and an amplitude of 1\nV, the energy consumption per computation event is 95.5 pJ. For optical synaptic operation, under\na light pulse with a width of 1 ms and using a read voltage of 0.1 V, the corresponding energy\nconsumption per synaptic event is 3.6 pJ. These results demonstrate that the device exhibits energy\nefficiency in both optical and electrical operating modes.\nFirstly, we compare the computation time and power consumption of device based activation\nfunctions (Table R4). The results demonstrate that our device achieves superior performance in\nenergy consumption. Then, a traditional CMOS circuit implementing the ReLU function consumes\n23.214 mW4, which is significantly higher than the power consumption achieved in this work.\nThe energy consumption has been added to line 226 and line 255 of the revised manuscript. And\nthe table is added in supporting information Table S1.\nFigure R4 The energy consumption when applied a) an electrical pulse with a width of 500 µs and\nan amplitude of 1 V and b) an optical pulse with a width of 1 ms and a bias of 0.1 V.\nTable R4 The computation time and power consumption among devices based activation function\nActivation Energy Power\nDevices Pulse width\nfunction consumption consumption\nPt/VO /Pt 1 Sigmoid - 0.3-2.38 nJ 11.9 µW\n2 3 2\nNIs/Pt 2 LeakyReLU 5 ms 33 nJ-1.42 µJ 1.65-71 µW\nMott device 3 ReLU 65 ns 199.5 pJ ~11 mW\nCBPS/MoS (This\nwork)\n1. Jerry M, Parihar A, Grisafe B, Raychowdhury A, Datta S. Ultra-low power probabilistic IMT\nneurons for stochastic sampling machines. In: 2017 Symposium on VLSI Technology) (2017).\n2. Liang H, et al. Artificial Neurons Based on a Threshold Switching Memristor with Ultralow\nThreshold Voltage. ACS Applied Electronic Materials 7, 3019-3029 (2025).\n3. Oh S, et al. Energy-efficient Mott activation neuron for full-hardware implementation of neural\nnetworks. Nat Nanotechnol 16, 680-687 (2021).\n4. Krestinskaya O, Salama KN, James AP. Learning in Memristive Neural Network Architectures\nUsing Analog Backpropagation Circuits. IEEE Transactions on Circuits and Systems I: Regular\nPapers 66, 719-732 (2019).\nComment 2:\nThe proposed CBPS device uses a heterostructure of relatively thick MoS and CBPS flakes (more\nthan five layers). The relationship between antiferroelectricity, optical absorption, and the thickness\n₂\nof both materials should be clarified. Please explain how the specific number of layers is\nadvantageous.\nRe: We sincerely thank you for raising this professional comment. We have carefully reviewed\nrelevant literature and found that, in 2021, Kazi M. Islam et al. reported that monolayer (0.61 nm),\nfew-layer (2.15 nm), and thin-film (33.5 nm) MoS₂ absorb approximately 7.4%, 12.6%, and 32.4%\nof the incident light, respectively1. As the thickness of MoS₂ increases from 0.61 nm to 2.15 nm, the\noptical absorption increases by 5%. A further increase to 33.5 nm yields only an additional 20%\ngain. Therefore, a moderately thick MoS₂ layer was selected in this work to balance absorption and\ncarrier transport. In addition, in 2022, Wei He et al. investigated CuBiP₂Se₆ and plotted the\nrelationship between and , where is the absorption coefficient2. In their study, CBPS\nflakes with thicknesses of 72 nm, 11.36 nm, 13.23 nm, 14.56 nm, 26.32 nm, and 74.15 nm were\n(𝛼ℎ𝜈) ℎ𝜈 𝛼\nexamined. At the same photon energy , thicker CBPS samples exhibited larger values of ,\nindicating higher optical absorption. It is also worth noting that the increase in absorption from2\nℎ𝜈 (𝛼ℎ𝜈)\n14.56 nm to 26.32 nm becomes less pronounced.\nWe further selected CuBiP₂Se₆ flakes with different thicknesses and experimentally evaluated their\nantiferroelectric properties. The results show that antiferroelectric behavior is preserved across all\ninvestigated thicknesses, as summarized in Figure R5. Consequently, when selecting the thicknesses\nof MoS₂ and CuBiP₂Se₆, using multilayer structures enhances optical absorption while maintaining\nthe antiferroelectric characteristics of CuBiP₂Se₆ at these thicknesses.\nThe relevant content has been added to line 143 and line 157 of the revised manuscript.\nFigure R5 P-E hysteresis loops of four CuBiP₂Se₆ devices with different thicknesses (18 nm, 23\nnm and 26 nm).\n1. Islam KM, Synowicki R, Ismael T, Oguntoye I, Grinalds N, Escarra MD. In‐Plane and Out‐of‐\nPlane Optical Properties of Monolayer, Few‐Layer, and Thin‐Film MoS2 from 190 to 1700 nm and\nTheir Application in Photonic Device Design. Advanced Photonics Research 2, (2021).\n2. He W, Kong L, Yu P, Yang G. Record-High Work-Function p-Type CuBiP Se Atomic Layers for\n2 6\nHigh-Photoresponse van der Waals Vertical Heterostructure Phototransistor. Adv Mater 35,\ne2209995 (2023).\nComment 3:\nSince the LTP behavior is not shown under self-powered operation, the authors should further clarify\nhow LTP and STP responses can be selectively achieved through the applied voltage and pulse\nparameters under both electrical and optical stimulation.\nRe: We sincerely thank the reviewer for raising this insightful question. Under self-powered\noperation, the device does not exhibit pronounced long-term plasticity (LTP), which originates from\nits intrinsic carrier dynamics. In the absence of an externally applied bias voltage, there is no\nadditional electric field to facilitate charge injection or trapping. Although photogenerated carriers\nare rapidly separated by the built-in electric field under illumination, they subsequently recombine\nquickly, making it difficult to form stable trapped charge states. As a result, the device does not\nexhibit persistent memory behavior under self-powered operation. When a read voltage of 0.1 V is\napplied, the external electric field enables partial trapping of photogenerated carriers at interfacial\nstates or localized traps, leading to a cumulative increase in conductance. With increasing optical\nstimulation duration or pulse number, the number of trapped carriers gradually increases,\nsignificantly prolonging the relaxation time. Consequently, the device exhibits a transition from\nshort-term plasticity (STP) to long-term plasticity (LTP).\nComment 4:\nFor Fig. 4b, please provide the corresponding circuit diagram. According to the Methods section,\nthe results in Fig. 4 appear to be fully simulated. Please specify whether any experimental data are\nincluded. Fabricating and testing a small device array would help bridge the simulation results with\nexperiments rather than relying solely on single-device characteristics.\nRe: Thank you for the insightful comment. The corresponding circuit diagram is shown in Figure\nR6, the dual-functional device proposed in Figure 4 follows the general architecture of in-sensor\nreservoir computing demonstrated in recent studies. First, the input optical signal is transduced into\nan electrical signal by the CBPS/MoS₂ device and subsequently converted into a voltage signal\nthrough an operational amplifier for computation. After the matrix multiplication operation in the\nRRAM array, the processed signal is routed through the processor and a multiplexer, and then fed\nback to the device along the red path for activation. The physically activated output is again\nconverted into a voltage signal and input into the array for the next matrix-multiplication stage,\ncompleting one forward computation cycle. For in-situ training, after each forward pass, the\nprocessor calculates the updated weights. The multiplexer then switches to the black path to program\nthe synaptic weights in the array, enabling on-chip learning.\nIn the simulation, we first characterize and store the device's 4 bit optical pulse response data.\nSubsequently, all 3D image frames were converted into temporal sequences of optical pulses based\non a time scale. These optical pulses were then transformed into corresponding current signals\naccording to the pre-characterized 4 bit pulse response and saved. Following this, a matrix\nmultiplication is performed on a computer. Upon its completion, the activation function model\nwhich previously saved based on electrical experiments is invoked to execute the nonlinear\nactivation. The result then underwent a final stage of computation via an electrical signal.\nThroughout this entire process, experimentally measured data from the physical device was utilized\nwhen it functioned as a reservoir and activation The weight operations, however, were handled by\nthe computer.\nTo demonstrate that the observed nonlinear behavior does not rely on the characteristics of a single\ndevice, we fabricated a 1 × 5 device (Figure R7a) array as well as several devices to evaluate device-\nto-device variability. The corresponding results are shown in Figure R7b. The red curve represents\nthe mean response, while the shaded gray region denotes the device-to-device variation quantified\nby the standard deviation. The devices exhibit quantitatively similar responses, indicating good\ndevice-to-device uniformity.\nThe circuit diagram and description are added in Supplementary Figure S15 and line 317 in revised\nmanuscript, respectively. And the 1×5 array and device-to-device variation have been added and\nhighlighted in line 137 and line 222 of the manuscript.\nFigure R6 Schematic of the circuit\nFigure R7 a Optical microscope image of the 1×5 CBPS/MoS2 array b Device-to-device variation\n(10 devices, the red line represents the mean value, and the gray shaded area indicates the error bar)\nComment 5:\nSimilarly, for Fig. 5, please clarify how the simulations are based on experimental results. The\nactivation function represents only a small portion of a transformer architecture, and it is not evident\nhow the simulated CBPS-based activation offers tangible energy efficiency advantages. The\ndemonstration of physical LeakyReLU activation in Fig. 5 appears somewhat redundant, as Fig. 4\nalready discusses both reservoir computing and activation functionality. These results could be\nmerged for clarity.\nRe: Thank you for your professional comment. First, the obtained discrete I-V data must be modeled\ninto a continuous and differentiable function, which is then saved for subsequent use. We model the\nmeasured – characteristics using a continuous piecewise-linear function (PWLF) consisting of\nsegments. The domain is partitioned by breakpoints:\n𝐼 𝑉\n𝑛𝑠𝑒𝑔 [𝑥min,𝑥max]\nwhere and .\nseg 𝑏 ={b0,b1,…,b𝑛𝑠𝑒𝑔}\nEach segment is linear:\n𝑏0 =𝑥min 𝑏𝑛 =𝑥max\nContinuity is enforced through:\n𝑓(𝑥)=𝑎𝑘𝑥+𝑐𝑘,𝑏𝑘 ≤𝑥 ≤𝑏𝑘+1\nThe locations of the internal breakpoints are not assigned manually but are automatically determined\n𝑎𝑘𝑏𝑘+1+𝑐𝑘 =𝑎𝑘+1𝑏𝑘+1+𝑐𝑘+1\nthrough a global optimization process. Specifically, the internal breakpoints\nseg\n𝑛seg −1\nare treated as free variables to be optimized within the domain .To determine the\n𝐛int ={𝑏1,𝑏2,…,𝑏𝑛 −1}\noptimal breakpoint set, we minimize the sum of squared residuals (SSR):\n[𝑥min,𝑥max]\n𝑁\n∗ 2\n𝐛 =arg m𝐛iinnt ∑[𝑓(𝑥𝑖;𝐛int)−𝑦𝑖]\nBecause the SSR landscape is non-convex 𝑖=a1nd contains multiple local minima due to the\ndiscontinuous dependence of the regression matrix on , we employ the differential evolution\nalgorithm for robust global optimization. In differential evolution, a population of candidate\n𝐛int\nbreakpoint vectors is evolved through mutation, crossover, and selection. For each generation , a\nmutant vector is generated as:\n𝑔\n(𝑔) (𝑔) (𝑔) (𝑔)\nWhere is the mutation factor (𝐯0.5–1=.0𝐱 i𝑟n1 o+ur 𝐹im(𝐱p𝑟l2em−en𝐱t𝑟a3tio)n, , each iteration randomly takes a\nvalue within this range), are distinct random individuals from the population. A trial\n𝐹\nvector is formed via binomial crossover:\n𝐱𝑟1,𝐱𝑟2,𝐱𝑟3\n(𝑔)\n𝐮 if\n(𝑔)\n(𝑔) 𝑣𝑗 , ra o n t d h ( e 0 rw ,1 i ) se <𝐶𝑟,\n𝑢𝑗 ={ (𝑔)\nwhere is the crossover probability (0𝑥.𝑗7 in, our implement,ation). The trial vector replaces the\nparent if it yields a lower SSR. After convergence, the differential evolution algorithm outputs the\n𝐶𝑟\noptimal breakpoints . For fixed breakpoints , the slopes and intercepts are obtained. Then, we\nreplace all instances o∗f the activation function i∗n the Vision Transformer model with the saved\n𝐛 𝐛\nfunction.\nThe model used for fitting is added in line 181 of revised manuscript and supplementary text 1 of\nsupporting information.\nFigure 5a illustrates the overall schematic of the Vision Transformer (ViT), including the process of\nimage patching and input embedding. The core of the model, however, is the section enclosed within\nthe dashed grey box on the right side, referred to as a block. In the Transformer architecture, multiple\nsuch blocks can be stacked as needed. A single block primarily consists of Layer Normalization,\nMulti-Head Attention, Multilayer Perceptron, and nonlinear activation. The purpose of Layer\nNormalization is to accelerate convergence and enhance training stability. Crucially, both the Multi-\nHead Attention and the Multilayer Perceptron are fundamentally performing linear operations.\nTherefore, the nonlinear mapping introduced by the activation function is extremely important.\nWithout this nonlinearity, the stacking of any number of blocks would be mathematically equivalent\nto a single linear transformation, rendering the deep architecture ineffective. Hence, the activation\nfunction is indispensable in the model. In our simulation, we employed a stack of 12 blocks,\nmeaning the activation function is applied 12 times sequentially. This further underscores its critical\nand essential role in the overall network function.\nGiven the difficulty in quantifying the total energy consumption of the full model computation, we\ntherefore focused on evaluating the change in energy efficiency resulting solely from replacing the\nactivation function. Based on above comparative analysis, it is reasonable to assert that our approach\nholds an advantage in terms of power consumption.\nWe appreciate your well-justified suggestion to merge Figures 4 and 5. Figure 4 primarily depicts\nthe dual-functional application based on our device. In contrast, Figure 5 aims to demonstrate the\ngeneralization capability of the proposed activation function. A viable activation function must\nperform well across diverse network architectures1,2,3. To enhance clarity, we have merged Figures\n4 and 5 in revised manuscript Figure 4.\n1. Oh S, et al. Energy-efficient Mott activation neuron for full-hardware implementation of neural\nnetworks. Nat Nanotechnol 16, 680-687 (2021).\n2. Xu B, Wang N, Chen T, Li M. Empirical Evaluation of Rectified Activations in Convolutional\nNetwork. arXiv e-prints, arXiv:1505.00853 (2015).\n3. Agarap AF. Deep Learning using Rectified Linear Units (ReLU). arXiv e-prints, arXiv:\n1803.08375 (2019).\nComment 6:\nThere are other studies of physical activation based on neuromorphic devices1-3. Please specify the\nadvantages of the proposed devices over these studies.\nRef. 1) Oh, Sangheon, et al. \"Energy-efficient Mott activation neuron for full-hardware\nimplementation of neural networks.\" Nature nanotechnology 16.6 (2021): 680-687.\nRef. 2) Li, Kun, et al. \"Configurable activation function realized by non-linear memristor for neural\nnetwork.\" AIP Advances 10.8 (2020).\nRef. 3) Chen, Ziqi, et al. \"Full-analog implementation of activation function based on phase-change\nmemory for artificial neural networks.\" IEEE Transactions on Industrial Electronics 71.8 (2023):\n9914-9922.\nRe: Thank you for pointing out the existing studies on physical activation based on\nneuromorphic devices (Refs. 1–3). These works indeed demonstrate the importance of hardware\nactivations, but their underlying physical mechanisms and functional positioning are fundamentally\ndifferent from our approach. In Ref. 1, a Mott device based on VO₂ nanowires exploits thermally\ninduced resistance switching and a voltage-divider circuit to emulate a ReLU-like activation. In Ref.\n2, nonvolatile memristors are driven into amplifier saturation to produce nonlinear clamping\nbehavior, while the activation function is not benchmarked against widely used neural network\nfunctions. In Ref. 3, nonlinear conductance change in phase-change memory is combined with a\nrelatively complex peripheral circuit to approximate a tanh-like activation. Although all three\nstudies achieve device-level activation, they differ from our work in several important aspects:\n(1) Type of activation functions implemented\nThe three studies target different activation primitives. Ref. 1 demonstrates a ReLU-like function\nwith low computational complexity (no exponential operation involved). Ref. 3 mimics a tanh-like\nactivation, which is beneficial for stable convergence and offset suppression in training.\nIn contrast, our device naturally realizes a LeakyReLU behavior, which not only preserves the low-\ncomplexity advantage of ReLU but also avoids the “dead-neuron” problem caused by zero gradients\nunder negative inputs. While all of these functions introduce essential nonlinearity, their\ncomputational roles differ, and the optimal activation choice depends on the target network\narchitecture and learning task.\n(2) Number of required components\nThe circuit complexity varies significantly among the reported approaches. Ref. 1 requires one VO₂\nnanowire (thermal switching unit) and one resistor (voltage-divider unit), totaling three physical\nelements to realize a single nonlinear ReLU unit. In Ref. 2, the memristor itself behaves linearly;\nthe operational amplifier is indispensable as the nonlinear element, thereby increasing peripheral\nhardware overhead. Ref. 3 employs a phase-change memristor with intrinsic nonlinearity, but\nadditional components (resistors, capacitors, transistors, op-amps, etc.) are still required to reshape\nthe response toward the tanh characteristic.\nIn our study, the CBPS/MoS₂ heterostructure intrinsically exhibits a nonlinear response highly\nconsistent with the LeakyReLU characteristic, thus no additional circuitry is required to construct\nthe activation unit.\n(3) Capability to process multiple types of signals\nRefs. 1–3 focus exclusively on activation functionality and cannot process other modalities. In\ncontrast, our device not only provides LeakyReLU-like nonlinear activation in the electrical domain,\nbut also exhibits memristive modulation under optical stimulation, enabling multifunctional\nsensing–memory–computing integration that is highly desirable for visual neuromorphic systems.\nMinor comments\n1. Include a quantitative metric (e.g., RMSE) to evaluate the linearity of experimental data in Fig.\n1d, Fig. 2b, and Fig. 3g.\nRe: We thank the reviewer for this excellent suggestion. We agree that a quantitative assessment of\nlinearity strengthens our analysis. Accordingly, we have calculated the Normalized Root Mean\nSquare Error (NRMSE) and the Coefficient of Determination (R²) for the linear fits in the\nspecified figures. Coefficient of determination ( ) is established upon the decomposition of the\ntotal sum of squares, serving as a measure to indica2te the goodness of fit of a regression equation to\n𝑅\nthe observed data. A closer alignment of the observed data points around the regression line signifies\na better fit of the model, resulting in a higher . Conversely, a poorer fit is indicated by a lower\nvalue. Ideally, a value of 1 for the R² corresponds 2to a perfect fit, where all data points are accurately\n𝑅\npredicted by the model. Consequently, an R² value closer to 1 indicates a better fit of the model to\nthe data.\nThese metrics have been added to the corresponding figure captions, and the analysis is discussed\nin the main text (line 183, 217 and 274). The results are as follows:\nFigure 1d: The fit model exhibits an NRMSE of 0.0098 and an R² of 0.999, demonstrating excellent\ngoodness-of-fit. This quantitatively confirms the strong linear relationship, as visually suggested in\nthe plot.\nFigure 2b: The curve demonstrates high linearity, with a NRMSE of 0.0722 and R² of 0.994. This\nsupports the use of a linear model for accurate quantification in this experiment.\nFigure 3g: The correlation between power density and response current is confirmed by the linear\nregression, which yielded a NRMSE of 0.0138 and an R² of 0.998. This provides robust quantitative\nevidence for the linear trend described.\nThese new quantitative results reinforce our original conclusions regarding the linear dependencies\nin our system. The low NRMSE values and high R² values across all figures indicate that the data\nare well-described by the linear models.\n2. In line 164, the role of MoS is unclear. Please elaborate.\n₂\nRe: Thank you for this valuable question. In our heterostructure, MoS₂ plays a crucial role in\ngenerating a built-in electric field at the CBPS/MoS₂ interface due to the band offset between the\ntwo materials. This built-in field strongly influences the migration of Cu⁺ ions that underlies the\npolarization-induced conductance modulation in CBPS.\nUnder forward bias, the external electric field weakens the built-in field, facilitating the drift of Cu⁺\nions and promoting the formation of ordered polarization states, thereby leading to a steeper\nactivation slope.\nIn contrast, under reverse bias, the Cu⁺ migration is partially suppressed because the built-in field\nacts align with the external field, hindering the formation of ordered polarization. Consequently, the\nconductance modulation is weaker, resulting in a much smaller reverse-bias slope, which matches\nwell with the desired nonlinear activation profile.\nWe have clarified this point in the revised manuscript (lines 185).\n3. The description of the device structure and type (line 176) should precede the discussion of the\nelectrical response (line 161), which could then be linked to Fig. 1a.\nRe: We thank the reviewer for this constructive suggestion regarding the manuscript's logical flow.\nWe fully agree that introducing the device structure prior to its electrical characterization is essential\nfor reader comprehension.\nIn revised manuscript, we have reordered the content as recommended in line 172 with highlight.\n4. The caption of Fig. 2e is incorrect ((h) → (d)). Fig. 2e could also be included as an inset of Fig.\n2d.\nRe: We appreciate the reviewer for pointing out this mistake, which has now been rectified with\ncorresponding updates in our revised manuscript. We also make corresponding adjustments to the\nfigure 2.\n5. Indicate the bias polarity in Fig. 2i.\nRe: We thank the reviewer for pointing out this issue. We agree that clearly indicating the bias\npolarity is essential for interpreting the electrical measurements. In response, we have updated the\nbias polarity in Figure 2i.\nReviewer #3:\nThe authors report the fabrication, structural and opto-electrical characterization, as well as selected\nproof of concept neural network applications of layered van der Waals heterostructure devices. The\nsubjects of the reported work, i.e., the hardware-realization of customizable activation functions and\nthe exploitation of short-term / long-term memory effects as a computational resource are highly\ntimely. The experimental and simulation-based study is overall properly carried out, however, some\nimportant aspects require more detailed discussion. I am pleased to recommend the manuscript for\npublication in Nature Communications, provided that the following points are satisfactorily\naddressed either in the main article or in the Supporting Information.\nRe: We sincerely thank the reviewer for the careful evaluation of our manuscript and for the positive\nassessment. We also appreciate the constructive comments highlighting aspects that require further\nclarification and improvement. These suggestions have been very helpful in improving the overall\nquality of the manuscript. In response, we have carefully revised the manuscript and the Supporting\nInformation, and we address all comments point by point below. We hope that the revised version\nadequately addresses the reviewer’s concerns.\nComment 1:\nPlease include data showing the device-to-device and cycle-to-cycle variability.\nRe: We thank the reviewer for this important comment. We have systematically evaluated both\ncycle-to-cycle and device-to-device variability of the proposed device.\nDevice-to-device:\nAt the current laboratory stage, the devices were fabricated using mechanical exfoliation, which\ninherently limits the number of devices available for large-scale statistical analysis. Therefore, we\nfabricated 10 devices and measured their I–V characteristics, as shown in Fig. R8. The red curve\nrepresents the mean response, while the shaded gray region denotes the device-to-device variation\nquantified by the standard deviation (0.023). The devices exhibit quantitatively similar responses,\nindicating good device-to-device uniformity.\nFigure R8 Device-to-device variation (10 device, the red line represents the mean value, and the\ngray shaded area indicates the error bar)\nCycle-to-cycle:\nFigure R9 summarizes the statistical behavior of the device over 500 consecutive cycles. The red\ncurve represents the mean response, while the shaded gray region denotes the cycle-to-cycle\nvariation quantified by the standard deviation (0.014). It can be observed that the individual cycles\nclosely overlap with the mean curve, and the variation remains narrow over the entire operating\nrange, indicating excellent cycle-to-cycle stability and reproducibility of the device.\nFigure R9 Cycle-to-cycle variation (500 cycle, the red line represents the mean value, and the gray\nshaded area indicates the error bar)\nIn revised manuscript, we have added the content in line 222 with highlight.\nComment 2:\nPlease discuss their effect on the accuracy of the outlined proof-of-concept classification tasks.\nRe: Device-to-device variability can indeed affect the performance of classification tasks. At the\ncurrent laboratory stage, the devices are fabricated by mechanical exfoliation, which inherently\nlimits uniformity. We believe that with the development of scalable fabrication techniques,\nimproved device-to-device uniformity can be achieved. In addition to device-to-device variation,\ncycle-to-cycle variability may also influence the computational results. Therefore, we quantitatively\nanalyzed the cycle-to-cycle variation by normalizing the device responses, averaging over multiple\ncycles, and calculating the corresponding mean standard deviation (0.014).\nTo evaluate the impact of such variability on classification performance, we further introduced\nGaussian noise with different standard deviations into the activation outputs and performed multiple\nclassification tasks, with the averaged results summarized in Figure R10. Figure R10a presents the\nclassification accuracy of ANN and LeNet model on the MNIST dataset under different levels of\nGaussian noise. Notably, even when the noise standard deviation is increased to 0.1, the\nclassification accuracy remains almost unchanged. For the larger-scale Vision Transformer model\nevaluated on the CIFAR-10 dataset (Figure R10b), the accuracy decreases by only approximately\none percentage point when the noise standard deviation reaches 0.07, and by about three percentage\npoints when the noise standard deviation further increases to 0.1. Since the maximum standard\ndeviation of the experimentally measured cycle-to-cycle variability in our device is only 0.018, we\nconclude that the intrinsic device variability has a negligible impact on the classification accuracy\nin the demonstrated tasks.\nThe corresponding result has been added in revised manuscript (line 374 to 380).\nFigure R10 The classification accuracy with the different standard deviation. a The classification\naccuracy of ANN and LeNet model on the MNIST dataset. b The classification accuracy of vision\ntransformer model on the CIFAR10 dataset.\nComment 3:\nShort-term and long-term memory is presented in Fig.S7. However, the data does not show any\nqualitative change in the current slow decay. Please clarify your quantitative criteria of STP / LTP\nbehavior.\nRe: We sincerely appreciate the reviewer’s professional and insightful comment. The study by\nChang et al.1, titled “Short-Term Memory to Long-Term Memory Transition in a Nanoscale\nMemristor,” is widely regarded as an authoritative reference for establishing quantitative criteria to\ndistinguish short-term and long-term memory. In their work, the authors demonstrated that the\nspontaneous retention loss in memristors can be accurately modeled using a stretched-exponential\nfunction (SEF), which is commonly employed to describe electronic or structural relaxation\nprocesses. The SEF, known as the Kohlrausch law, is expressed as:\n𝛽\nWhere is the relaxation function, τ is the charac−t(e𝑡r/i𝜏s)tic relaxation time, I\n0\nis the prefactor, and\n𝜙(𝑡)=𝐼0∗𝑒\nβ is the stretch index ranging between 0 and 1. As they pointed out, “It seems natural to suggest two\n𝜙(𝑡)\nmemory regimes exist in the memristor device, consisting of a regime with short τ ≈ few seconds\nand sensitive to additional stimulations, and another regime with much longer τ ≈ minutes\nand relatively insensitive to additional stimulations.” and “We argue that the key attributes of the\nSTM-to-LTM transition process have been demonstrated in the memristor device including the\nsignificant increase in memory retention after repeated stimulation and the resulting structural\nchange.” Following this established criterion, we extracted the characteristic relaxation time\nfrom the relaxation curves in Figure S7a, as shown in the Figure R11. After 5 pulses, the extracted\n𝜏\nis approximately 1.67 s, corresponding to short-term memory. As the number of applied pulses\nincreases, the relaxation time gradually increases, and when 100 pulses are applied, reaches\n𝜏\nnearly 1 minutes, satisfying the quantitative criterion for long-term memory formation. Therefore,\n𝜏\nwe conclude that our device indeed exhibits a clear transition from STP to LTP.\nThe corresponding quantitative criteria has been added in line 258 to 267 and highlighted in the\nmanuscript.\nFigure R11 Relaxation time variation with pulse number (a 5 pulse, b 10 pulses, c 20 pulses, d\n100 pulses).\n𝜏\n1. Chang T, Jo S-H, Lu W. Short-Term Memory to Long-Term Memory Transition in a Nanoscale\nMemristor. ACS Nano 5, 7669-7676 (2011).\nComment 4:\nThe range of conductance relaxation seems moderate and the rate of relaxation is second-scale.\nPlease discuss how many conductance states a single device can access when you employ it as an\nRC node. Also, what is the optimum frequency and affordable length of the temporal signal which\nis fed into such a node?\nRe: Thank you for the valuable comments. The conductance relaxation behavior and temporal\noperating conditions are key to the reservoir computing (RC) function. Our clarifications are\nprovided below.\n(1) Tunability of the conductance relaxation range\nThe relaxation range is not fixed; instead, it depends sensitively on the applied pulse parameters. As\nshown in Figure RX, increasing the number of pulses broadens the relaxation time constant, and\nFigure X further demonstrates that the relaxation time constant scales with pulse width. Similar\ntunable fading memory dynamics have also been reported in other memristive reservoirs1,2,3, where\npulse amplitude or duration modulates the relaxation behavior. Therefore, when different RC tasks\nrequire different fading memory depths, the relaxation dynamics can be flexibly engineered by\nadjusting the pulse number, width, or amplitude.\n(2) Number of accessible conductance states\nThe number of accessible states is theoretically limited by the sampling resolution rather than by\nthe absolute relaxation magnitude. Because conductance decays continuously, arbitrarily dense\nstates can be extracted by choosing appropriate sampling intervals within the fading memory. Thus,\nthe device inherently offers a sufficiently rich state manifold for RC.\n(3) Optimum operating frequency and temporal sequence length\nAt present, there is no universally accepted criterion for determining the optimal operating\nfrequency of a RC system. In our design, the optimal frequency is primarily constrained by the\nintrinsic frequency response of the device. As shown in Fig. 3d, the device maintains clearly\ndistinguishable responses to optical pulses at 1 kHz (1-ms pulse width), and exhibits even stronger\nand more stable responses at 200 Hz (5-ms pulse width). These results indicate that the optimal\noperating frequency of the device lies in the range of 1 kHz, and that the device can reliably process\ninput signals with pulse widths shorter than 1 ms.\n1. Wu X, Wang S, Huang W, Dong Y, Wang Z, Huang W. Wearable in-sensor reservoir computing\nusing optoelectronic polymers with through-space charge-transport characteristics for multi-task\nlearning. Nature Communications 14, 468 (2023).\n2. Zha J, et al. A 2D Heterostructure‐Based Multifunctional Floating Gate Memory Device for\nMultimodal Reservoir Computing. Advanced Materials 36, (2023).\n3. Chen R, et al. Thin-film transistor for temporal self-adaptive reservoir computing with closed-\nloop architecture. Sci Adv 10, eadl1299 (2024).\nComment 5:\nIs the second-scale relaxation not a problem in the ReLU application?\nRe: Thank you for the professional and insightful comment. In activation applications, it is indeed\nnecessary for the device state to return to its initial condition prior to each computation. Owing to\nthe spontaneous depolarization inherent to antiferroelectric materials, the device rapidly relaxes\nback to its original state once the external electric field is removed.\nIn our electrical measurements, we demonstrate this behavior using pulse width dependence\ncharacteristic (Fig. 2g in the manuscript). By extracting the device state immediately before each\npulse is applied, we obtain the results shown in Fig. R12. In the time window from 0.02 s to 0.04 s,\nno programming pulse is applied and only a small readout bias of 0.1 V is used. The measured pre-\npulse states remain highly consistent across each measurement, indicating that the device reliably\nreturns to its initial state through spontaneous depolarization after field removal. These observations\nconfirm that the relaxation process does not hinder the practical implementation of the activation,\nas the device naturally resets itself between computational steps.\nFigure R12. Device state of pre-pulse\nComment 6:\nPlease state/assess the computational time and energy in the outlined proof-of-concept classification\ntasks and compare them to the SoA.\nRe: Thank you for the insightful comments. Since the total computation time for the entire\nclassification task encompasses the processing time of neural network layers, and this study is\nspecifically directed towards the isolated activation function unit, it is not feasible to provide the\noverall task's computation time and power consumption within this work. Therefore, our\ncomparative analysis focuses primarily on the time and power consumption of the activation\noperation itself. We have calculated the energy consumption of the device operating as both an\nelectrical activation unit and an optical synapse. The results are summarized in Figure R13. Under\nan electrical pulse with a width of 500 µs and an amplitude of 1 V, the energy consumption per\ncomputation event is 95.5 pJ. For optical synaptic operation, under a light pulse with a width of 1\nms and using a read voltage of 0.1 V, the corresponding energy consumption per synaptic event is\n3.6 pJ. These results demonstrate that the device exhibits energy efficiency in both optical and\nelectrical operating modes.\nTable R5 compares the computation time and power consumption of state-of-the-art device based\nactivation functions. The results demonstrate that our device achieves superior performance in\nenergy consumption.\nThe energy consumption has been added to line 226 and line 255 of the revised manuscript. And\nthe table is added in supporting information Table S1.\nFigure R13 The energy consumption when applied a) an electrical pulse with a width of 500 µs\nand an amplitude of 1 V and b) an optical pulse with a width of 1 ms and a bias of 0.1 V.\nTable R5 The computation time and power consumption among devices based activation function\nAcitvation Energy Power\nDevices Pulse width\nfunction consumption consumption\nPt/VO /Pt 1 Sigmoid - 0.3-2.38 nJ 11.9 µW\n2 3 2\nNIs/Pt 2 LeakyReLU 5 ms 33 nJ-1.42 µJ 1.65-71 µW\nMott device 3 ReLU 65 ns 199.5 pJ ~11 mW\nCBPS/MoS (This\nwork)\n1. Jerry M, Parihar A, Grisafe B, Raychowdhury A, Datta S. Ultra-low power probabilistic IMT\nneurons for stochastic sampling machines. In: 2017 Symposium on VLSI Technology) (2017).\n2. Liang H, et al. Artificial Neurons Based on a Threshold Switching Memristor with Ultralow\nThreshold Voltage. ACS Applied Electronic Materials 7, 3019-3029 (2025).\n3. Oh S, et al. Energy-efficient Mott activation neuron for full-hardware implementation of neural\nnetworks. Nat Nanotechnol 16, 680-687 (2021).\nComment 7:\nFigs 2&3 exhibit very different current scales from uA’s to 100’s of pA. Please discuss.\nRe: Thanks for your professional comment. The difference in current scales between Figs. 2 and\nFigs. 3 arises from the fundamentally different operating conditions of the device.\nIn Figs. 2, the CBPS/MoS₂ heterostructure is operated under an externally applied bias voltage. The\ndrift current is externally enhanced by the electric field, resulting in currents on the order of μA.\nThis behavior is common phenomenon with typical biased 2D heterojunction devices. In contrast,\nthe current scales of 100’s pA in Figs. 3 were obtained under zero external bias, where the measured\nphotocurrent originates solely from the photogenerated carriers driven by the built in electric field\nof the heterojunction. Such self-driven (zero-bias) current is naturally much smaller than that\nproduced under an externally applied electric field. This self-driven current level is consistent with\nseveral related studies. For example, Zou et al. reported a vertical GaSe/MoS p−n heterojunctions1,\n2\nand Yan et al. demonstrated HfZrO /β-Ga O heterojunctions2, both showing self-driven\n2 2 3\nphotocurrents on the order of 100 pA.\n1. Zou Z, et al. Liquid-Metal-Assisted Growth of Vertical GaSe/MoS p-n Heterojunctions for\n2. Yan S, et al. High-Performance Self-Driven Solar-Blind Ultraviolet Photodetectors Based on\nHfZrO /beta-Ga O Heterojunctions. ACS Appl Mater Interfaces 15, 22263-22273 (2023).\n2 2 3\nComment 8:\nFig.S5: Is there a sweep-rate dependence?\nRe: Thank you for the professional comment. We have characterized the CBPS/MoS₂ device at five\ndifferent voltage sweep rates (with step sizes of 0.5 mV, 1 mV, 2 mV, 5 mV, and 10 mV). The results\nare presented in Figure R14. The device exhibits a very small memory window across all tested\nsweep rates, demonstrating minimal variation. Therefore, it can be concluded that the memory\nwindow of our device shows negligible dependence on the scan rate.\nThe sweep-rate dependence is added in the Figure 2b and the line 202 of the revised manuscript.\nFigure R14 Bidirectional I-V scan at different scan step.\nComment 9:\nPlease add references to line 67.\nRe: Thank you for your valuable suggestion. We have identified two relevant studies in this research\narea. Both referenced studies employ antiferroelectric material (HZO) as the channel material in\ntransistor structures. As stated in first article1, “The intrinsic accumulated polarization/spontaneous\ndepolarization of Hf Zr O films implements the integration/leaky behavior of neurons, avoiding\n0.2 0.8 2\nexternal capacitors and reset circuits. Moreover, the anti-ferroelectric neuron exhibits low energy\nconsumption (37 fJ/spike), high endurance (>1012), high uniformity and high stability.” The second\narticle2 further illustrates that “The ability of the device to return to its initial state without requiring\nan additional reset operation allows for compact and low-power device designs.” Taken together,\nthese findings demonstrate that the spontaneous depolarization inherent to antiferroelectric\nmaterials substantially reduces the energy consumption associated with polarization switching.\nAdditionally, the autonomous return to the initial state enables continuous and repeated computing\noperations without the assistance of extra circuit, offering significant advantages for analog\ncomputing operations that demand repetitive execution.\nThe corresponding references have been added at line 67 in the revised manuscript.\n1. Cao R, et al. Compact artificial neuron based on anti-ferroelectric transistor. Nat Commun 13,\n7018 (2022).\n2. Gao J, et al. Reconfigurable neuromorphic functions in antiferroelectric transistors through\ncoupled polarization switching and charge trapping dynamics. Nat Commun 16, 4368 (2025).\nComment 10:\nLine 227 and further on: I find the term ‘self-powered’ misleading. Although the externally applied\nvoltage bias is zero here, the device is still exposed to considerable optical power.\nRe: We thank you for the professional and insightful comments. We agree that the term “self-\npowered” is not appropriate in this context, as the device is still driven by optical illumination even\nthough no external electrical bias is applied. Although some previous studies have referred to this\nphenomenon as “self-powered”, we agree that your suggestion is more accurate and professional.\nTo avoid misleading, we have replaced “self-powered” with the more accurate and commonly used\nterm “self-driven” throughout the manuscript. This terminology has been widely adopted in\noptoelectronic and 2D-material literature to describe devices’ photoresponse under zero electrical\nbias1,2,3.\nThe corresponding terminology in the manuscript has been fully replaced and highlighted.\n1. Zeng X, et al. A molecular pyroelectric enabling broadband photo-pyroelectric effect towards\nself-driven wide spectral photodetection. Nat Commun 14, 5821 (2023).\n2. Lv Q, Yan F, Wei X, Wang K. High‐Performance, Self‐Driven Photodetector Based on Graphene\nSandwiched GaSe/WS Heterojunction. Advanced Optical Materials 6, (2017).\n2\n3. Zeng LH, et al. Fast, Self‐Driven, Air‐Stable, and Broadband Photodetector Based on Vertically\nAligned PtSe /GaAs Heterojunction. Advanced Functional Materials 28, (2018).\nThe manuscript needs a thorough English proof-reading.\nRe: Thank you for this valuable suggestion. The manuscript has been thoroughly proofread and\nrevised to improve clarity, grammar, and overall language quality throughout the text."}, {"round": 2, "reviewer_comments": {"reviewer_1": "After careful reading of the revised version, the authors have demonstrated that they have successfully addressed the initial concerns. I have no further comments.", "reviewer_2": "The author has invested considerable effort in validating the energy efficiency and layer-dependent physics. The author also provided comparisons with recent studies on physical activation, highlighting its dual functionality for energy-efficient in-sensor reservoir computing. The minor comments have also been addressed.\nHowever, the core experiment shown in Fig. 4 is mostly based on simulation. The figure set does not clearly indicate the exact experimental setup, including the array size, input size, readout timesteps used as reservoir outputs, and details of the subsequent classifier. The author additionally reported 1x5 devices as a prototype to validate the video and image simulations, which is a great breakthrough as I noted initially. Nevertheless, characterizing five devices independently and merely showing consistency is not sufficient to bridge the gap between the experimental and simulation results that handle 64 frames of 64x64 images and 16x16 patches. I would highly recommend experimentally utilizing these devices to validate in-sensor reservoir computing with five activation neurons by employing a much simpler dataset (e.g., 5×5 letter images). Such results should be used as a core figure set, together with the corresponding circuit diagram and size information (Fig. S15).\nIf my main concerns regarding the lack of array-scale experiments have been adequately addressed, I recommend the publication of the revised manuscript, which thoroughly covers and discusses these concerns as suggested by the author in the response.", "reviewer_3": "In due response to the reviewers' comments, the authors have included a significant amount of new results, details and explanations. The quality of the manuscript has been satisfactorily improved. I am pleased to recommend its publication in Nature Communications."}, "author_response": "Point-by-Point Response to Reviewers’ Comments\nWe sincerely thank the Editor and the reviewer for their careful evaluation of our manuscript and\nfor the constructive and insightful comments. These comments have helped us significantly improve\nthe clarity, quality, and scientific rigor of the manuscript. We have carefully addressed all comments\nand revised the manuscript accordingly. All changes are highlighted in the revised version.\nReviewer #2 (Remarks to the Author):\nThe author has invested considerable effort in validating the energy efficiency and layer-dependent\nphysics. The author also provided comparisons with recent studies on physical activation,\nhighlighting its dual functionality for energy-efficient in-sensor reservoir computing. The minor\ncomments have also been addressed.\nHowever, the core experiment shown in Fig. 4 is mostly based on simulation. The figure set does\nnot clearly indicate the exact experimental setup, including the array size, input size, readout\ntimesteps used as reservoir outputs, and details of the subsequent classifier. The author additionally\nreported 1x5 devices as a prototype to validate the video and image simulations, which is a great\nbreakthrough as I noted initially. Nevertheless, characterizing five devices independently and\nmerely showing consistency is not sufficient to bridge the gap between the experimental and\nsimulation results that handle 64 frames of 64x64 images and 16x16 patches. I would highly\nrecommend experimentally utilizing these devices to validate in-sensor reservoir computing with\nfive activation neurons by employing a much simpler dataset (e.g., 5×5 letter images). Such results\nshould be used as a core figure set, together with the corresponding circuit diagram and size\ninformation (Fig. S15).\nIf my main concerns regarding the lack of array-scale experiments have been adequately addressed,\nI recommend the publication of the revised manuscript, which thoroughly covers and discusses these\nconcerns as suggested by the author in the response.\nRe: Thank you for the constructive comments. Currently, realizing large-scale arrays using\nquaternary compound materials remains technically challenging1, and most existing studies are\nrestricted to single-device or small-scale array demonstrations2, 3. In light of this, we conducted\nexperiments based on a small-scale array in this work.\nWe experimentally implemented a 4 × 5 letter image recognition task, as illustrated in Figure R1.\nThe circuit schematic of the implementation is shown in Figure R1a. First, the input optical signal\nis transduced into an electrical signal by the CBPS/MoS₂ device and subsequently converted into a\nvoltage signal through an operational amplifier for computation. After the matrix-multiplication\noperation in the RRAM array, the processed signal is routed through the processor and a multiplexer,\nand then fed back to the device along the red path for activation. The physically activated output is\nagain converted into a voltage signal and fed into the array for the next matrix-multiplication stage,\ncompleting one forward computation cycle. In this demonstration, multilevel input signals were\nencoded using four-bit electrical pulses. As shown in Figure R1b, the CBPS/MoS₂ heterojunction\nexhibits stable and well-separated current responses under four-bit pulse stimulation, enabling\nreliable multilevel signal representation. The corresponding readout network architecture and\nreadout RRAM array are presented in Figure R1c and Figure R2, consisting of five input neurons,\nfive hidden neurons, and three output neurons. To assess the accuracy of weight programming, we\ncompared the simulated synaptic weights with the experimentally written weights in both the first\nand second layers. As shown in Figures R1d and R1e, the experimentally programmed weights\nclosely match the target values obtained from simulation, indicating good controllability and\nreproducibility of the weight update process. Figures R1f and R1g further compare the ideal network\noutputs with the experimentally measured outputs at the hidden layer and output layer, respectively.\nBoth simulations and experimental measurements achieved correct recognition for all three letters.\nThe close agreement between the simulated and experimental results confirms that the CBPS/MoS₂-\nbased in-sensor system can faithfully reproduce the expected neural network behavior in a hardware\nimplementation.\nThe corresponding results are added in revised manuscript with highlight.\nFigure R1. Experimental demonstration of a 4 × 5 letter image recognition task using the\nCBPS/MoS₂ based in-sensor computing system. a Schematic diagram of the experimental circuit\nconfiguration used for the 4 × 5 image recognition task. b Experimental read-current responses\ngenerated by sixteen 4-bit optical pulse trains ranging from (0000) to (1111). c Architecture of the\nreadout neural network, consisting of five input neurons, five hidden neurons, and three output\nneurons. d-e Comparison between the simulated synaptic weights and the experimentally\nprogrammed weights in the (d) first and (e) second layer. f Comparison between the ideal network\noutput and the experimentally output for the (f) hidden layer and (g) output layer.\nRRAM\nFigure R2. Readout RRAM array.\n1. Zuo Y, et al. Robust growth of two-dimensional metal dichalcogenides and their alloys by active\nchalcogen monomer supply. Nature Communications 13, 1007 (2022).\n2. Men M, et al. Polarization-modulated programmable photovoltaic performance of a designed\nferroelectric heterojunction. Nature Communications, (2026).\n3. Liang S, et al. Interferroic magnetoelectric coupling at CuCrP2S6/Fe3GeTe2 van der Waals\nheterojunctions. Nature Electronics 9, 23-32 (2026)."}, {"round": 3, "reviewer_comments": {"reviewer_2": "The authors further validate their simulation results through additional experiments combining the electro-optical responses from multiple CBPS/MoS₂heterojunction devices. The experimental results are consistent with the simulations and strengthen the claims regarding the proposed in-sensor computing system. No further revisions are necessary, and I recommend this work for publication in Nature Communications."}, "author_response": ""}]

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