Human-in-the-Loop Optimization for Deep Stimulus Encoding in Visual Prostheses
Authors: Jacob Granley
Tristan Fauvel
Matthew Chalk
Michael Beyeler
Venue: NeurIPS 2023 poster (2023)
Keywords: Brain Computer Interfaces
BCI
Stimulus Encoding
Visual Prostheses
Bayesian Optimization
Preferential Bayesian Optimization
Human-in-the-loop Optimization
Sensory Neuroprostheses
Neuroprostheses
Patient-Specific Optimization
Latent Space Bayesian Optimization
TL;DR: We use deep stimulus encoding combined with Bayesian optimization to personalize stimulation strategies in visual prostheses.

Abstract: Neuroprostheses show potential in restoring lost sensory function and enhancing human capabilities, but the sensations produced by current devices often seem unnatural or distorted. Exact placement of implants and differences in individual perception lead to significant variations in stimulus response, making personalized stimulus optimization a key challenge. Bayesian optimization could be used
to optimize patient-specific stimulation parameters with limited noisy observations, but is not feasible for high-dimensional stimuli. Alternatively, deep learning models can optimize stimulus encoding strategies, but typically assume perfect knowledge of patient-specific variations. Here we propose a novel, practically feasible approach that overcomes both of these fundamental limitations. First, a deep encoder network is trained to produce optimal stimuli for any individual patient by inverting a forward model mapping electrical stimuli to visual percepts. Second, a preferential Bayesian optimization strategy utilizes this encoder to learn the optimal patient-specific parameters for a new patient, using a minimal number of pairwise comparisons between candidate stimuli. We demonstrate the viability of this approach on a novel, state-of-the-art visual prosthesis model. Our approach quickly learns a personalized stimulus encoder and leads to dramatic improvements in the quality of restored vision, outperforming existing encoding strategies. Further, this approach is robust to noisy patient feedback and misspecifications in the underlying forward model. Overall, our results suggest that combining the strengths of deep learning and Bayesian optimization could significantly improve the perceptual experience of patients fitted with visual prostheses and may prove a viable solution for a range of neuroprosthetic technologies

Human-in-the-Loop Optimization for Deep Stimulus Encoding in Visual Prostheses
Jacob Granley
Tristan Fauvel
Department of Computer Science University California, Santa Barbara jgranleyOucab. edu
Institut de la Vision, Sorbonne Université rue Moreau, F-75012 Paris, France
Now with Quinten Health fauvel healthheathh com
Matthew Chalk
Michael Beyeler
Institut de la Vision, Sorbonne Université 17 rue Moreau, F-75012 Paris, France matthew www.kkinserm....
Department of Computer Science
Department of Psychological & Brain Sciences University of California, Santa Barbara mbeyeler@ucsb edu
Abstract
Neuroprostheses show potential in restoring lost sensory function and enhancing human capabilities, but the sensations produced by current devices often seem unnatural or distorted. Exact placement of implants and differences in individual perception lead significant variations in stimulus response, making personalized stimulus optimization a key challenge. Bayesian optimization could be used to opti- stimulation parameters with limited noisy observations, but is not feasible for nigh-dimensional stimuli. A Alternatively, deep learning models can optimize stimulus encoding strategies, but typically assume perfect knowledge of patient-specifie variations. Here we propose a novel, practically feasible approach that overcomes both of these fundamental limitations. First, deep encoder net- work is trained to produce optimal stimuli for any individual patient by inverting a forward model mapping electrical stimuli to visual percepts. Second, a preferential Bayesian optimization strategy utilizes this encoder to optimize patient-specific parameters for a new patient, using a minimal number of pairwise comparisons be- tween candidate stimuli. We demonstrate the viability of this approach state-of-the-es visual prosthesis model. We show that our approach quickly learns personalized stimulus encoder, leads to dramatic improvements in the quality of restored vision, and robust to noisy patient feedback and misspecifications in the underlying forward model. Overall, strengths of deep learning and Bayesian optimization could significantly improve the perceptual experience of patients fitted with visual prostheses and may prove a viable solution for a range of neuroprosthetic technologies.
mize
novel,
results suggest that combining the
Introduction
Sensory neuroprostheses are devices designed to restore or enhance perception in individuals with sensory deficits. They often interface with the nervous system by electrically stimulating neural tissue in order to provide artificial sensory feedback to the user 2]. For instance, visual prostheses have the potential restore vision to people living with incurable blindness by bypassing damaged parts of the visual system and directly stimulating the remaining cells in order to evoke visual percepts (phosphenes) 3 However, patient outcomes with current technologies are limited. Patients
37th Conference on Neural Information Processing Systems (NcurIPS 2023).

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Deep Stimulus Encoder (DSE)
Human-in-the-Loop Optimization (HILO)
Target Percept
Encoder
Encoder
prefer...
3
f
f-1
Target Percept
S1
fxed
3
Perceptual Error
Patient Parameters
Stimulus
f foed
S2
VPU
Φ2
3
f fixed Decoder
Acquisition function
Gaussian process model of preference
Preferential Bayesian Optimization
Figure 1: Left: Deep stimulus encoder (DSE), A forward model (f) is used to approximate the perceptual response to electrical stimuli, subject to -ptient-specific parameters Φ. An encoder (f-1) is then learned to minimize the perceptual error between predicted and target percept. Right: Human- in-the-loop optimization (HIL.O). Patient-speciffi parameters é of the DSE are optimized with user preferences: the patient performs a series of binary comparisons between percepts evoked with different encoders. New pairs of parameters to compare are adaptively selected so as to efficiently find the parameters maximizing the patient's preference. The target changes each iteration.
require extensive training to learn to interpret the evoked percepts, which are typically described as "fundamentally different" from natural vision 77. Moreover, phosphene appearance varies widely across patients S making personalized stimulus optimization major outstanding challenge (9].
Much work has gone into developing computational models that can predict the neuronal or perceptual response to an electrical stimulus [8] [10 [1]] (often called forward models). Once the forward model inverse, thereby identifying the required stimulus to elicit desired percept [12 However, these inverse models typically assume perfect knowledge of the speeift mapping from stimulation to perception (which is not practically feasible) and are heavily reliant on the forward model's accuracy over the entire stimulus space.
known, a deep neural network can approximate
Alternatively, Bayesian optimization has been successful in personalizing stimulation strategies for many existing neural interfaces [15 16). However, this approach is limited in practice because requires the stimulus dimension to be small (typically 30 117. which is orders of magnitudes smaller than the number of stimulus parameters in current implants), and optimization must be repeated for every stimulus. Moreover, visual prosthesis users can typically only give indirect feedback (c.g., verbal phosphene descriptions), unsuitable for traditional Bayesian optimization.
To address these challenges, stimulus inversion into a preferential Bayesian optimization strategy to learn a patient-specific stimulus encoder (Fig. T. First, deep stimulus encoder (DSE) is trained to optimize stimuli assuming perfect knowledge of a set of patient-specific parameters (Fig. [ left). Second, we embed the DSE within a numan-in-the-loop optimization (HILO) strategy based on preferential Bayesian optimization, which iteratively learns the ground-truth patient-specific parameters through a series of 'duels', where the patient is repeatedly asked their preference between two candidate stimuli. The resulting DSE can then be deployed as personalized stimulation strategy.
propose novel framework that integrates deep learning- based
To this end, we make the following contributions:
We introduce a forward model for retinal implants that achieves of-the response predic- tions. Unlike previous models, this allows us to train deep stimulus encoder to predict optimal stimuli across dimensions of patient-specific parameters.
We propose personalized stimulus optimization strategy for visual prostheses, where human- in-the-loop optimization (HII.O) Bayesian optimization algorithm iteratively learns the optimal speccnt- parameters for deep stimulus encoder.

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We demonstrate the viability of our approach by conducting a comprehensive series of evaluations on a population of simulated patients. We show HILO quickly learns a personalized stimulus encoder and leads to dramatic improvements in the quality of restored vision, outperforming exist- ing encoding strategies. Importantly, HIILO resilient to noise patient feedback and performs well even when the forward model is misspecified. Code for the forward model, DSE, and HILO algorithm is available at btttp::/ggthnn www.//ioniciiiionabbbooooooo//aa
Neur HILLO
2 Background and Related Work
Visual Neuroprostheses Numerous groups worldwide are pursuing a visual prosthesis that stimu- lates viable neuronal tissue in the hope of restoring a rudimentary form of vision people who are blind (Fig. [ left) [3 Analogous to cochlear implants, these devices electrically stimulate sur- viving cells in the visual pathway to evoke visual percepts (phosphenes). Existing devices generally provide an improved ability to localize high-contrast objects and perform hasic mobility tasks.
Much work has focused on characterizing phosphene appearance neuroanatomical parameters 2 [8]2]. In epiretinal implants, phosphenes often appear distorted due to inadvertent activation of nerve fiber bundles in the optic fiber layer of the retina [8] causing elongated percepts (Fig. 2 center). In addition, the exact brightness and shape of these clicited percepts depends on the applied stimulus [19] and differs widely across patients (Fig. 2 right). Granley et al. [ captured these individual differences by including a set of patient-specife parameters in their phosphene model, denoted by 6, which includes both neuroanatomical (e.g.. implant location) and stimulus-related parameters (e.g., how brightness scales with amplitude).
function of stimulus and
Deep Stimulus Encoding Many works attempt to mitigate distortions in prosthetic vision, but do
not describe comprehensive stimulation strategies [22 Those that describe strategies in detail typically require simplification (25] or strong assumptions (26] to be used in practice. Due to the complexities of optimization, deep learning-based stimulus encoders have risen in popularity [4)
In [2], authors proposed an innovative approach where the latent representations of an autoencoder are treated as stimuli and decoded with a phosphene model. However, they used an unrealistic binary phosphene model. Their approach has since been adapted for cortical models [27], and for non-differentiable forward models [13. Granley et al. (14] generalized the approach, showing it could work with realistic forward models across a small range of patients without needing to retrain.
Given forward (phosphene) model f (mapping stimuli to percepts given Φ), it is straightforward to show that the optimal stimulus encoder (mapping target images stimuli) the pseudoinverse of f [14. However, to account for the wide range of individual differences in phosphene perception, most realistic forward models are highly nonlinear and not analytically invertible. Thus, previous works have proposed to use the forward model [12 14 as fixed decoder within deep autoencoder trained to minimize the reconstruction error between target images and the predicted pereepts. After training, the encoder can be extracted and used to encode target visual inputs in real time. Deep
Inpler
Simulated Prosthetic Vision
Example Patient Variations
mitina
3
Miccoectrade
srepy
Retroged by
Tee
and caner
Figure 2: Left: Visual prosthesis. Incoming target images transmitted from camera to implant in the retina, which encodes the image as an electrical stimulus pattern. Center: Electrical stimulation (red disc) of nerve fiber bundle (gray lines) leads elongated tissue activation (gray shaded region) and a phosphene (bottom). Right: The same stimulus parameters may lead to widely varying visual perceptions in different patients. Adapted with permission from [4]
3

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stimulus encoders trained using this approach produce high quality stimuli, but assume knowledge of Ø. Additionally, the forward model f is not extremely accurate over the whole stimulus space, then the encoder network might learn to exploit inaccuracies in the model, producing stimuli that don't t generalize to real patients [4] We utilize an enhanced variant of this approach our experiments.
Preferential Bayesian Optimization Preferential Bayesian optimization (PBO) is an efficient method for optimizing expensive black-box functions based on binary comparisons (28 29 Since the subject's ss response to stimulation cannot be directly observed, PBO instead builds a Bayesian model of the subject's preferences, 9. typically modeled using a Gaussian process. An approximate inference algorithm (expectation propagation; (30) 31) is used to infer the posterior distribution of the preference function given binary comparison data, p(g) _). which is then used to select new configurations for the next trial according to an acquisition rule. The acquisition rule must balance the exploration-cxploitatiii trade-off inherent to any black-box optimization problem [32].
PBO was previously used to tune BCI stimulation parameters for transcranial 33 and spinal cord stimulation 34 However, these works directly optimized only handful of stimulation parameters and cannot translate to visual prostheses, where complex and varying visual inputs have to be mapped to high- digheniiinnii stimuli. To this end, Fauvel & Chalk [35] reduced optimization complexity by inverting a model of phosphene perception, then used PBO to generate encodings preferred by sighted subjects viewing simulated prosthetic vision. However, a linear approximation was used to invert the perception model, which is unrealistic for real-world applications.
Summary We identify 3 main limitations of previous work that this study aims to address:
Generalizability of deep stimulus encoders. Autoencoder-like deep stimulus encoders can accurately optimize stimuli, but require perfect knowledge of patient-specifer parameters [14. which can be difficult or impossible to determine in practice [T]. Further, these approaches heavily rely the accuracy of the forward model K [4], while real patients will likely deviate from the forward model. We overcome this limitation by optimizing the learned stimulus encoder based on patients' preferences, which we show not bounded by a misspecified forward model. Applicability of Bayesian optimization. Bayesian optimization is ideally suited for optimizing stimulation parameters based on limited, noisy measurements, but can only optimize small number of parameters [17]. We train deep stimulus encoder to output optimal stimuli for any specific patient with known parameters, reducing the search space from the entire stimulus space (hundreds or thousands of parameters) to the low-dimensional space of patient-specific parameters (13 parameters with our model), enabling Bayesian optimization.
Simplistic models of perception. Most previous approaches use overly simplified forward models that do not match empirical data g 19]. More accurate models [1 are too computationally expensive to support deep stimulus optimization over wide range of patients. We overcome this by developing a new phosphene model that matches patient data better than existing models, with significantly reduced memory and time complexity
3 Methods
General Framework We consider a system attempting to optimize stimuli for a new patient, specified by set of (unknown) parameters Φb. The goal of optimization is patient-specific stimulus encoder mapping target perceptual responses t (c.g., visual percepts) to stimuli s.
We assume there exists forward model f which predicts the patient's perceptual response to stimulation: f. = [s; Φ). It follows that the optimal stimulus encoder is the (pseudo)inverse of f. The inverse can be approximated using an autoencoder-like deep neural network, with f as the fixed decoder and f-1 as the learned stimulus encoder 14]. The encoder's weights w are updated using gradient descent to minimize the reconstruction error, measured by some distance function d, between the target t and the predicted response i averaged across patients and a dataset of targets (Eq.
w R arg min E., w t
[d(t. t)]
f = 8= ft Φ)
(2)

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Table 1: Patient-Specific Parameters +
Phosphene Model Parameters
Implant Parameters
(dva)
4g
91
4g
0g
04
OD₂ (jm)
OD2 (jo)
x (jm)
y (jm)
rot (deg)
Lower Upper
1.5
.45
9
.27
.42
005
-2
-0.5
3700
-500
-500
-30
8
.8
1.1
.57
.62
.05
.7
-0.1
4700
1000
500
500
30
Once trained, the encoder can accurately predict stimuli, but requires knowledge of the patient-specific parameters Φb. For new patient, Bayesian optimization used to optimize & based on user feedback, thereby learning personalized DSE. Since the patient's 's response cannot be directly measured for visual prostheses, the user is presented with a 'duel', i.c. a binary comparison, where they are asked to decide which of two candidate stimuli they prefer [35]. A Gaussian process model of preferences is updated based on the patient's response, and an acquisition function used to generate new candidate stimuli. The process can be repeated iteratively tune the DSE the patient's preferences.
The phosphene model is a differentiable approximation of the underlying biological system (also called forward model (14), which maps an electrical stimulus to a visual percept. Although phosphene models exist for visual prostheses, current models either do not match patient data well
Phosphene Model
g
10 19
or are too computationally expensive [1].
Thus, developed new phosphene model for epiretinal prostheses (See Appendix A for full details). The model takes in a stimulus vector s E IR specifying the frequency, amplitude, and pulse duration of biphasic pulse train each of n. electrodes. The output phosphene for each electrode is a Gaussian blob centered over the electrode's 's location pe (e( with covariance matrix (s. Φ) constructed so that the resulting percept will have area (e Ø). eccentricity (e Φ) and orientation 0e (Ø). These functions allow phosphene properties to vary locally with stimulus (e.g.. current spread) and anatomical parameters (e.g.. electrode location, underlying axon nerve fiber bundle trajectory). The percept for an electrode located at Mes is a multivariate Gaussian blob, renormalized have maximum brightness (s, Φ):
b(x, y) 2mbe det (E.) N( ")" (pee Ee),
(3)
where bes Me, and En are implicitly parametrized by s and db The covariance matrix Eg RE calculated from the eigenvalue matrix Eo and rotation matrix R:
oa 0
cos On sin 0g sin Og
En
R
32
cos Or
The cigenvalues ae and Be depend on the intended phosphene area (pe) and elongation (Ae):
2
Pe
32 = 2π
Pe
2T
X
Blobs from individual electrodes are summed into a global percept [36. Although the sum across electrodes is linear, modulating the size and eccentricity of phosphenes with stimulus parameters makes the final result nonlinear function of stimulus parameters, preventing analytic inversion. Motivated by previous studies, we used square 15 15 array of 150pm electrodes, spaced 400pm apart [14]. In total, the model is parameterized by 13 patient specific parameters, shown in Table [. The ranges for each parameter were chosen to conservatively encompass all observed patients,
centered on the mean value across patients 8 10
19 37
Deep Stimulus Inversion A deep stimulus encoder (DSE) is deep neural network responsible for approximately inverting the forward model to produce the optimized stimulus for a target image and a specific patient (s& = f- (t, o)) [14). We used network (45M parameters) consisting of blocks, each containing fully connected layers, batch normalization, and a residual connection. The architecture is illustrated in Appendix B.I The flattened target image and the patient specific parameters were passed separately through one block each, concatenated, and passed through another block, after which the amplitude is predicted. The amplitudes were concatenated to the prior intermediate representation, fed through a final block, after which frequency and pulse duration were predicted. The output layers use ReLU activation; all others use leaky ReL.U. During training, & were randomly sampled from the range of allowed parameters (Table Tp. Tensorflow 2. 12, an NVIDIA RIX 3090, Adam optimizer, and batch size of 256 (38 39) were used to train the network.
5

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Human-in-the-Lowee Optimization We propose using preferential Bayesian optimization (PBO) to optimize the patient-specific parameters & of the pretrained DSE. Given two sets of patient-specific parameters, Φ1 and d2,, we assume that the probability of a subject preferring Φ1 to Φ (returning a
response @1 > (b2) depends on a preference function g( modeled using a Gaussian process model:
p(11 > <219) = 4 (g(()) g(
where is the normal cumulative distribution 440 +T The larger the value of g( relative to g(02), the higher the likelihood that the subject reports preferring Φ1 over 22-
We used the Maximally Uncertain Challenge 42 select new comparisons to query, although other
popular acquisitions performed similarly (Appendix C.3). Searching within the bounds in Table I
this acquisition function selects a 'champion', Φ1, which maximizes the expectation of g. and 'challenger', 62, for which subjects' preferences are most uncertain:
Ø1 + arg max (1())))
(5)
2 arg max V ( ((d)))),
(6)
where V denotes the variance. This algorithm is designed to balance exploitation (values of ø that maximize 9) and exploration (values of & for which the response is uncertain).
The performance of PBO crucially depends the Gaussian process kernel and its hyperparameters, which encode our prior assumptions about the latent preference function. Inferring the kernel's hyperparameters online would slow down the algorithm and could lead to overfitting. Thus, adopted a transfer learning strategy, which could also be applied to real-life patients (see Appendices C.1 and C22 for full details and discussion of alternatives). In brief, for each of 10 patients (with parameters different from those used in the following PBO experiment), we simulated 600 random duels and fit candidate hyperparameters for each of 4 commonly used kernels. We then selected the kernel and hyperparameters that generalized best to the other 9 patients (measured using Brier score [3] on held-out test set). The 5/2 Matérn kernel performed best, and was used for all subsequent experiments.
Simulated Patients In silico experiments on simulated patients were used to demonstrate the viability of our approach. Each patient was assigned a set of patient-specific parameters o. uniformly sampled from the ranges specified in Table [ When challenged with a duel between two candidate stimuli S,, and s the simulated patient ran each stimulus through the phosphene model (using ground-truth patient-specific parameters), obtaining the predicted percepts ts, = [S01 Φ) and to = fs Φ). The users' preferences were modeled with a Bernoulli distribution, with probability p modulated by the difference in reconstruction error between each percept and the target image:
+ cxp( d(ts, .t))
Here, is a configurable parameter that scales the width of the sigmoid, introducing noise into the response, We set a to be 0.01, chosen empirically based on conservative estimate: when the error difference was greater than 0.01 it was obvious which percept was better to human observers.
Data and Metrics We used MNIST images as target visual percepts throughout the experiments. Images were resized to be the same size the output of f (49 x 49 pixels), and scaled to have a maximum brightness of (aligned with range(f)). Inspired by 12 14,, we used a perceptual similarity metrie designed to capture higher-level differences between images (44. Let by (t) be function that extracts the downstream representations of target t imput to a VGG19 network pretrained on ImageNet [45]. The perceptual metric is then given by equation
d(t, f) = [t]
(llt - i + 3 (t) - (t(
(8)
This metric was used by the deep stimulus encoder as a training objective, by the simulated patient to choose a duel winner, and throughout HILO as an evaluation metric. / = 2.5e-5 was selected via cross-validation (see [14] App. B). To aid interpretability, we also report a secondary metric based on how identifiable the predicted percepts were. We first pretrained a separate deep net to 99% test accuracy on MNIST classification. We then measured the accuracy of this classifier on the predicted percepts at every iteration of HILO.

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Target
Target
6
7
Naive
DSE
Naive
DSE
?
7
7
7
7
7
6
6
1
7
1
7
7
7
7
7
6
6
1
7
7
7
7
7
7
6
6
6
6
7
1 7
7
7
7
7
7
6
6
7
7
7
7
7
7
7
7
7
6
Figure 3: Percepts resulting from a naive encoder and the trained DSE for two example target images
across 25 randomly selected patients.
4
Results
4.1
Phosphene Model
To verify that our phosphene model's predictions line up with observed results from real prosthe- sis users, we repeated analyses from previous state-of-the-ar art models, evaluating how phosphene
appearance changes with electrode location [8] and stimulus parameters [TO 19 37
We used
the same datasets, consisting of thousands of phosphene drawings and brightness and size ratings collected across multiple epiretinal prosthesis (3] patients over several years. To evaluate phosphene appearances with electrode location, we calculated the correlation between predicted and observed phosphenes (R.) for three shape descriptors: area, eccentricity, and orientation. The final score reported is - -; R [ To evaluate how phosphene appearance was modulated by stimulus parameters, we calculated the mean squared error between the size and brightness of predicted percepts and patient ratings amplitude, fireuuency, and pulse duration were varied. The reported values correspond to Figures 4a-c and in [11].
Evaluation results are presented in Table 2 Our model significantly outperforms all baselinse on the Beyeler al. evaluation, and matches SOTA on the Granley er evaluations. Additionally, our model is on average 45x faster, and uses 120x less memory than [11] A detailed description of evaluation methods and additional analysis can be found in Appendix A.2
Table 2: Evaluation of Phosphene Model
Electrode Location
Stimulus Parameters
Model
S1
$2
4A
4B
4C
Nanduri et al.
19
37.3
19.5
294.8
11.1
72.9
160.9
Beyeler al.
2.43
7.07
1.15
215.6
108.7
5.52
190.2
Granley et al. Proposed
[
2.43
7.07
1.15
0.9
2.1
0.16
49.5
0.28
0.57
0.38
0.73
2.3
0.1
48.6
4.2 Deep Stimulus Encoder
We trained a deep stimulus encoder (DSE) to invert our phosphene model (decoder). The encoder was trained across 13 patient-specific parameters, randomly sampled at every epoch, including for the first time implant position and rotation. This is in contrast to previous DSEs, which either require can only vary two patient-specifer parameters [14].
retraining for every patient 212 1 27),
We compared the performance of the DSE to a traditional ('naive") encoder [14 currently used by retinal prostheses 3 illustrated in Fig. 3 The DSE achieved test perceptual loss of 0.05 and a MNIST accuracy of 95.6%, significantly outperforming the naive encoder (5.68 and 51 % respectively). Note that this performance is when the true patient-specific parameters known.
7

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A
Target
Target
Early Duel
1
prefer...
Late Duel
a
prefer...
2
B
C
100%
DSE-0
Naive
MNIST Accuracy
75%
DSE-
Error
DSE-0 Gues
50%
Nalve
0.1
25%
DSE-0
50
100
150
100 Number of Duels
50
150
Number of Duels
4
HILO
4
{
4
5
5
5
5
5 5 7
DSE-4
5
7
5
o
Nalve
$
$
$
5
Figure 4: Human-in-the-lowwe optimization of a deep stimulus encoder. A: Two example duels, from which patient preferences are learned. B: Reconstruction error throughout optimization across 100 simulated patients. Insets show the predicted percept resulting from stimulation with various encoders. Note the axis is on a log scale. C: MNIST accuracy of a pretrained classifier on reconstructed phosphenes. Both plots show smoothed median (window size of 3), with error bars denoting IQR. D: Example percepts after optimization for Naive, DSE without HILO, and HILO encoders for random patients. Note, brightness is capped for display for the Naive encoder.
This performance slightly better than the values reported in [14 (L1 loss of 108 .12 in despite training across 11 additional patient-specific parameters.
4.3 Human-in-the-Loop Optimization
We ran deep Cearning-based HILO for 100 randomly sampled simulated patients. After every duel, evaluated the DSE parameterized by the current prediction of patient-specifie parameters on a subset of the MNIST test set. The performance of the learned encoder over time ("HILO'') is illustrated in
Figure 4 which plots the joint perceptual loss (Figure 4 B) and MNIST accuracy (Fig. 4C).
As baselines for comparison used naive encoder, a non-personalized DSE where the patient- specific parameters are guessed (DSE-&Guusss) and an ideal DSE using the true & (DSE-OTrac) To guess di we consider two approaches, one which selects the midpoint from the ranges in Table [ and another where performance was averaged across random selections of Φ from the same ranges. In real patients, estimate that the performance of deep stimulus encoder without patient-specific optimization would likely fall somewhere between these two methods, since the distribution real patients might deviate slightly from Table [ We therefore plot the region bounded by the performance of a DSE with either of these approaches for guessing d. Example percepts after optimization are shown in Fig. 4D.
The HILO encoder starts with random predictions, but, after a short initial exploration period, quickly surpassed the baselines. After about 75 iterations, performance approached the ideal DSE encoder, however the HIL.O encoder still resulted high-quality percepts after as few as 20 iterations. Averaged across patients, the final reconstruction error of the HILO encoder .071 + .0031 (SEM)

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Noise Level
B
Thresholds 300% Off
Original
0%
26%
38%
48%
86%
DSE-2
DSE-4
DSE
0.1
DSE-P
Error
C
Axon Trajectories Off
Original
Out of Distribution
Original
DSE-9
DSE- Ques
Guas
DSE-0
DSE-0.
25
50
75
100
25
50
75
100
Number of Duels
Figure 5: Reconstruction error through optimization for noisy patient responses (upper left) and for various misspecifications in the forward model assumed by the DSE. Noise level denotes the percentage of duels where the decision was essentially random (p E [0.35, 0.65)), corresponding to o of le-4, 0.005, 0.01, 0.02, and 0.05, respectively. All y axes some error bars omitted for clarity.
log scales. Naive encoders and
and MNIST accuracy was 92% + 1.0%. DSE-OGuess had an error of between .25 and 1.1 and MNIST accuracy between 58.6 and 78.3%, and the DSE with true á had error of ,05 .001 and accuracy of 95.5% + 1%.
4.4 Robustness
In reality, it likely that patient's perceptions will not be perfectly captured by the phosphene model. Further, patient responses for visual prostheses are notoriously noisy [7] To test HILOO's resiliency these variations. we conducted additional robustness experiments, each with the same 25 simulated patients (Figure 5 First, we varied the noise parameter in simulated patients' decision making (Figure A). Next we constructed various 'misspecified' forward models, where the ground- model used to decode stimuli differed from the forward model assumed by the DSE. First, we varied the trajectories of the simulated axon bundles [47), thereby changing the orientation of phosphenes (Figure (C). Second, threshold amplitudes for stimulation are notoriously hard to predict, and have been shown drift by up to 300% over time 48)). Therefore, we tested variant where the threshold assumed by the encoder was incorrect by up to 300% (Figure Lastly, we used the same forward model. but with pptient-specific parameters outside the ranges in I (Figure 5D).
At r=1c-4, the patient response was noiseless. For equal to .005, .01, and .02, HILO performed similarly to the noiseless model, despite the patient on average making 'random' (p E [0.35, 0.65)) decisions in 26%, 38%, and 48% of duels. At ==0.05, the decision was 'random' 2/3 of the time, and HILO performed similarly or slightly better than the baseline DSE-éGuess- The DSE itself is very resilient to misspecifications in axon trajectory, so HILO performs similarly for this misspecification to the original patients. When thresholds varied, HILO still outperformed the baselines, but converged to slightly worse encodings than without misspecification Further, HILO surpassed the DSE encoded with the ground-truth db This demonstrates that even when the forward model assumed by the DSE incorrect, HILO still tends to converge set of patient-specific parameters that work well for the

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misspecified patient. For out-of-distributie o, HILO again outperformed both the baseline and true DSEs, but performed worse than in-distribution patients.
Discussion
Our experiments show that HILO optimization of deep stimulus encoder led to high-quality, personalized stimulation strategies that outperformed previous state-of-the of-the-art art techniques. HILO led increase in percept quality compared to using a non-personallzed DSE for 99 out of 100 simulated patients, demonstrating the viability of our approach. To enable our HILO algorithm, we also developed a new phosphene model, which is computationally simpler and matches patient data better than previous models, and trained a new DSE, which is able to produce high-quality encodings across all 13 dimensions of patient-specific variations included in our phosphene model. Together, these significantly advance state-of-the-an in patient-specific stimulus encoding, and are important steps towards pnactiaall--fesiibee personalized prosthetic vision in real patients.
The proposed framework combining Bayesian optimization and deep stimulus encoding offers significant improvements over both components in isolation. Use of DSE allows to incorporate prior information, reducing the dimensionality of the Bayesian optimization search space from the large stimulus space to the much smaller model parameter space. Our results demonstrate that even when the DSE's predictions are incorrect, this parameterization is still useful for Bayesian optimization based on patient preferences. Additionally, DSEs are able invert highly nonlinear forward models, enabling encoder-pant paaader-paameterizeed Bayesian optimization to be applied to a much larger set of problems. Lastly, the learned encoder can be applied for any target percept, without needing additional optimization. On the other hand, without adaptive feedback from HILO, deep stimulus encoders have method for learning the individual differences of new patient, which we show leads to suboptimal stimuli. DSEs rely on the accuracy of their assumed forward model over the entire stimulus space. We show that our approach produces stimuli that work well for the patient, even when the forward model is misspecified, or when the patient's 's responses are noisy.
This approach is practical for stimulus optimization in the wild. The encoder learned during opti- mization is lightweight, and once deployed, can predict individual stimuli in less than 5 ms on CPU, allowing for high frame rates for prosthetic stimulation. During HILO, updating the Gaussian process model and producing new stimuli on average took 3 seconds, meaning that stimulus optimization matter of minutes. HILO strategy could be bundled with future visual
could be performed prostheses, allowing for patients to periodically re-calibrate their devices when they feel the device is not performing adequately, without requiring a clinical professional.
Broader Impacts Although we demonstrate this approach in the context of visual prostheses, our framework is general and could be applied to a variety of sensory devices. Our approach is applicable when the stimulus search space is large and there exists a forward model mapping stimuli to responses. Forward models [49 (2) and deep stimulus encoders [53 55) have been successfully used across multiple sensory modalities, and could potentially be adapted for personalization with HILO.
Limitations Although promising, our approach is not without limitations. We assumed that the preference of patients for different stimuli is related to the distance metric used to measure perceptual similarity, which may not be true in practice. However, results by 351 suggest that PBO is robust to a mismatch between the distance metric used to invert the forward model and the preference of patients. Another limitation is that evaluation of our approach was only performed on simulated patients with a simulated perceptual model. However, this is mitigated by the fact that HII.O showed robustness to model inaccuracies. Still, since it difficult to predict the behavior of deep learning models, using a deep stimulus encoder in real patients could raise safety concerns. It may be possible for deep encoder to produce unconventional stimuli, potentially leading to adverse effects. However, most devices come with firmware responsible for ensuring stimuli stay within FDA-approved safety limits.
In conclusion, our results suggest that combining the strengths of deep learning and Bayesian optimization could significantly improve the perceptual experience of patients fitted with visual prostheses and may prove viable solution for a range of neuroprosthetic technologies.
10

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6 Acknowledgements
Research reported in this publication was supported by the National Library of Medicine of the National Institutes of Health under Award Number DP2LM014268. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.
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Appendix
A Phosphene Model
A.1 Methods
This section describes the phosphene model used to simulate patient's perception resulting from stimulation. The model takes in stimulus vector E RR x3 specifying the frequency (freg), amplitude (amp), and pulse duration (pdur) a biphasic pulse train on each electrode. In addition, the model also takes in vector of patient-specific parameters & (see Table I. We break these parameters down into implant parameters (æ, y, rol), global parameters (p, A, W. OD ODy), and stimulus-related parameters (dg-az); all explained below.
Exact implant locations vary patient-to-penn to-paiennt. The three implant parameters allow our model to account for these changes. We used simulated implant inspired by designs of real epiretinal implants 56 and those used in previous simulation studies [1]. consists of 225 disk electrodes (radius 75 um arranged onto a square, 15 x 15 grid with 400 pm spacing, initially centered over the fovea. The three implant-related parameters translate and rotate the initial implant be centered (r, y), and to be rotated by rot degrees. The implant used is depicted in Figure A.2 overlaid on top of
simulated map axon nerve fiber bundles
Original Implant
Example Rotation and Offset
2000
(microns)
superior
superir
Lesmpo
-4000
inferior
inferiar
X (microns)
[micronst
Figure A.1: The implant used for optimization, and an example implant after rotation and translation based on patient-specific parameters Φ The white circle on the right is the optic disc. Arced lines depict simulated axon nerve fiber bundles.
The remaining model parameters are inspired by various psychophysical and electrophysiological studies 8
10 18
19 58 and are summarized in the following list:
p Average phosphene size. This will be modified locally based on stimulus parameters.
Average phosphene eccentricity (a measure of phosphene elongation; not to be confused with retinal eccentricity). This will be modified locally based on stimulus parameters.
Orientation scaling factor. The orientation of phosphenes will be the orientation of the underlying axon bundle, scaled by w (Eq. 12).
ODz, ODy: The and location of the patient's optic disc, into which axon nerve fiber bundles terminate.
a0-a2: Coefficients to modulate phosphene brightness with stimulus parameters (Eq.
ag Coefficient to modulate phosphene size with stimulus parameters (Eq. TOp
04 Coefficient modulate phosphene eccentricity with stimulus parameters (Eqq
Fach electrode's location on the retina can be determined from the implant parameters. The cor- responding location in the visual field (p.) is determined using the retinotopic map described in
15

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Watson er al. [59]. Each electrode's phosphene orientation is then 0g wfaaonn where aaznn is the orientation of the axon nerve fiber bundle (NFB) underlying the cell (pixel), Axon NFBs are modeled as spirals originating at the optic disc and terminating at each simulated cell. These spirals follow a simulated axon map [4 based on tracings of axon trajectories in 55 human eyes. summary, phosphene size, eccentricity, brightness, and orientation are modulated based on stimulus parameters and implant location according to the following equations:
be ao (ampe)) ) + a2 (freq)
(9)
Pe p ag ampe
(10)
pdur
(11)
0.45
0. Oazon
(12)
The phosphene for each electrode is a multivariate Gaussian blob, centered at the electrodes location visual field (fe)), and with covariance matrix Σg constructed such that the resulting phosphene will have brightness be, size eccentricity λe. and orientation te. as shown in the following equations (repeated from main text for convenience):
b(x, v) 2Tb, det (E.) (V y]
|Pes Ee),
(13)
The covariance matrix E. REOR" is calculated from the eigenvalue matrix Eo and rotation matrix R:
a2 0
cos f. sin 0
sin 0g] cos 0,
Eg
R
0
32
The eigenvalues ae and Be depend on the intended phosphene area (p.) elongation (Ae), and constant (set to e 2
Pe 1 X
Pe 8² 2T In X
2x In
This formulation guarantees that the Gaussian blob, when thresholded using e, will have the intended area, orientation, eccentricity, and brightness.
Blobs from individual electrodes are summed into global percept. This linear summation is supported by recent studies, which have shown that percepts from multi mllti-elecctroe stimulation are often linearly related to the percepts from stimulation the individual electrodes (36). Although the sum across electrodes is linear, modulating the size and eccentricity of phosphenes makes the final result a nonlinear function of stimulus parameters, preventing analytic inversion.
A.2 Evaluation
Our model is motivated by similar anatomical and psychophysical phenomena as the previous state- of-the-art model for epiretinal prostheses [I1), but its formulation allows for favorable computational properties. In comparison, our model is average 45x faster run, and consumes about 120x less GPU memory. These computational benefits are the main reason a new model was necessary, and enables more advanced deep stimulus encoder by allowing training with larger encoder models, longer training duration, and larger batch sizes.
Nonetheless, we also verified that the model produces of-th--r predictions, as described in Section 4.1. Despite its similar design, our model achieves much better scores on the Beyeler er al. 8 evaluation for phosphene shape. This is likely because our formulation allows much tighter control of phosphene shape attributes (e.g., size, eccentricity), allowing (for the first time) positive R² on shape descriptors for held-out electrodes. Our model performs similarly to the previous state-of-the-art model on the Granley el al. [T] evaluation, which is to be expected given that the equations modulating phosphene appearance with stimulus parameters in both models are very similar.
16

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Fig. reproduce the plots from Figures 4A-C and of [T], but with our proposed model included. These higures show the brightness or size rating from Argus patient(s) stimulus parameters vary 19 37 in subjective units. For brightness, '0p means the same the reference pulse, '20' means twice bright, etc. For size, '1" means the same as reference pulse, '2' means twice as large (notation matching 11 19 3.
4A
4B
35
22
State-of-the-Art, MSE:0.93, R²:0.91
State-of-the-Art, MSE:2.07, 84:0.97
Proposed Model, MSE:0.73, R²:0.94
Proposed Model, MSE:2.31, R²:0.96
30
Brightness
Brightness
15
10
2
5
6
20
40
60
80
100
120
Amplitude
Frequency
4C
5
State-of-the-AAt, MSE:0.16, R²:0.97
50
State-of-the-AAt, MSE:49.48, R
Proposed Model, MSE:0.10, R2:0.98
Proposed Model, MSE:48.63, R2:0.62
Brightness
30
5ize
3
10
5
6
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
Amplitudc
Amplitude
Figure A.2: Evaluation of phosphene brightness and size as stimulus parameters vary. Reproduced from [1I, but with our proposed phosphene model included. State-of-the-art denotes the phosphene model from [1]. Units are subjective, in comparison to a reference pulse (i.e. brightness of 20 means twice bright, size of 3 means times bright) [99
17

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B Deep Stimulus Inversion
B.1 Architecture
The encoder architecture described in Section
is illustrated in Fig. B.1
Block (B)
FC
FC
FC
BN
1024
1024
1024
3
FC
Flatten
FC
1024
Target Response
FC
FC
FC
B
Freq
2024
Amp
Stimulus
FC
cp
BN
FC
Pdur
1824
Patient-Specific Parameters
Figure B.1: Deep stimulus encoder architecture. FC: fully connected layer, BN: batch normalization layer, B: block layers (shown top). Two arrows merging into one fully connected layer denotes concatenation. 45M total parameters.
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C Human-in-the-Loop Optimization
C.1
Kernel Selection and Hyperparameters
This section gives more details on fitting the hyperparametees' for the Gaussian process (GP) kernel used in preferential Bayesian optimization (PBO). As stated previously, the performance of PBO crucially depends on the GP kernel and its hyperparameters, which encode our prior assumptions about the latent preference function. To seleet hyperparameters, selecting hyperparameters that generalized best within a small validation group of simulated patients (see Appendix C.2 for discussion).
used transfer learning strategy,
We simulated 600 random duels (Ø1 and Φ2 chosen randomly) on each of 10 simulated patients. For each patient, we fit four commonly used kernels (Squared Exponential, Squared Exponential with Automatic Relevance Determination (ARD), Matérn 3/2, and Matérn 5/2) and inferred hyperparame- ters using type II maximum likelihood estimation [60]. The bounds for each hyperparameter were (exp(-10), exp(] For each these candidate serrel-hyperparamete pairs, we fit GP with corresponding kernel and hyperparameters to 50 training duels for each of the other 9 patients. Then, the performance of the candidate GP was evaluated on the remaining 550 data points using Brier score 43 commonly used metric measuring the accuracy of probabilistic predictions:
1 Σ yttrue Upred)
BS
(14)
where Vtrue is the true duel outcome (1 or O) decided by the simulated patient, and Upred is the probability of Φ1 being selected as the winner (corresponding to outcome of 1), as predicted by the Gaussian process.
The kernel and hyperparameters with the lowest Brier score, averaged across all 9 other patients, were selected (Matérn 5/2). To verify that this kernel performed well, we also ran human-in-the-looy optimization (HILO) for 20 random simulated patients, using the best hyperparameters for each of the four previously mentioned kernels. The results are shown in Figure C. The Matérn 5/2 kernel performed slightly better than the Matérn 3/2 kernel, and significantly better than the ARD kernel. While performance was similar to the Squared Exponential kemel, we ultimately selected Matérn 5/2 due to its lower Brier score.
Kernel Performance
ARD
Squared
Exponential Matern 3/2 Matern 5/2
2
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Loss
1
0.25
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60
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Figure C.1: Joint perceptual loss (y axis, log scale) plotted throughout HILO with different Gaussian process kernels. Error bars denote SEM.
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C.2 Hyperparameter Optimality
The Gaussian process kemnel hyperparameters selected with transfer learning strategy performed well in our simulations, leading to higher-quality patient-specific stimulus encodings (Figure ( This transfer learning approach was chosen match clinical setting, where limited human data availability. However, certainly possible that better performing hyperparameters exist. To investigate the optimality of our hyperparameters, we examine two other strategies: an ideal where pptienttoptimal" hyperparameters are used for each patient, and an online strategy where hyperparameters are updated during optimization with each patient,
Patient-optimal Hyperparameter Selection In this strategy, hyperparameters were precomputed for each patient by simulating 200 random duels. Kernel parameters were again fit using type II maximum likelihood estimation 66]. These ppttinttoppimal hyperparameters were then used during HILO for the patient.
2
transfer
patient-optimal
1
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Error
0.1
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0
25
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Figure C.2: Reconstruction error using Gaussian process kernel hyperparameters selected via transfer learning and "patient-optimal" strategies throughout HILO.
Optimization results for 20 random patients are shown in Figure patient-optimal settings led similar performance, and there was no significant difference between the final reconstruction errors (p > .05, two-sided paired t-test). Thus it seems the transfer learning strategy indeed selected hyperparameters that generalize well for new patients. Note that in general the transfer learning selection strategy more practically applicable than the patient-optimal strategy since it does not require a long calibration period, but the patient-optimal strategy is an alternative that could be used for the first human subjects when human data (only simulated data) is available.
Both the transfer and the
Online hyperparameters selection While it is common to keep kernel hyperparameters constant during optimization [33] 61 62). online optimization is alternative, where kernel parameters are periodically re-fit to the patient data during optimization. We tested online optimization where hyperparameters were recalculated with an update period of 1, 5, 10, or 20 duels, were never updated. In all settings, the initial hyperparameters were chosen using the transfer learning strategy.
The results for online hyperparameters optimization are shown in Figure C All update periods eventually converged to similar performance as with transfer learning strategy (i.e never updating hyperparameters) but since recalculating hyperparameters is costly, online hyperparameter updates increased the optimization time required to reach a desired performance (Figure C.3) right). This suggests that just using the transfer learning hyperparameters is a better strategy than online updates.
20

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HILO Performance
Time Needed Reach Performance
2
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None
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Error
Figure C.3: Reconstruction (left) and Bayesian optimization time required to reach specified reconstruction error (right) for HILO with online updates of GP hyperparameters.
C.3 Acquisition function
The acquisition function is responsible for choosing Φ1 and Φ2 for each duel, and must balance exploration of the search space with exploiting values of á that are expected to work well. The Maximally Uncertain Challenge (MUC) 42) acquisition presented the main text was initially compared against 2 other top-ranking 42 acquisition functions: Bivariate Expected Improvement (Bivariate EI) [63] and Dueling Upper Credibility Bound (Dueling UCB) [64]. In addition, we also compare against baseline acquisition, where Φ1 and d2 chosen randomly for each duel. We ran HILO for the same 20 random patients for each acquisition.
The joint perceptual loss throughout optimization for each acquisition is presented in Figure All of the tested acquisition functions dramatically outperformed the random baseline, which converged to value near the mean DSE without HILO. Although MUC and Dueling UCB performed similarly, we ultimately selected MUC due to its slightly lower final loss.
Acquisition Performance
Bivariate
Dueling
MUC
Random
Loss
M0nn
0.25
40
60
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Number of Duels
Figure C,4: Joint perceptual loss (y axis, log scale) plotted throughout HILO with different acquisition functions. Error bars denote SEM.
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C.4 Batch Bayesian Optimization
While the proposed Bayesian optimization strategy of sequentially presenting the user with stimuli would likely not be prohibitively time consuming (about 17 minutes with 100 duels, 10 seconds per duel), is possible that batch Bayesian optimization could speed up optimization. We consider two formulations of batch Bayesian optimizations: 1) the user selects their preference from a batch of stimuli each iteration, and 2) each duel still has only two options, but batches of duels are precomputed to save on updated the Gaussian process posterior and the acquisition function time between duels.
Option is theoretically more ideal, since more information acquired in each comparison would hopefully allow for fewer comparisons. However, this would require the patient remember an entire batch of stimuli before making comparison, and in practice phosphenes can be very difficult discriminate 77. It difficult evaluate the effect of this cognitive burden on simulated patients, and we thus leave it to future work to consider whether the parallelization of data acquisition would make up for the increased difficulty of the task.
Therefore, option 2 was tested by precomputing batches of 1 (i.e. original), 3, 6, or 10 duels at a time. We used a batch variant of the maximally-unceraa challenge acquisition function 42 Results for 20 simulated patients are shown in Figure C.5 Precomputing batches reduced the optimization time required reach desired performance, but the cost of requiring more duels. In practice, the optimal batch size could be determined by balancing the time required per duel with the time required for optimization. Faster acquisitions (e.g. KernelSelfSparring 665 could further reduce optimization time.
HILO Performance
Time Needed to Reach Performance
2
350
Batch Size
Batch Size
1
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Error
150
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25
50
75
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0.24
0.18
0.12
0.06
Number of Duels
Erro
Figure C.5: Reconstruction error (left) and Bayesian optimization time required to reach specified reconstruction error (right) for HILO with different batch sizes.
C.5 Baselines and Robustness
In this section, we provide further details for the naive encoder we compared against, and the robustness experiments.
Naive Encoder The naive encoder is the encoding strategy currently used in commercial epiretinal prostheses 3 This encoder operates under the assumption that each electrode can be thought as a pixel in an image. The optimal stimulus under this assumption is therefore simply downsampled version the target image. The frequency and pulse duration are constant across all electrodes. This naive encoder has been previously shown to be suboptimal [14), but we still include it comparison the currently used encoding strategy.
In section 4.4 we evaluate the robustness of human-in-the-lone optimization (HIL.O) to misspecifications in the forward model. Here, we provide specific details on the implementation of these misspecifications, and how we adapted the baseline encoders to the misspecified scenarios.
Robustness
22

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Axon Trajectories: The simulated axon map from [4 has two parameters, fins and Soup- which control the axon trajectories in the inferior and superior retina, respectively. [47 also
reports the observed ranges for these parameters: Paup 122.5, -1.3 1.3] and āng E [0.1. 1 1.3]
The unmodified model uses the centers these ranges. Under misspecification, we randomly set both Ssup and finf to one of these bounds for each patient.
Threshold is the amplitude at which a phosphene becomes visible to a patient 50 % of the time. In epiretinal prostheses, thresholds are notoriously noisy, and vary significantly across electrodes, patients, and over time [48]. While some progress has been made towards predicting these thresholds [66]. most state-of-the-ar models assume that thresholds are known.
Thresholds:
With this misspecification, the assumed threshold on each electrode modified by random but systematic amount. Specifically, the threshold on each electrode was randomly selected to be between -x and 2x its original value for the 100% condition and between 1 and 4x its original value for the 300% condition.
is also possible that new patient does not fall within our assumed ranges. Thus, we tested variant where the true patient-specific parameters & were sampled from outside the ranges Table [ Specifically, each parameter was sampled to be 0-50% above or below the specified range (some parameters were clipped to stay within defined ranges, egg., À cannot be outside of [0, 1)).
Out of Distribution:
During HILO, the acquisition functions have specified bounds that constrain candidate ø We therefore tested two variants, one where PBO was allowed expand the bounds, and another where it was confined to within its original bounds. The end results were similar in terms of DSE performance, so the variant with its original bounds is presented in the main text.
DSE-QGuess is our best approximation of what a DSE would guessed patient-specific parameters would perform, and is bounded by the performance of DSE with mean é, and random from the ranges in Table [ encoded with the same as in the unchanged patient, but since the phosphene model for the patient is changed, the resulting loss is different. DSE-cTrue is still parameterized with the patients true o, however, the true é are longer perfect description of the misspecified patient. This is shown by the fact that HILO surpasses the true encoders performance: under the misspecified model, there exists some other é which leads to pereepts with improved perceptual quality when decoded using the misspecified phosphene model, compared to those encoded with the true ó. This highlights the robustness of optimization based on user preferences.
For each of the misspecifications, the mean and random ø baseline DSEs are still
23


Reviews:
[{"review_id": "V3qTL3N3F5", "reviewer": "Reviewer_YFQD", "summary": "* This paper proposes a flexible framework addressing personalized stimulus optimization predominantly seen in _visual prostheses_. \n* The authors propose integrating the state-of-the-art deep learning with a preferential Bayesian Optimization (BO) strategy to learn optimal patient-specific parameters in fewer trials. \n* The proposed approach is a two-stage process, with the first stage aiming at learning a Deep Stimulus Encoder (DSE) to optimize stimuli, and the second stage aiming at embedding the DSE learnt in the first stage in a sample-efficient preferential Bayesian optimization strategy.", "questions": "* Line 159: What does $n_e$ stand for? number of electrodes?\n* Line 169: What is the significance of threshold $\\epsilon$ and why authors have set it to $e^{-2}$? \n* Line 198: Why do authors considered only 10 simulated patients for transfer learning? is that not sparse? \n* Line 200: The hyperparameters considered and their bounds are neither mentioned in the main paper nor in the supplementary material. Could authors confirm the hyperparameter set of each kernel?\n* Line 214: The noise parameter s is set to be $\\frac{1}{0.01}=100$, whereas in Line 285, s is set to 1e-4, is this a typo or it is $\\frac{1}{1e-4}$?\n* Line 221: What is the significance of $\\beta$ in equation (7)?\n* Line 235: What does $R_i$ stands for? Is $i \\in$ {$ 1,...,n_e$}?\n* Line 239: Why authors have not considered comparing their empirical results with Beyeler et al. 2019?\n* Line 250: How do the results compare with Granley et al. 2022 if L1 is used in computing the test loss for DSE?\n* Line 302: Could Batch-BO strategies further reduce the latency and thus provide a quicker solution by parallelizing the data acquisition?\n* Figure 3: Why there is an increasing (or decreasing) trend in loss (or accuracy) plot during the initial phase of the optimization?\n* Figure 4: Why there is a lot of variance in the bottom right plot for \"Out of Distribution\" misspecification?\n\n\nFollowing are the minor (typographical) errors, that needs to be fixed.\n\n* Inconsistent referencing style and hyperlinks are missing throughout the paper. It is strongly suggested to not modify the style files provided by NeurIPS.\n* Line 59: \"...visual prostheses that, where ....\" \n* Figure 2: The current font size in the Leftmost plot is illegible.\n* Line 151: The section/Sub-section number has to be clearly mentioned. \n* Line 204: Provide a quick reference to the Brier score in the main paper, even though it is mentioned in the supplementary.\n* Line 237: \"ratings as amplitude, frequency,....\"\n* Line 259: :...  perceptual loss (figure 3.B)....(figure 3.C)\"\n\n**References**\n\n* Michael Beyeler, Devyani Nanduri, James D. Weiland, Ariel Rokem, Geoffrey M. Boynton, and Ione Fine. A model of ganglion axon pathways accounts for percepts elicited by retinal implants. Scientific Reports, 9(1):1–16, June 2019.", "limitations": "* The optimization performance of PBO crucially depends on the _ generalization performance of the inherent GP surrogate model_. Authors reduce latency by avoiding online inference and instead use a transfer learning strategy. However, the source considered in the adopted transfer learning uses sparse data generated from 10 patients, thus, raising concerns about the optimality of kernel parameters and generalizability of the GP surrogates.\n* Although the authors discuss the empirical results, the lack of sufficient experiments and competing baselines (Beyeler et al. 2019, Granley et al. 2022) in the empirical results makes it hard to conclude the superiority of the proposed approach. (Please refer to the Questions section).\n* Sequential PBO may not be very suitable in time-critical situations, thus, more efficient strategies such as batch-BO could be of great use to reduce the possible latency in finding the optimal stimuli on-the-fly.\n\n**References**\n\n* Michael Beyeler, Devyani Nanduri, James D. Weiland, Ariel Rokem, Geoffrey M. Boynton, and Ione Fine. A model of ganglion axon pathways accounts for percepts elicited by retinal implants. Scientific Reports, 9(1):1–16, June 2019.\n\n* Jacob Granley, Lucas Relic, and Michael Beyeler. Hybrid Neural Autoencoders for Stimulus Encoding in Visual and Other Sensory Neuroprostheses. October 2022.\n", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "* This paper aims at advancing the state-of-the-art in sensory neuroprostheses that have a significant impact on the present world.\n* The authors propose to overcome the strong assumptions made on the accuracy of the knowledge on patient-specific parameters, thus aiming to improvise the accuracy of the deep stimulus encoder by optimizing the stimuli.\n* The authors use a sample-efficient Bayesian optimisation (Human-in-the-loop Optimization (HILO)) method to optimally select the patient-specific parameters used in deep stimulus encoder. \n* Authors have empirically evaluated the proposed approach in optimizing the personalized stimulus encoder for several simulated patients.\nFurther, the authors evaluate the performance of their method when the preferential inputs are noisy, thereby proving its robustness.\n", "weaknesses": "* The main weakness of this paper lies in its _limited novelty_, as the proposed approach is merely a _combination_ of the state-of-the-art of forward models and sample-efficient Bayesian optimization to optimally find personalized stimuli. \n* Although this paper improvises the techniques used in the visual prostheses domain, the overall contribution of this paper is in the _application of the existing ML/DL techniques_ in neuroprostheses, visual prostheses in particular, thus may not advance the state-of-the-art in ML/DL community. \n* Though the paper reads well in many parts, it demands significant knowledge/domain expertise in visual prosthesis for a thorough understanding of the paper. \n* Authors have missed defining/describing a few important mathematical quantities or parameters that break the flow of understanding and also raise questions about its reproducibility (Please refer to the Questions section).\n* The details provided in _Section 4_ give the impression that the proposed framework is tightly coupled with the problems in visual prostheses. \n* The authors have discussed a few experimental settings in Section 4 that are apt to discuss in Section 5, though they do not contribute to the proposed method.\n* The visualization schemes used to show the empirical results do not effectively demonstrate the superiority of the proposed approach. Also, the authors do not discuss in brief the trends and the possible reasons behind them. \n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We are grateful for the reviewer’s attentive analysis and helpful feedback. \n## Weaknesses/Limitations\n> The main weakness lies in its limited novelty, as the proposed approach is merely a combination of state-of-the-art forward models and Bayesian optimization.\n\nAs the reviewer points out, our work builds on several previous ideas. However, combining these ideas into a realistic HILO scheme required significant improvements to each individual component, as well as complex design choices to integrate components into the optimization framework. Our specific points of novelty are:\n- A HILO strategy combining PBO with deep stimulus encoding. Our DSE was trained to output optimal stimuli conditional upon a latent set of patient-specific parameters, allowing PBO to optimize the latent parameters instead of the high dimensional stimuli. This unique combination addresses the main limitations of previous approaches to HILO in BCI: reliance on simplistic encoders [30] or very limited optimization dimensionality [55-61]. HILO proved highly effective, improving phosphene quality and robustness (Figures 3, 4).\n- A new phosphene model, which matches patient data significantly better (revised Table 2) and improves computational efficiency (~50x faster, ~120x less memory than [14]).\n- A significantly improved DSE, which performed better than the SOTA (.108 vs .12 L1 loss) [14], despite having realistic (13 vs 2) parameters of patient variations. Previous approaches require retraining for new patients, preventing HILO. \n\n> This paper … may not advance state-of-the-art in ML/DL\n\nWe agree advances in this paper mainly benefit the neuroprosthesis and BCI communities. Thus, this paper targets the “Neuroscience and cognitive science (e.g., neural coding, brain-computer interfaces)” track in the call for papers.\n> ...the proposed framework is tightly coupled with visual prostheses.\n\nWhile our implementation is specific to visual prostheses, the proposed framework of 1) building a forward model, 2) training a DSE across patients and 3) learning optimal patient parameters is not domain specific. Forward models [48-51] and DSEs [52-54] have been developed for multiple sensory modalities and could potentially be adapted for HILO. \n> GP Hyperparameter Optimality\n\nThe reviewer raises an excellent point. We consider it a strength that HILO worked using only 10 transfer learning patients, which was chosen to match clinical settings with limited human data availability. To test optimality we ran HILO again, finding hyperparameters for each patient prior to optimization using 200 random duels. Using these ‘patient-optimal’ hyperparameters, HILO performed similar to the transfer approach (Fig R3). While keeping hyperparameters constant is common [57-60], online optimization is an alternative method. We tested this using update periods of 1, 5, 10, or 20 duels (Fig. R1). All update periods eventually converged to similar performance as with transfer learning, but required more optimization time. Together, these suggest that transfer learning is a good strategy for HILO.\n> Comparing results with Beyeler 2019 [8]\n\nAlthough the previous SOTA model [11] is a simple improvement to [8], we agree that readers unfamiliar with these details would benefit from a direct comparison and have added additional baselines to Table 2 (see pdf).\n> Batch BO\n\nWhile sequential BO would be quick (~17 minutes with 100 iterations, 10 seconds each), batch-BO indeed could speed up optimization. We consider 2 options: 1) the user compares a batch of stimuli in each iteration, and 2) batches of duels are precomputed, to save on acquisition time between duels. While 1) acquires more information per response, patients must remember multiple stimuli before making comparisons, increasing cognitive burden. Future work might consider whether parallelization of data acquisition makes up for the increased difficulty. We tested 2) using batched MUC [40] with 1, 3, 6, or 10 duels (Fig R3). Batched MUC reduced acquisition time required to reach a desired performance, at the cost of requiring more duels. In practice, batch size could be determined by balancing patient response and acquisition time. Faster acquisitions (e.g. KernelSelfSparring [64]) could further improve this time.\n## Questions \n> What does $n_e$ stand for?\n\nNumber of electrodes\n> What is the significance of $\\epsilon$, why $e^{−2}$?\n\nThe phosphene model is derived so an electrode’s phosphene will have area (#pixels > $\\epsilon$) of $\\rho$. $e^{-2}$ was chosen based on thresholds in [11]. \n> Could authors confirm the hyperparameter set?\n\nFor lack of space, we refer to [4] supplementary 4, who used the same kernels and hyperparameters (lengthscales and scaling factor), each with bounds of [exp(-10), exp(10)].\n> s is set to be 1/0.01, whereas in Line 285, s is set to 1e-4, is this a typo?\n\nYes, the referenced quantity should be 1/1e-4. We will modify Eq 6 and update notation through the paper. \n> What is the significance of $\\beta$ in Eq 7?\n\n$\\beta$ controls the weighting between MSE and VGG extracted features. See [14] App B for discussion.\n> What is $R_i$?\n\n$R_i^2$ is the coefficient of determination ($R^2$) for the ith shape descriptor (area, eccentricity, orientation). See equations 10-13 in [8] for more details. \n> Why is there an increasing trend in loss during the initial phase of optimization?\n\nThis is a common pattern in PBO (e.g. Fig. 5 in [22]). The estimate of the maximum of the GP mean (Eq. 4) rapidly changes in initial phases of optimization, meaning the optimum estimate might worsen. This is in contrast to noise-free approaches, where the maximum is taken over previously sampled points and guaranteed to never worsen performance. \n> Why there is a lot of variance for OOD misspecification?\n\nNote the smaller y axis on the OOD plot, causing variance to appear larger. We have improved the visualization to use uniform scaling, showing similar variance for OOD patients (Revised Fig 4).\n"}, {"review_id": "XdITe0Xv8d", "reviewer": "Reviewer_bw3i", "summary": "In this work, the authors proposed a pipeline for optimizing the deep neural network based encoder, which is to generate visual stimulus for neuroprostheses. The pipeline considers human-in-the-loop optimization. The authors use preferential Bayesian optimization techniques to reduce the number of queries to the human making the decision. The major contributions claimed by the authors are as follows:\n1. Introduced a forward model for retinal implants suitable for fast simulation experiments.\n2. Proposed a personalized human-in-the-loop (HILO) patient-specific stimulus parameter optimization strategy using preferential Bayesian optimization.\n3. Demonstrated HILO can quickly learn personalized stimulus encoder and the robustness of HILO, on simulated patients.\n", "questions": "1. The simulated patient has access to t, which is the target percept or ground truth. Is it realistic to assume the blind person could have access to that? \n2. In line 219 it’s written that the metric in equation (7) is also used to train the deep stimulus encoder (DSE). So the encoder’s parameters are getting updated in a rather conventional way as in the visual prosthesis literature. How to distinguish the contribution between the improvement of the encoder and the selection of patient-specific parameters? Could it be that the update of the encoder contribute the most? Ablation studies might be needed.\n", "limitations": "Other than the concerns listed in the weakness and question sections, the limitations mentioned in the work are adequate. ", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Originality and significance:\nAs far as I know, this work is the first work in considering the patient-specific stimulation parameter calibration problem for visual neuroprostheses that does not assume direct access to the output of the forward model. Instead, the authors introduce the technique of human-in-the-loop training with preferential Bayesian optimization in the pipeline. This setting is steps more realistic than previous works. \n\nQuality and clarity:\nThe writing in general is very structured and easy to follow.\n", "weaknesses": "1. It is not made super clear whether and how the parameters w of the encoder is being updated in the manuscript. \n2. The authors could have demonstrated a small amount of humans with sight to show the effectiveness of this optimization method. \n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We are grateful to the reviewer for their encouraging comments and thoughtful questions. \n## Weaknesses\n\n> 1. It is not made super clear whether and how the parameters w of the encoder is being updated in the manuscript.\n\nWe apologize for any confusion, and will update the paper with improved notations and clarity in this regard. During DSE training, the weights $w$ of the encoder are updated using standard gradient descent with the Adam optimizer. The loss function minimized during training is the reconstruction error between target images and the predicted percepts resulting from stimulation (Eq 7). Thus, the encoder learns to output optimal stimuli for given target images for the input patient specified by $\\phi$. This all occurs before HILO begins. During HILO, the weights of the encoder are held constant, and are not updated. The only parameters optimized during HILO are the patient-specific parameters $\\phi$, using the PBO strategy described in the paper. \n\n\n> 2. The authors could have demonstrated a small amount of humans with sight to show the effectiveness of this optimization method.\n\nWe agree that this would have been an ideal way to verify whether our simulated subjects make decisions in the same way humans do. Unfortunately a human subjects experiment was outside the time and scope of this project. However, in [30], authors also conducted PBO on sighted humans in a similar, albeit much less realistic setting. Despite using a linear decoder and unrealistic phosphene model (as opposed to our deep neural network encoder and realistic phosphene model), their results still showed that PBO could be used with sighted humans viewing simulated prosthetic vision.\n\n## Questions\n\n> 1. The simulated patient has access to t, which is the target percept or ground truth. Is it realistic to assume the blind person could have access to that?\n\nThe reviewer raises an excellent point. With human patients, the subject indeed could not directly observe the target t. However, the user could be informed indirectly of the target, either verbally (e.g. asking ‘which looks more like the number 5’) and/or with tactile targets the subject could feel. In [30], authors demonstrated this with human subjects, who were only verbally told the target image. \n\nWe do note that communicating targets with verbal or tactile representations would be limited to targets simple enough to communicate to the patient during training, such as letters, numbers, or simple objects. However, perception of simple stimuli would still be a huge improvement for current devices, which currently barely support letter recognition without prolonged head scanning [63]. Further, prior work ([12, 14, 36]) demonstrated that DSE’s also improve performance for natural images. We leave it as a question for future research, to determine how encoder improvements from HILO with simple stimuli transfer to more complex visual scenes.\n\n> 2. In line 219 it’s written that the metric in equation (7) is also used to train the deep stimulus encoder (DSE). So the encoder’s parameters are getting updated in a rather conventional way as in the visual prosthesis literature. How to distinguish the contribution between the improvement of the encoder and the selection of patient-specific parameters? Could it be that the update of the encoder contribute the most? Ablation studies might be needed.\n\nThe reviewer is correct that the metric in equation (7) is used to train the DSE prior to HILO. During HILO, however, the DSE parameters are held constant, and only the patient-specific parameters $\\phi$ are modified. Therefore, all of the performance improvements shown in the figures are due to the selection of patient-specific parameters.\nThe other DSE baselines (marked as mean and random in the submitted Figure 3 and 4) are meant to serve as a sort of ablation, illustrating what performance would be like if only the DSE were used, without updating the patient-specific parameters.\n\n"}, {"review_id": "zuC5fUhRl4", "reviewer": "Reviewer_HJZJ", "summary": "The authors present a method to improve perceptions for patients using visual prostheses using a combination of a deep learning encoding model and a patient-specific tuned set of parameters for stimulation learned via preferential Bayesian optimization. They use simulated data and patient choices to demonstrate the method’s performance across a range of possible patient types and noise considerations. \n\nETA: After review and rebuttal, raising my score from a 5 to a 6. ", "questions": "i.\tLine 43 says <30 is too few parameters, but then the authors used only 13 dimensions of parameters? \nii.\tLine 129-130 appears to have a sentence cut off abruptly.\niii.\tLine 127: BO can’t optimize more than a small number of parameters -- clarify please? BO gets difficult in high dimensions, but this is true of many methods. How specifically does the DSE reduce this? \niv.\tClarify the issue in lines 154-158. The logic is not clear what the exact problem is and how it is solved here. \nv.\tIf you didn’t restrict the range of parameters in Table 1 as heavily, would it still find the optimal values? E.g. if you increased the range by a factor of 2. \nvi.\tLine 232 first mention of Argus II, needs explanation and citation. \nvii.\tWhat does it mean to outperform the true DSE? Line 289\nviii.\tLine 296 how does the approach fail?", "limitations": "The authors addressed some limitations in the discussion, noting some drawbacks of predicting the behavior of deep learning algorithms but that hardware-engineered safety constraints would provide patient protection. ", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "Originality: This work presents a nice combination of deep learning and Bayesian optimization. Each component of their approach (phosphene model, encoding model, and parameter optimization) has in general been done before, but here the authors modify each element and combine them to overall improve performance. The phosphene model is described as a new model with performance exceeding current SOTA. This was then combined with a deep stimulus encoder (DSE) to yield performance comparable to other methods. Finally, their human-in-the-loop (HILO) method to tune parameters using PBO was used to iteratively improve the DSE per patient. \n\nQuality: In general the work is well-sourced and supported from many previous works. The benchmarking and evaluation of performance was good, and the authors compared to similar methods. The code in particular was very well written and documented.\n\nClarity: Overall well-written, well-sourced, nicely explained work. There were some points of confusion or ambiguity mentioned below. \n\nSignificance: This kind of patient-specific tuning of stimulation for visual prostheses is certainly needed, and the authors do good job of demonstrating the significance of their contribution. The authors also suggest it could be used in other areas beyond visual stimulation, but with the results being tied closely to the patient-specific parameters in Table 1 it is unclear how broadly this method might be applied.  ", "weaknesses": "The primary weakness is the reliance on simulated data, and it is not clear that simulated patient choice or patient parameters to generate the data was sufficiently grounded in experimentally collected datasets. There is some discussion of how the ranges for the parameters were chosen in their simulated data, but nothing about the expected variability and how these parameters were determined in the first place (is it considered ground truth? were patient preferences included?). If the method is sufficiently generalizable to many populations of patients, as expected, then why not simulated patients outside of those limited ranges in Table 1? Lines 263-265 appear to suggest that their ranges of parameters are unlikely to be same as in the real world. A similar concern is for simulating patient preference, but here the authors' simulations (up to 33% incorrect decisions from the patient) appear like a robust demonstration. \n\nOne other weakness not discussed is the feasibility of their approach for actual human patients. Even if it only takes 3 seconds to update the GP and generate new stimuli, the patient must sit through and compare difficult to discern visual percepts for 100 duels. Is it likely the patient would persist? Does their judgement change over time? If this could be changed every so often, does the system need re-tuning for all ~100 duels at once? Additionally, humans see visual scenes with certain image statistics -- so MNIST may not be a reasonable or sufficient dataset for testing human perception on. Could this approach be extended to natural images, including color? \n\n\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their positive review and insightful analysis. \n## Weaknesses\n> Simulated Data and Patient Ranges\n\nWe agree that proper selection of patient parameters is crucial for realism. The process of choosing these ranges of patient parameters was complicated by the variety of data sources [8,10,11,18,19,37,62], each using very different experimental setups. \nWe used fits from the mentioned sources, based on psychophysical tasks such as drawings and brightness ratings, to obtain a distribution of possible values in patients. Our ranges were chosen empirically to encompass all observed patients with a wide additional margin (~2x the observed distribution), adjusted to be within allowed boundaries (e.g. $\\lambda$ cannot be larger than 1). \nTherefore, the ranges in Table 1 are actually quite wide, more than account for all reported data, and only appear small due to the units. For example, $a2$ goes from 0.005 to 0.025, meaning that a frequency increase from 20 to 120 Hz would lead to a percept being between 1.5x and 3.5x as bright, a larger range than observed in patients [19].\nUnfortunately, we do not have time to retrain our DSE and run experiments again with increased ranges. However, HILO still led to large improvements for out of distribution patients (even without retraining, Fig 4), so we do not expect patients outside our ranges to prevent HILO from performing well.\n> 263-265 suggest that their ranges of parameters are unlikely to be same as in the real world.\n\nWe only included this to acknowledge that any estimate is likely slightly different from reality. The only result that depends heavily on these ranges is the mean DSE baseline, which uses the mean value of the reported ranges as the guess for $\\phi$. This is of course expected to work better on our simulated patients (from the exact same range) than on real patients (likely a similar, yet slightly different range).\n> Practical feasibility, changing perception, and natural images:\n\nThe reviewer raises interesting questions. Based on the difficulty of standard clinical tasks [63] often involving hundreds of trials over multiple hours, we do not expect HILO to be too difficult. We also note that our method showed clear performance improvements after only 20 duels. Prior work suggests that phosphenes remain relatively stable over time [46]. If perception changes, HILO is short enough (~17 minutes if all 100 duels are needed, 10 seconds per duel) that it could easily be performed again.\nThe reviewer is certainly correct that perceiving MNIST digits is not the eventual goal of visual prostheses. However, seeing even simple characters without prolonged head scanning would be a significant improvement in perception for existing devices [63]. DSE’s have already shown improvements for natural images [14,12], which could enable a similar approach to ours with complex targets. Unfortunately, detailed color perception is not possible with current visual prostheses [47].\n\n## Questions\n> Line 43 says <30 is too few parameters...\n\nThis is saying that PBO conventionally requires less than 30 parameters.\n> Line 127: BO can’t optimize more than a small number of parameters -- clarify please? … How specifically does the DSE reduce this?\n\nAlthough many optimization methods become difficult in higher dimensions, PBO quickly becomes inefficient with more than ~30 parameters [17]. In contrast, DNNs excel at high dimensional optimization. Our stimuli are high dimensional: 225 electrodes, each with 3 stimulation parameters. Further, we want to optimize stimuli not just for one target image, but for any target image in the training set. This is a regime where direct BO is clearly not possible. \nOur DSE is first trained to output optimal stimuli for any input patient (specified by $\\phi$). Then, BO is used to infer $\\phi$ for a new patient. Once known, the DSE can produce optimal stimuli for that patient. $\\phi$ is low dimensional (13 parameters), and thus is a suitable candidate for BO, whereas the original stimulation pattern (675 parameters) is not. Thus, the DSE takes care of the high-dimensional optimization, while BO incorporates human feedback.\n> Clarify the issue in lines 154-158...\n\nWe apologize for the confusion. The problem with existing phosphene models (besides inferior performance) is that they are too slow for gradient descent and too large for GPUs. We also observed that training over large ranges of patients with previous models was unstable and did not converge. Lines 154-158 are some potential reasons for this, but ultimately it is an open area of research (effects of nonstandard NN functions on gradient loss landscape). Since we are uncertain in this regard, we will remove these lines.\n> Line 232 first mention of Argus II...\n\nWe apologize for the omission, and have added a citation and explanation. Argus II is the most successful commercial visual prosthesis, with ~300 users [3], and was used to collect the data used for Table 1.\n> What does it mean to outperform the true DSE?\n\nFor patients whose perception is precisely predicted by our phosphene model, the DSE with true $\\phi$ is likely the ideal encoder for HILO. In reality no phosphene model is perfect, so it’s important for encoders to work when the assumed model is misspecified. For these patients, the true DSE is no longer guaranteed to be optimal, because the DSE was trained on non-misspecified patients. Our revised Fig 4 better illustrates that the True DSE performs worse on misspecified patients, while HILO performance is not as affected. HILO allows for users to guide optimization towards encoders that perform well for their misspecified forward models, a strong indicator that HILO is robust and has the potential to work on real patients.\n> How does the approach fail?\n\nFor 1 of the 100 patients, HILO led to a final performance that was between the mean and random DSE baselines, but still an improvement over the naive encoder used by Argus II.\n\n"}]

Author rebuttal:
We thank the reviewers for their thoughtful analysis and feedback, which has been invaluable for understanding how to improve our paper. We are pleased that reviewers in general agreed on the paper’s significance towards realistic optimization of prosthetic vision, and that it advances state of the art in this domain (YFQD, bw3i, HJZJ). We are also glad reviewers found HILO to be “steps more realistic than previous approaches” (bw3i), well evaluated (HJZJ), and robust (YFQD). While general ideas behind individual components of our algorithm have been proposed in isolation (phosphene model, deep stimulus encoding, PBO), most reviewers recognized the novelty and practical feasibility of our approach, which improves each component while integrating them into a realistic and efficient optimization pipeline (bw3i and HJZJ). Reviewers raised thoughtful questions about Batch BO and BO hyperparameters (YFQD), use of simulated data (HJZJ), and the feasibility of the approach on human patients (bw3i, HJZJ). 

In the following responses, we address each of the reviewers’ questions and concerns in detail. Additional experiments were conducted regarding batch Bayesian optimization and optimization of GP kernel hyperparameters to address reviewer’s feedback. We have uploaded a pdf containing figures for these experiments, a revised Table 2 with more baseline comparisons, as well as improvements in visualization schemes for original figures 3 and 4, in accordance with reviewer feedback. Reviewer feedback will be integrated into a revised version of the paper, which, if accepted, will present our results with improved clarity and include the experiments and improvements suggested by reviewers. 

## Additional References for rebuttals:

[46] Luo et al. 2016. “Long-Term Repeatability and Reproducibility of Phosphene Characteristics in Chronically Implanted Argus II Retinal Prosthesis Subjects.” American Journal of Ophthalmology

[47] Yue et al. 2021. “Restoring Color Perception to the Blind – an Electrical Stimulation Strategy of Retina in Patients with End-Stage Retinitis Pigmentosa.” Ophthalmology

[48] Dorman et al. 2005. “Acoustic Simulations of Combined Electric and Acoustic Hearing (EAS).” Ear and Hearing

[49] Okorokova et al. 2018. “Biomimetic Encoding Model for Restoring Touch in Bionic Hands through a Nerve Interface.” Journal of Neural Engineering

[50] Saal et al. 2017. “Simulating Tactile Signals from the Whole Hand with Millisecond Precision.” Proceedings of the National Academy of Sciences

[51] Mileusnic et al. 2006. “Mathematical Models of Proprioceptors. I. Control and Transduction in the Muscle Spindle.” Journal of Neurophysiology

[52] Drakopoulos et al. 2023. “A DNN-Based Hearing-Aid Strategy For Real-Time Processing: One Size Fits All.” In ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

[53] Drakopoulos et al. 2022. “A Differentiable Optimisation Framework for The Design of Individualised DNN-Based Hearing-Aid Strategies.” In ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

[54] Drakopoulos et al. 2023. “A Neural-Network Framework for the Design of Individualised Hearing-Loss Compensation.” IEEE/ACM Transactions on Audio, Speech, and Language Processing

[55] Ding et al. 2018. “Human-in-the-Loop Optimization of Hip Assistance with a Soft Exosuit during Walking.” Science Robotics

[56] Nielsen et al. 2015. “Perception-Based Personalization of Hearing Aids Using Gaussian Processes and Active Learning.” IEEE/ACM Transactions on Audio, Speech, and Language Processing

[57] Louie et al. 2021. “Semi-Automated Approaches to Optimize Deep Brain Stimulation Parameters in Parkinson’s Disease.” Journal of NeuroEngineering and Rehabilitation

[58] Lorenz et al. 2019. “Efficiently Searching through Large TACS Parameter Spaces Using Closed-Loop Bayesian Optimization.” Brain Stimulation 

[59] Tucker et al. 2020. “Preference-Based Learning for Exoskeleton Gait Optimization.” 

[60] Lorenz et al. 2021. A Bayesian optimization approach for rapidly mapping residual network function in stroke. Brain 144, 2120–2134

[61] Zhao et al. 2021. “Optimization of Spinal Cord Stimulation Using Bayesian Preference Learning and Its Validation.” IEEE Transactions on Neural Systems and Rehabilitation Engineering 

[62] Nanduri, Devyani. 2011. “Prosthetic Vision in Blind Human Patients: Predicting the Percepts of Epiretinal Stimulation.” ProQuest Dissertations and Theses. Ph.D., United States -- California: University of Southern California. 

[63] Da Cruz et al. 2013. “The Argus II Epiretinal Prosthesis System Allows Letter and Word Reading and Long-Term Function in Patients with Profound Vision Loss.” British Journal of Ophthalmology 

[64] Sui, Yanan, Vincent Zhuang, Joel W. Burdick, and Yisong Yue. "Multi-dueling bandits with dependent arms." arXiv preprint (2017).


Meta-review: This paper discusses a method to personalize stimulation parameters for a visual prosthesis.  
All reviewers were in favor of publication.   The results are impressive, but the weakest part of the 
paper is that the studies are done on "simulated people".   There was a robust rebuttal discussion 
and reviewers were happy with the outcome but request that these new details be added to the paper.
Decision: Accept (poster)