---
title: Any-Resolution Neural Signal Sampler
url: https://www.emergentmind.com/topics/any-resolution-neural-signal-sampler
type: topic
---

# Any-Resolution Neural Signal Sampler

Searching arXiv for the cited papers to ground the article in current literature.
"Any-Resolution Neural Signal Sampler" (*Editor's term*) denotes a class of acquisition, representation, and reconstruction schemes in which the effective sampling density, sensor locations, sample rate, or output resolution can vary without requiring the core neural or neuromorphic model to be redesigned. In current literature, this idea appears in several technically distinct forms: operator-learning systems that accept arbitrarily sampled point clouds and map them into fixed-length embeddings, event-driven and level-crossing ADCs whose sampling density is reconfigured by signal activity or control voltage, and multirate neural pipelines that decouple learned processing from a single training-time discretization [2407.13010] [2211.15319] [2310.15750] [2501.18470].

## 1. Conceptual scope and problem setting

A recurring limitation in neural signal processing is that the learned system is tied to a fixed discretization. In the Deep Operator Network setting, the solution field can be evaluated at any location within the domain, but input functions must be discretized at identical locations, which limits practical applications [2407.13010]. In neural audio effect models, the sample rate of the training data is implicitly encoded in the model weights and therefore not readily adjustable at inference [2501.18470]. In DNN-based watermarking, previous resolution-agnostic methods reduce the variant resolution watermarking problem to a fixed resolution watermarking problem, and that reduction process can potentially introduce artifacts and low robustness [2405.08340].

Taken together, these results suggest that “resolution” is not a single quantity. It may refer to sensor count and sensor placement, temporal event density, ADC precision, output sample rate, or spatial sampling density. The shared technical objective is to separate the learned representation of the signal from a single fixed discretization. In some works, this is done by learning a continuous signal model; in others, by making sampling event-driven or by wrapping a fixed-rate neural model inside explicit resampling stages.

A common misconception is that resolution independence means the underlying sampling constraints disappear. The literature does not support that interpretation. The RI-DeepONet formulation assumes that input functions are discretized arbitrarily but sufficiently finely [2407.13010]. The neuromorphic FRI framework gives explicit sufficient conditions on the temporal contrast threshold for perfect reconstruction and requires at least \(2K+1\) events for recovery of \(K\) Dirac or pulse positions and amplitudes [2310.15750].

## 2. Function-space embeddings and resolution-independent neural operators

The most explicit “any-resolution” construction in operator learning is the resolution-independent DeepONet and the Resolution Independent Neural Operator. The central step is to map an arbitrarily sampled input function \(u(x)\), given as a point cloud, into a fixed-length embedding in a learned function space [2407.13010].

This is accomplished by learning a dictionary of continuous basis functions \(\{\psi_l(x)\}_{l=1}^Q\), where each basis function is parameterized as an implicit neural representation. The paper specifically uses sinusoidal representation networks as trainable INR basis functions. For a sample \(i\), the representation is

$$
u^{(i)}(x) \approx \sum_{l=1}^Q \alpha_l^{(i)} \psi_l(x)
= \boldsymbol{\Psi}^T(x)\,\boldsymbol{\alpha}^{(i)}.
$$

The projection coefficients are obtained by minimizing a reconstruction loss with \(L_2\) regularization:

$$
\boldsymbol{\alpha}^{(i)} =
\arg\min_{\boldsymbol{\alpha}}
\sum_{j=1}^{M^{(i)}}
\left|
\bar{u}^{(i,j)} - \boldsymbol{\Psi}^T(x^{(i,j)})\boldsymbol{\alpha}
\right|^2
+ \lambda \|\boldsymbol{\alpha}\|_2^2.
$$

The dictionary learning algorithm is an efficient alternating minimization procedure, inspired by dictionary learning and the ADMM, that jointly and iteratively learns the basis functions and the sample-specific embedding codes. At each step, a new basis function is added, initialized randomly, and trained to fit the current residual across all samples [2407.13010].

Once each input function is embedded as \(\boldsymbol{\alpha}\), operator learning proceeds as usual. In RI-DeepONet, the embedding replaces the fixed-grid input of the branch network:

$$
\mathcal{G}(u)(y) \approx
\sum_{k=1}^{P}
\text{br}_k(\boldsymbol{\alpha}(u); \theta)\cdot \text{tr}_k(y; \theta).
$$

RINO extends the same dictionary-learning idea to output data. The dictionary learning algorithms identify basis functions for output data, and the operator learning task reduces to mapping coefficients of input basis functions to output basis functions [2407.13010].

The paper reports experiments on antiderivative, 1D/2D nonlinear Darcy, and parametric Burger’s equation. In these studies, the method trains and successfully infers on input functions sampled at random, varying numbers, and locations of sensors, and achieves errors that are stable and essentially unchanged even as the input sampling pattern and counts are randomized, so long as the sampling is sufficiently rich and meets the Nyquist sampling criterion for the underlying signal’s bandwidth. It also reports that dictionary learning with INRs outperforms classical gappy POD in reconstructing masked data, especially for extremely undersampled or irregularly sampled data, and that the learned basis can be much lower dimensional than the native discretization [2407.13010].

| Feature | Vanilla DeepONet | RI-DeepONet/RINO |
|---|---|---|
| Input discretization requirement | Fixed grid, same for all | Arbitrary (point clouds), variable across samples |
| Input encoding | Direct, grid values | Learned function-space embedding via INR dictionary |
| Handles arbitrary sensor counts | No | Yes |

## 3. Event-driven acquisition and reconfigurable sampling density

A second major lineage treats any-resolution sampling as a hardware or encoder property rather than a learned embedding problem. In the Neuron-ADC, the signal is sampled using level-crossing sampling, where the input analog signal is only sampled when it crosses predefined voltage thresholds, and a digital spike is generated to denote whether the input has moved above or below a reference level [2211.15319].

The key control mechanism is a bio-inspired refractory circuit that enforces a minimum time interval between successive spikes. The refractory period duration is controlled by the refractory voltage applied to the NMOS load. Adjusting the refractory voltage directly tunes the maximum rate at which the ADC can generate output spikes: a higher refractory voltage shortens the refractory period, while a lower voltage increases it. The ENOB and output data rate thus become tunable parameters via the refractory circuit, allowing the ADC to effectively serve as an “any-resolution” neural signal sampler [2211.15319].

The reported performance figures are concrete. Simulation results of 40 nm CMOS process show that the Neuron-ADC achieves a maximum ENOB of 6.9 bits with a corresponding FoM of 97 fJ/conversion under 0.6 V supply voltage. The proposed dynamic comparator can reduce static power up to 41.1% when tested with a 10 kHz sinusoidal input, and the detailed summary further reports power of 229.8 nW at maximum [2211.15319].

The sampling-theoretic neuromorphic formulation is developed much more explicitly for sparse signals with a finite rate of innovation. In that setting, events \(\{(t_m,p_m)\}\) are recorded whenever the filtered signal changes by a fixed temporal contrast threshold \(C\), with polarity \(p_m \in \{+1,-1\}\). Given the initial amplitude, all subsequent amplitude samples are determined by the event sequence through the \(t\)-transform,

$$
f(t_m) = f(t_0) + C \sum_{i=1}^m p_i.
$$

For FRI signals such as streams of Diracs, sums of pulses, and piecewise-polynomial functions, the framework uses kernel-based sampling and Fourier-domain analysis to show that perfect signal reconstruction is possible via parameter estimation using high-resolution spectral estimation methods. The minimum number of events is \(2K+1\), and the threshold condition is

$$
0 < C < \frac{f_{\max} - f_{\min}}{2K+1}.
$$

The paper also extends the analysis to multichannel neuromorphic sampling in SIMO and MIMO configurations, showing that signal parameters can be jointly estimated using multichannel measurements [2310.15750].

These two lines of work address different regimes. The Neuron-ADC emphasizes reconfigurable sampling, low power, and asynchronous spike output for biomedical applications [2211.15319]. The FRI framework emphasizes perfect reconstruction guarantees, minimal sample complexity equal to the rate of innovation, and explicit threshold and kernel conditions [2310.15750]. Their commonality is event-driven, nonuniform acquisition.

## 4. One-bit, unlimited-dynamic-range, and reconstruction-centric formulations

A third formulation treats “any-resolution” not as variable sensor placement or event density, but as the ability to obtain high-fidelity reconstructions from extremely low-precision measurements while retaining effective dynamic range. The UNO framework combines unlimited sampling with one-bit quantization [2301.10155].

The method first applies a modulo operator to continuous-time bandlimited signal samples,

$$
\tilde{x}_k = \mathcal{M}_\lambda(x_k)
= x_k - 2\lambda \left\lfloor \frac{x_k}{2\lambda} + \frac{1}{2} \right\rfloor,
$$

and then performs one-bit quantization with time-varying thresholds,

$$
r_k^{(\ell)} = \operatorname{sgn}\left(\tilde{x}_k - \tau_k^{(\ell)}\right),
\quad \ell = 1,\dots,m.
$$

The resulting inequalities define a polyhedron, and the modulo samples are reconstructed via the randomized Kaczmarz algorithm. In the presence of noise, the framework employs plug-and-play priors with ADMM to integrate state-of-the-art regularizers in the reconstruction process [2301.10155].

The distinctive claim is that information on the distance between the input signal value and the threshold is stored and utilized to accurately reconstruct the one-bit sampled signal. Numerical experiments illustrate superior performance compared to one-bit Sigma-Delta sampling. The paper further states that error can be made arbitrarily small by increasing the number of threshold ensembles and/or sampling rate [2301.10155].

This does not make the sampler “resolution independent” in the same sense as arbitrary point-cloud operator learning. Rather, it suggests an adjacent interpretation: the effective resolution of the recovered signal can be increased by reconstruction from dense one-bit measurements, even though the frontend quantizer itself is minimal.

## 5. Multirate neural pipelines and cross-domain resolution-agnostic representations

Resolution-agnostic processing also appears in systems where the neural model itself is fixed, but the signal is transformed so that the model can operate outside its native discretization. In multirate neural audio effect processing, one proposed solution is to wrap the neural network in real-time signal resampling stages: incoming audio is resampled to the model’s native training rate, the neural model runs exactly as trained, and the output is resampled back to the desired rate [2501.18470].

The paper investigates several resampling filter designs and reports that a two-stage design consisting of a half-band IIR filter cascaded with a Kaiser window FIR filter can give similar or better results to the previously proposed model adjustment method with many fewer filtering operations per sample and less than one millisecond of latency at typical audio rates. An example in the detailed summary gives approximately 24 operations/sample and approximately 0.07 ms latency for the two-stage design, compared with approximately 44 operations/sample and 0.24 ms latency for a single-stage NB-Kaiser example [2501.18470].

Audio super-resolution addresses a different problem: reconstructing missing samples within a low-resolution signal. The model is trained on pairs of low- and high-quality audio examples and is evaluated at upscaling ratios of \(2\times\), \(4\times\), and \(6\times\). The architecture is fully convolutional, with residual connections and a 1D version of the subpixel shuffling layer, and the paper reports that it outperforms baselines on standard speech and music benchmarks [1708.00853]. The fully convolutional nature allows it to process input signals of arbitrary length and, with appropriate training, at arbitrary upscaling ratios, although the same source notes that handling truly arbitrary fractional scaling ratios may require additional training or data preprocessing [1708.00853].

A broader resolution-agnostic pattern is also visible outside time-series acquisition. RAIMark fits an implicit neural representation \(F_{im}: \mathbb{R}^2 \mapsto \mathbb{R}^3\) to an image and then fine-tunes the INR so that any sampled image with arbitrary resolution carries the watermark, reporting averagely improved bit accuracy by \(7\%\sim29\%\) and robustness against all watermarking attacks considered [2405.08340]. NeuralSampler decouples shape generation from surface sampling so that both input and output point clouds can vary in size [1901.09394]. JAFAR upsamples low-resolution features from any Foundation Vision Encoder to an arbitrary target resolution by cross-attention with Spatial Feature Transform modulation and reports that learning at low upsampling ratios and resolutions generalizes remarkably well to significantly higher output scales [2506.11136]. These are not signal samplers in the ADC sense, but they reinforce the same continuous-representation strategy.

## 6. Limits, misconceptions, and research directions

The literature imposes several clear limits on what “any-resolution” can mean. First, arbitrary sampling locations are not equivalent to arbitrary information content. The RI-DeepONet and RINO formulation works when input functions are discretized arbitrarily but sufficiently finely, and its empirical robustness is explicitly conditioned on the sampling being sufficiently rich and satisfying the Nyquist sampling criterion for the underlying signal’s bandwidth [2407.13010].

Second, event-driven acquisition is not intrinsically lossless. In the FRI setting, perfect reconstruction requires a suitable kernel, explicit threshold conditions, and at least \(2K+1\) events [2310.15750]. In the Neuron-ADC, a lower refractory voltage yields fewer samples, lower power, and lower resolution, while a higher refractory voltage yields more samples, higher power, and improved resolution or accuracy [2211.15319]. The system is reconfigurable, but the tradeoff is fundamental rather than eliminable.

Third, resolution-agnostic inference often depends on separating representation from discretization rather than making the neural model itself universally invariant. The audio resampling framework keeps the RNN at its native rate and assigns the rate conversion to explicit DSP blocks [2501.18470]. The watermarking framework avoids fixed-resolution reduction by directly watermarking the continuous signal instead of image pixels [2405.08340]. The operator-learning framework makes the branch network compatible with arbitrary point clouds by changing only the input encoding [2407.13010].

A plausible implication is that future “any-resolution” systems will continue to combine continuous signal parameterizations, adaptive acquisition, and explicit reconstruction layers rather than rely on a single universal architecture. The present record already includes arbitrary point-cloud operator learning, level-crossing and neuromorphic event encoders, unlimited one-bit sampling, real-time resampling wrappers for learned audio systems, and INR-based continuous representations [2407.13010] [2211.15319] [2301.10155] [2501.18470]. What unifies them is not a single model family, but a design principle: the signal is treated as more fundamental than any one discretization of it.

Source: https://www.emergentmind.com/topics/any-resolution-neural-signal-sampler