NeuroFilter: Neural Adaptive Filtering

• NeuroFilter is a collection of neural-inspired filtering methods that integrate neural architectures and adaptive learning to combine prior predictions with real-time observations.
• It employs techniques such as EKF-inspired neural networks, neural particle filters, and spiking architectures to robustly estimate states and suppress noise in dynamic and high-dimensional systems.
• These approaches offer practical benefits over classical filters by improving accuracy, scalability, and privacy safeguards across applications like system identification, neuromorphic event filtering, and LLM privacy protection.

NeuroFilter encompasses a range of neural, neuromorphic, and neuro-inspired filtering approaches that enhance inference, prediction, signal extraction, and adaptive processing in dynamical, physical, sensory, and privacy-sensitive systems. Methods labeled "NeuroFilter" are unified by leveraging neural principles—network architectures, sample-based computations, Hebbian or non-Hebbian adaptation, or internal model representations—to optimally combine prior predictions and observations, suppress noise, enforce domain-specific guardrails, or extract relevant dynamics. Across domains such as nonlinear system identification, Bayesian neural decoding, real-time neuromorphic filtering, and LLM privacy enforcement, NeuroFilter frameworks provide robust, often principled, alternatives to classical linear filters by exploiting neural computation and adaptation.

1. Principles and Mathematical Foundations

NeuroFilter methods are often built upon two complementary mathematical principles: (1) optimal Bayesian fusion of prior model predictions with incoming data, and (2) dynamic adaptation or selection of filter parameters and structures based on neural architectures or activation statistics.

In dynamical system modeling, the NeuroFilter (Oveissi et al., 2024) borrows from the Extended Kalman Filter (EKF), extending it by replacing the analytical system model $f$ with a neural network approximation $NN(x,u;\theta)$. The state prediction proceeds as $$\hat{x}_{k|k-1} = NN(\hat{x}_{k-1|k-1}, u_{k-1}; \theta)$$, followed by measurement correction using the Kalman gain $K_k$ derived from neural network Jacobians and measurement function gradients. The overall recursion maintains bounded error and covariance over long horizons, outperforming open-loop neural network predictors.

In Bayesian neural decoding, the Neural Particle Filter (NPF) (Kutschireiter et al., 2015) and its spike-based variant (Kutschireiter et al., 2018) replace weighted particle filtering (which suffers from the curse of dimensionality) with unweighted, sample-based filtering driven by stochastic differential equations:

$$dz_t^{(i)} = f(z_t^{(i)}) dt + W_t (dy_t - g(z_t^{(i)}) dt) + \Sigma_x^{1/2} dW_t^{(i)}$$

with the gain $W_t$ empirically matched to the covariance structure of the particles, thereby enabling robust estimation even in high dimensions.

In privacy enforcement for LLMs, the NeuroFilter (Das et al., 21 Jan 2026) framework formulates privacy-violating intent as linearly separable in model activation space. The normal vector $w^\ell$ and bias $b^\ell$ are learned via logistic regression on layer-$\ell$ activations, so the detection statistic is $s^\ell(p)=w^\ell a_t^\ell+b^\ell$. Multi-turn manipulation is countered by monitoring activation velocity $v_t^\ell=a^\ell_t-a^\ell_{t-1}$ and its cumulative drift $C_t$.

2. Neural Architectures and Implementation Strategies

NeuroFilter designs employ a variety of neural architectures, ranging from fully connected feedforward networks in dynamical state estimation (Oveissi et al., 2024) to recurrent and sample-based networks in Bayesian filtering (Kutschireiter et al., 2015, Kutschireiter et al., 2018), spiking neural networks (SNNs) for on-sensor event filtering (Kulkarni et al., 2023), and single/multilayer linear probes for LLM monitoring (Das et al., 21 Jan 2026).

In system identification, the neural state-update map employs configurable layer sizes matching state complexity (e.g., $2 \rightarrow 10 \rightarrow 2$ for pendulum, $$4 \rightarrow 10 \rightarrow 10 \rightarrow 10 \rightarrow 10 \rightarrow 4$$ for double pendulum), ReLU activations in hidden layers, and linear output layers (Oveissi et al., 2024).

In neuromorphic filtering, hardware designs utilize leaky integrate-and-fire neuron models with integer parameters and evolutionary optimization of network topology, as seen in the NeuroFilter SNN for high-energy collider data-rate reduction and efficient hardware implementation (Kulkarni et al., 2023).

Reservoir computing approaches augment fixed nonlinear reservoirs with linear FIR filters at the output stage, multiplying feature dimensionality and memory capacity, and enabling efficient FPGA deployment for robust signal processing tasks (Carroll, 2020).

3. Filter Adaptation, Learning, and Data Requirements

NeuroFilter frameworks emphasize adaptive correction and flexible learning rules—Hebbian, spike-amplitude-dependent, or maximum likelihood—allowing the filter to compensate for model bias, noise, or sparsity in training data.

The neural particle filter adapts its gain matrix via online maximum likelihood estimation applied to non-Gaussian, multimodal posteriors, outperforming standard filters in dimensional scaling and sample efficiency (Kutschireiter et al., 2018, Kutschireiter et al., 2015).

Memristor-based NeuroFilters exploit amplitude-dependent plasticity (SADP) to realize on-chip habituation, sensitization, and contrast enhancement, with conductance evolution governed directly by input spike amplitude and coordination chemistry of the device (Wang et al., 2017).

The NeuroFilter in LLM privacy detection is trained on extensive labeled datasets (up to 150,000 examples) via efficient logistic regression, with probe calibration to maintain zero false positive rate on benign queries and trajectories, and robust detection performance demonstrated across model scales and quantization levels (Das et al., 21 Jan 2026).

4. Performance Characteristics and Empirical Validation

Established NeuroFilter methods consistently yield improvements in prediction accuracy, robustness to noise, dimensional scalability, and practical deployment compared to classical or open-loop approaches.

• In nonlinear system state estimation, RMSE and covariance trace for long-horizon trajectories are reduced by an order of magnitude or more compared to open-loop NN predictors; filter performance is resilient even when NNs are weakly trained (Oveissi et al., 2024).
• In high-dimensional Bayesian neural decoding, sNPF and NPF maintain tracking accuracy with particle requirements scaling linearly in dimension, while weighted particle filters require exponential growth (Kutschireiter et al., 2018, Kutschireiter et al., 2015).
• In spiking neural event filtration for collider sensor data, NeuroFilter SNN achieves 91.9% signal efficiency and 26.5% data reduction with half the parameter count of equivalent DNN classifiers (<1k parameters), meeting stringent latency and power constraints for real-time hardware (Kulkarni et al., 2023).
• For LLM privacy guardrails, the NeuroFilter linear probe yields 100% true positive rate with zero false positives and up to $10^8$ lower inference cost compared to full LLM checking, robustly detecting both single-shot and mosaic adversarial manipulations (Das et al., 21 Jan 2026).
• In neuromorphic adaptive image denoising, neuron-based edge-preserving mean filters achieve PSNR improvements up to +1.3 dB and MSE reductions by nearly 49% over conventional mean filters, albeit with increased analog front-end power requirement (Irmanova et al., 2017).

5. Domain-Specific Applications and Extensions

NeuroFilter architectures are explicitly designed to address filtering challenges across diverse scientific and engineering domains:

• Nonlinear dynamical systems: robust long-term state estimation and feedback control for chaotic and undertrained dynamical models (Oveissi et al., 2024).
• Bayesian neural decoding: real-time inference of hidden stimulus dynamics from large populations of spiking neurons, surmounting the curse of dimensionality and multimodality (Kutschireiter et al., 2015, Kutschireiter et al., 2018).
• Neuromorphic sensor arrays: adaptive spatial filtering, signal denoising, and contrast enhancement in vision and high-rate particle physics systems (Irmanova et al., 2017, Kulkarni et al., 2023).
• Image processing: Hebbian-adaptive, Gabor-like filters for feature extraction and pulse-based edge detection in configurable microcircuits (Mayr et al., 2014).
• Memristive hardware: amplitude-sensitive filtering, habituation, and long-term memory encoding in hybrid ionic/electronic devices with coordination-regulated time constants (Wang et al., 2017).
• Privacy-preserving LLM deployment: real-time, activation-space linear filtering and drift monitoring to enforce contextual integrity in conversational AI agents (Das et al., 21 Jan 2026).

6. Limitations, Trade-offs, and Future Directions

Various NeuroFilter approaches involve domain-specific trade-offs:

• EKF-inspired NeuroFilter requires the measurement function $g(x)$ to be known a priori and assumes local linearizability of both NN and measurement maps (Oveissi et al., 2024).
• Sample-based particle filters and sNPF/NPF methods reduce the curse of dimensionality but may incur increased computational cost in extremely high dimension or under highly concentrated posteriors (Kutschireiter et al., 2018, Kutschireiter et al., 2015).
• Neuromorphic hardware filters (e.g., spiking SNNs, memristors) are constrained by analog front-end power dissipation, routing complexity, quantization effects, and limited scalability of physical microcircuit arrays (Irmanova et al., 2017, Kulkarni et al., 2023).
• LLM privacy probes can be sensitive to model updates, requiring retraining upon instruction tuning or underlying architectural changes; thresholds must be calibrated for zero FPR, and ensemble probes may be needed for compositional or heterogeneous threats (Das et al., 21 Jan 2026).

Prospective directions include physics-informed neural field filtering for scalable parameter inference (Hao et al., 2024), stacking layers of normal-mode-extracting neurofilters for hierarchical dynamical prediction (Golkar et al., 2024), ensemble and context-aware probes in privacy guardrails, and hardware-driven adaptation of synaptic time constants and filter structures.

7. Summary Table: Selected NeuroFilter Approaches

Application Domain	NeuroFilter Type	Key Technical Feature
Nonlinear system estimation	EKF-inspired neural filter	NN-based state update + measurement correction (Oveissi et al., 2024)
Bayesian neural decoding	Neural Particle Filter/sNPF	Weightless sample-based stochastic filtering (Kutschireiter et al., 2015, Kutschireiter et al., 2018)
Reservoir computing	Filter-augmented readout	FIR/Bessel filters for feature/memory expansion (Carroll, 2020)
Memristive synapses	SADP NeuroFilter	Amplitude-dependent plasticity and filtering (Wang et al., 2017)
Image processing	Hebbian-adaptive microcircuit	Gabor-like pulse-based edge detection (Mayr et al., 2014)
On-sensor event selection	SNN-based NeuroFilter	Efficient, evolutionary-optimized spiking filter (Kulkarni et al., 2023)
Privacy in LLMs	Activation-space NeuroFilter	Linear probe and velocity drift detection (Das et al., 21 Jan 2026)

NeuroFilter frameworks, therefore, provide robust, adaptive solutions across domains where classical filters and open-loop neural estimators fall short, leveraging neural computation, sample-based correction, and domain-specific adaptation for high fidelity prediction, denoising, and contextual guardrails.