Poisson

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Latest papers 13

Oct 1, 2026cs.NE

Controllable Stochastic Quantization Encoding for Adversarially Robust Spiking Neural Networks

Spiking Neural Networks (SNNs) have attracted increasing attention due to their impressive temporal dynamics, energy efficiency, and brain-inspired mechanisms. Although SNNs have demonstrated promising performance in image classification tasks, recent studies have shown that they remain vulnerable to adversarial attacks, where imperceptible perturbations are added to input images to mislead model predictions. Existing defense methods mainly focus on training strategies, while the role of input encoding remains less explored. An observation is that the robustness advantage of Poisson encoding over direct encoding may benefit from its inherent randomness. Motivated by this, we propose a stochastic quantization encoding method that encodes the input image with controllable randomness adjusted by the quantization scale, thereby improving the adversarial robustness of SNNs. We further show that this method constitutes a general framework that reduces to both Poisson encoding and direct encoding under different choices of the quantization scale. Since it enhances robustness at the input encoding stage, it can be combined with existing training-based defenses for further gains. Experimental results on CIFAR-10 and CIFAR-100 demonstrate the effectiveness of the proposed stochastic quantization encoding method. To sum up, this work highlights the importance of input encoding for the adversarial robustness of SNNs, providing a new perspective for understanding and improving it.

Yujia Liu, Peiyu Liu, Yajing Zheng +1

NERCVT, School of Computer Science, Peking University, China · State Key Laboratory for Multimedia Information Processing, School of Computer Science, Peking University, China · Institute for Artificial Intelligence, Peking University, China

Spiking Neural Networks Neural Network Poisson

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Sep 28, 2026cs.CV

BMND: Direct Poisson Denoising by N-Dimensional Block Matching and Collaborative Filtering

Poisson denoising of scientific data requires methods that account for signal-dependent noise while accommodating different data dimensionalities and preserving quantitative intensity information. We present BMND, a dimension-independent extension of block matching and collaborative filtering for Gaussian and Poisson observations. Building on the two-stage structure of BM3D and BM4D, BMND processes Poisson data directly, without a variance-stabilizing transform, by combining noise-aware patch matching with propagation of signal-dependent noise variances through collaborative filtering and aggregation. A dimension-independent reference-patch traversal scheme supports arrays with an arbitrary number of axes. An optional aggregation-aware mass conservation preserves the observed total intensity after weighted overlap-add. We evaluate the framework on one-dimensional physiological signals, two-dimensional images, and three-dimensional volumes, using controlled noise experiments and measured fluorescence microscopy acquisitions. The experiments demonstrate improved reconstruction quality from noise-aware matching and Wiener filtering, while low-count phantom experiments show reduced denoising-induced intensity loss through mass conservation. The framework provides a unified, non-learning-based approach to denoising across arbitrary data dimensions and is released as an open-source library.

Christof Duhme, Lars Schiefelbein, Florian Büther +1

University of Münster

Iterative Denoising Methods Poisson Physiological Signals Collaborative Filtering 3D Generation

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Aug 12, 2026cs.LG

Adversarial Resilience of Poisson-Process Submodular Maximization over Matroids: From Robust Offline Optimization to Full-Bandit Learning

We study nonnegative submodular maximization subject to a general matroid when the offline algorithm is given an arbitrary controlled value oracle. Our main result is an adversarial resilience theorem for the Spiteful Greedy Swap Poisson Process (SGS-Poisson): without modifying its Poisson intensity, single-element exchange rule, or spiteful drop step, the algorithm retains limiting approximation factors

1/e

for non-monotone objectives and

1-1/e

for monotone objectives. More precisely, under every controlled oracle

\widehat f

satisfying

|\widehat f(S)-f(S)|\le ξ

for every set

S

, our implementation returns a feasible set with expected value at least

(1/e-\varepsilon)\OPT-O(kξ)

and

(1-1/e-\varepsilon)\OPT-O(kξ)

, respectively, using

\widetilde O(nk^2\varepsilon^{-2})

oracle calls. As a consequence, the offline-to-online reduction yields full-bandit CMAB algorithms for general matroid-constrained submodular rewards with exact limiting approximation-regret factors

1/e

and

1-1/e

and

\widetilde O(n^{1/5}k^{4/5}T^{4/5})

regret.

Vaneet Aggarwal

V. Aggarwal is with Purdue University, West Lafayette IN, USA

Submodular Functions Robust Optimization Poisson

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Jul 18, 2026math.ST

The Value of Depth in Message Passing on Sparse Graphs: A Kesten-Stigum Dichotomy

How deep does a graph neural network need to be on a sparse graph? We study its purest statistical form: node classification on the sparse contextual stochastic block model (CSBM) with average degree

Δ=O(1)

, whose local weak limit is a broadcast-labelled Poisson Galton-Watson tree. Prior work derived a message-passing classifier

h_\ell

that aggregates from each vertex at distance

k\le\ell

the attenuated evidence

2\operatorname{artanh}(γ^k t(X_v))

, with

γ

the edge signal and

t

a bounded likelihood-ratio transform of the feature. We prove that the value of depth is governed by a single number, the Kesten-Stigum ratio

κ=γ^2Δ

. Below the threshold (

κ<1

), the error sequence is Cauchy at a geometric rate,

|\mathcal{E}(\ell)-\mathcal{E}(\ell')|\le Cκ^{(\ell+1)/3}

for all

\ell'>\ell

, so all layers beyond depth

O(\log(1/ε))

change the error by less than

ε

; conversely, under mild regularity each sufficiently deep layer still flips the decision with probability at least

cκ^{\ell/2}

, the empirically sharp exponent. Above the threshold (

κ>1

), depth is geometrically productive:

\mathcal{E}(\ell)

is driven to a branching-process floor of order at most

1/(κ-1)

at any geometric rate

κ^{-s\ell}

s<1

(this bound has content only for

κ>17

). No local classifier of any depth beats the universal floor

e^{-Δ}Φ(-ζ)

set by isolated roots (

ζ

the feature signal-to-noise ratio), while the first layer provably helps by an explicit total-variation amount. Simulations with an exact belief-propagation baseline on the same trees show that the pairwise rule's error curve is mildly non-monotone in

\ell

, so an optimal finite depth exists (an exact instance is certified in the appendix), while BP saturates strictly faster, at an effective per-layer ratio below

κ

that we identify.

Aseem Raj Baranwal

Message Passing Neural Networks Circuit Depth Poisson Signal-To-Noise Ratio Value

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Jul 3, 2026cs.LG

Poisson-Gamma Modeling of Inter-Relational Dependencies in Dynamic Knowledge Graphs

Dynamic knowledge graphs are ubiquitous in today's AI applications, as we represent molecular structures, social relationships, and language information using these graph models. As knowledge graphs evolve over time and are often noisy and incomplete, modeling their temporal and relational dependencies becomes crucial for downstream tasks. To address these challenges, this paper proposes PGRE (Poisson-Gamma Relational Evolution), a probabilistic model for modeling inter-relational dependencies in dynamic knowledge graphs. PGRE represents multi-relational temporal links via a Poisson-Bernoulli formulation. It introduces Gamma-distributed latent variables to capture entity-factor associations and cross-relation dependencies mediated by shared latent communities. A Gamma Markov process further models the temporal evolution of these latent variables, enabling principled characterization of relational dynamics. Experiments on benchmark datasets show that PGRE achieves competitive performance in link prediction, particularly in sparse settings, while revealing meaningful relational evolution patterns in dynamic knowledge graphs.

Nan Fang, Yijun Wang, Hao Liao +1

School of Computing and Information Technology, Great Bay University, Dongguan, Guangdong, China · Tsinghua University, Shenzhen, Guangdong, China · College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, Guangdong, China +1

Knowledge Graphs Poisson Associations

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May 28, 2026cs.LG

Ridge Regression from Poisson Resetting: A Renewal Perspective on Spectral Regularization

We connect stochastic resetting from non-equilibrium statistical physics with ridge regularization in statistical learning. For linear gradient flow, resetting to the origin at rate

r

produces stationary mean

(X^\top X+rI)^{-1}X^\top y

, exactly the ridge estimator with penalty

λ=r

. This uses the known Laplace-transform relationship between ridge regression and exponential-time averaging of gradient flow, with the exponential time now interpreted as the stationary age associated with Poisson resetting. We then extend this identity to general renewal reset laws: the exponential reset time distribution is the unique renewal law whose stationary mean reproduces scalar ridge in every eigendirection as an exact filter identity for every positive curvature, while non-exponential renewal laws generate alternative spectral filters. At the fluctuation level, we study a separate additive Ornstein-Uhlenbeck extension with constant diffusion, interpreted as a stylized SGD approximation. In this setting, the equality holds only at the level of the mean, since the reset process has a nonzero stationary covariance from accumulated OU noise and reset-timing variance, whereas deterministic ridge is a fixed estimator with the same center. Stylized experiments compare the deterministic renewal-induced filters directly and illustrate when filters induced by non-exponential reset-time laws can differ predictively from ridge. The results for the stationary mean and the induced spectral filters are established for continuous-time gradient flow with isotropic resetting on quadratic objectives; the covariance and risk formulas additionally assume additive noise with state-independent covariance.

Petar Jolakoski

Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia

Kernel Ridge Regression Regularization Poisson Stochastic Gradient Descent Covariance Statistical Physics+2

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May 20, 2026physics.geo-ph

Neural Negative Binomial Regression for Weekly Seismicity Forecasting: Per-Cell Dispersion Estimation and Tail Risk Assessment

Standard approaches to forecasting the weekly number of earthquakes on a spatial grid rely on the Poisson distribution with a single global dispersion assumption. We show that this assumption is systematically violated in seismic data from Central Asia (2010-2024), where a likelihood-ratio test with boundary correction strongly rejects the Poisson hypothesis (p < 10^{-179}). The main contribution of this work is the EarthquakeNet architecture, which provides an endogenous per-cell estimate of the overdispersion parameter alpha via a neural network (spatial embeddings + MLP), without explicit spatial covariance specification. In contrast to existing negative binomial regression approaches in seismological forecasting, which typically assume a single global alpha, the proposed per-cell formulation allows the model to identify spatial heterogeneity in seismic clustering and to construct probabilistic risk-aware alerts via quantiles of the predicted distribution. A walk-forward evaluation (2018-2023) over four systems shows an 8.6 percent reduction in mean pinball deviation (MPD) relative to a negative binomial GLM baseline. The strongest improvements are observed in the tail regime (Y >= 5), where the continuous ranked probability score (CRPS) of the proposed model is 12.5 percent lower than that of the baseline, indicating improved calibration in extreme-event forecasting.

Alim Igilik

[physics.geo-ph]

Full Waveform Inversion Probabilistic Forecasting Poisson Dispersion Logistic Regression

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Apr 27, 2026eess.IV

Shared-kernel Wavelet Neural Networks for Poisson Image Reconstruction

The Laplacian operator transforms the image into its Laplacian field, which usually is sparse and satisfies a stable distribution. On the other hand, an image can be uniquely reconstructed from its Laplacian field via solving a Poisson equation with a proper boundary condition. Such uniqueness is mathematically guaranteed. Thanks to these properties, we propose to use the sparse Laplacian field to present the image. We first show that the Laplacian field is sparse and satisfies a stable distribution on hundreds images. Then, we show that the image can be accurately reconstruct from its Laplacian field. For the reconstruction task, we propose a shared-kernel wavelet neural network, which solves the Poisson equation and has three advantages. First, it has less than {\bf 0.0002M} parameters, which is compact enough for most of devices. Second, it has linear computation complexity, leading to a real-time reconstruction. Third, it achieves higher accuracy than previous methods. Several numerical experiments are conducted to show the effectiveness and efficiency of the sparse Laplacian field and the proposed Poisson solver. The proposed method can be applied in a large range of applications such as image compression, low light enhancement, object tracking, etc.

Yuanhao Gong, Tan Tang, Qianyan Liu

Image Reconstruction Graph Laplacians Wavelets Fourier Neural Operators Poisson Neural Network

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Apr 23, 2026cs.RO

Full-Body Dynamic Safety for Robot Manipulators: 3D Poisson Safety Functions for CBF-Based Safety Filters

Collision avoidance for robotic manipulators requires enforcing full-body safety constraints in high-dimensional configuration spaces. Control Barrier Function (CBF) based safety filters have proven effective in enabling safe behaviors, but enforcing the high number of constraints needed for safe manipulation leads to theoretic and computational challenges. This work presents a framework for full-body collision avoidance for manipulators in dynamic environments by leveraging 3D Poisson Safety Functions (PSFs). In particular, given environmental occupancy data, we sample the manipulator surface at a prescribed resolution and shrink free space via a Pontryagin difference according to this resolution. On this buffered domain, we synthesize a globally smooth CBF by solving Poisson's equation, yielding a single safety function for the entire environment. This safety function, evaluated at each sampled point, yields task-space CBF constraints enforced by a real-time safety filter via a multi-constraint quadratic program. We prove that keeping the sample points safe in the buffered region guarantees collision avoidance for the entire continuous robot surface. The framework is validated on a 7-degree-of-freedom manipulator in dynamic environments.

Meg Wilkinson, Gilbert Bahati, Ryan M. Bena +3

Computing and Mathematical Sciences, California Institute of Technology. · Mechanical and Civil Engineering, California Institute of Technology.

Control Barrier Functions Safety Filters Collision Avoidance Robotic Manipulator Poisson

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Apr 18, 2026stat.ML

Neighbor Embedding for High-Dimensional Sparse Poisson Data

Across many scientific fields, measurements often represent the number of times an event occurs. For example, a document can be represented by word occurrence counts, neural activity by spike counts per time window, or online communication by daily email counts. These measurements yield high-dimensional count data that often approximate a Poisson distribution, frequently with low rates that produce substantial sparsity and complicate downstream analysis. A useful approach is to embed the data into a low-dimensional space that preserves meaningful structure, commonly termed dimensionality reduction. Yet existing dimensionality reduction methods, including both linear (e.g., PCA) and nonlinear approaches (e.g., t-SNE), often assume continuous Euclidean geometry, thereby misaligning with the discrete, sparse nature of low-rate count data. Here, we propose p-SNE (Poisson Stochastic Neighbor Embedding), a nonlinear neighbor embedding method designed around the Poisson structure of count data, using KL divergence between Poisson distributions to measure pairwise dissimilarity and Hellinger distance to optimize the embedding. We test p-SNE on synthetic Poisson data and demonstrate its ability to recover meaningful structure in real-world count datasets, including weekday patterns in email communication, research area clusters in OpenReview papers, and temporal drift and stimulus gradients in neural spike recordings.

Noga Mudrik, Adam S. Charles

Department of Biomedical Engineering Center for Imaging Science Kavli Neuroscience Discovery Institute Johns Hopkins University Baltimore, MD 21218, USA

Dimensionality Reduction Poisson Behavioral Embeddings Neighbors Neural Recordings

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Mar 5, 2026cs.RO

Safe-SAGE: Social-Semantic Adaptive Guidance for Safe Engagement through Laplace-Modulated Poisson Safety Functions

Traditional safety-critical control methods, such as control barrier functions, suffer from semantic blindness, exhibiting the same behavior around obstacles regardless of contextual significance. This limitation leads to the uniform treatment of all obstacles, despite their differing semantic meanings. We present Safe-SAGE (Social-Semantic Adaptive Guidance for Safe Engagement), a unified framework that bridges the gap between high-level semantic understanding and low-level safety-critical control through a Poisson safety function (PSF) modulated using a Laplace guidance field. Our approach perceives the environment by fusing multi-sensor point clouds with vision-based instance segmentation and persistent object tracking to maintain up-to-date semantics beyond the camera's field of view. A multi-layer safety filter is then used to modulate system inputs to achieve safe navigation using this semantic understanding of the environment. This safety filter consists of both a model predictive control layer and a control barrier function layer. Both layers utilize the PSF and flux modulation of the guidance field to introduce varying levels of conservatism and multi-agent passing norms for different obstacles in the environment. Our framework enables legged robots to safely navigate semantically rich, dynamic environments with context-dependent safety margins.

Lizhi Yang, Ryan M. Bena, Meg Wilkinson +4

Caltech MCE · Tufts ME

Safety-Critical Scenarios Legged Robots Poisson Guidance Point Clouds

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Feb 19, 2026cs.LG

Efficient privacy loss accounting for subsampling and random allocation

We consider the privacy amplification properties of a sampling scheme in which a user's data isused in

k

steps chosen randomly and uniformly from a sequence (or set) of

t

steps. This sampling scheme has been recently applied in the context of differentially private optimization (Chua et al., 2024a; Choquette-Choo et al., 2025) and communication-efficient high-dimensional private aggregation (Asi et al., 2026), where it was shown to have utility advantages over the standard Poisson sampling. Theoretical analyses of this sampling scheme (Feldman & Shenfeld, 2025; Dong et al., 2025) lead to bounds that are close to those of Poisson sampling, yet still have two significant shortcomings. First, in many practical settings, the resulting privacy parameters are not tight due to the approximation steps in the analysis. Second, the computed parameters are either the hockey stick or Renyi divergence, both of which introduce overheads when used in privacy loss accounting. In this work, we demonstrate that the privacy loss distribution (PLD) of random allocation applied to any differentially private algorithm can be computed efficiently. When applied to the Gaussian mechanism, our results demonstrate that the privacy-utility trade-off for random allocation is at least as good as that of Poisson subsampling. In particular, random allocation is better suited for training via DP-SGD. To support these computations, our work develops new tools for general privacy loss accounting based on a notion of PLD realization. This notion allows us to extend accurate privacy loss accounting to subsampling which previously required manual noise-mechanism-specific analysis.

Vitaly Feldman, Moshe Shenfeld

Apple · The Hebrew University of Jerusalem · *Work partially done while author was an intern at Apple.

Standard Differential-Privacy Subsampling Optimal Sample Complexity Stochastic Gradient Descent Privacy Secure Aggregation+2

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Date pendingcs.RO

Layered Safety: Enhancing Autonomous Collision Avoidance via Multistage CBF Safety Filters

This paper presents a general end-to-end framework for constructing robust and reliable layered safety filters that can be leveraged to perform dynamic collision avoidance over a broad range of applications using only local perception data. Given a robot-centric point cloud, we begin by constructing an occupancy map which is used to synthesize a Poisson safety function (PSF). The resultant PSF is employed as a control barrier function (CBF) within two distinct safety filtering stages. In the first stage, we propose a predictive safety filter to compute optimal safe trajectories based on nominal potentially-unsafe commands. The resultant short-term plans are constrained to satisfy the CBF condition along a finite prediction horizon. In the second stage, instantaneous velocity commands are further refined by a real-time CBF-based safety filter and tracked by the full-order low-level robot controller. Assuming accurate tracking of velocity commands, we obtain formal guarantees of safety for the full-order system. We validate the optimality and robustness of our multistage architecture, in comparison to traditional single-stage safety filters, via a detailed Pareto analysis. We further demonstrate the effectiveness and generality of our collision avoidance methodology on multiple legged robot platforms across a variety of real-world dynamic scenarios.

Erina Yamaguchi, Ryan M. Bena, Gilbert Bahati +1

Department of Mechanical and Civil Engineering and the Department of Aerospace, Caltech, Pasadena, CA 91125, USA

Collision Avoidance Safety Filters Control Barrier Functions Poisson Point Clouds

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