Title: Rethinking Out-of-Distribution Detection and Generalization with Collective Behavior Dynamics
Venue: NeurIPS 2025
Accepted: yes
Keywords: domain shift

out-of-distribution detection

out-of-distribution generalization

transfer learning
Abstract: Out-of-distribution (OOD) problems commonly occur when models process data with a distribution significantly deviates from the in-distribution (InD) training data. In this paper, we hypothesize that a $\textit{field}$ or $\textit{potential}$ more essential than features exists, and features are not the ultimate essence of the data but rather manifestations of them during training. we investigate OOD problems from the perspective of collective behavior dynamics. With this in mind, we first treat the output of the feature extractor as charged particles and investigate their collective behavior dynamics within a self-consistent electric field. Then, to characterize the relationship between OOD problems and dynamical equations, we introduce the $\textit{basin of attraction}$ and prove that its boundary can be represented as the zero level set of a differentiable function of the potential, $\textit{i.e.}$, the spatial integral of field. We further demonstrate that: $\textit{i)}$ InD and OOD inputs can be effectively separated based on whether they are steady state solutions for specific field conditions, enabling robust OOD detection and outperforming prior methods over three benchmarks. $\textit{ii)}$ the generalization capability correlates positively with the basin of attraction. By analyzing the dynamics of perturbations, we propose that the potential is well-characterized by a Fourier-domain form of the Poisson equation. Evaluated on six benchmark datasets, our method rivals the SoTA approaches for OOD generalization and can be seamlessly integrated with them to deliver additional gains.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a novel, physics-inspired framework CBD to address Out-of-Distribution (OOD) detection and generalization. The authors conceptualize high-level features extracted from neural networks as interacting charged particles governed by the Vlasov-Poisson equations, analyzing their collective behavior within a dynamically evolving self-consistent electric field. They formally define a basin of attraction that distinguishes In-Distribution (InD) from OOD data and propose two distinct but complementary methods derived from this framework: (i) an OOD detection method based on identifying steady-state solutions to distinguish InD and OOD features, and (ii) an OOD generalization method leveraging a dispersion relation to stabilize perturbations and enlarge the basin boundary.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The paper uniquely leverages theoretical constructs from physics (Vlasov-Poisson dynamics, charged particle behavior) to fundamentally rethink the OOD detection and generalization problems, offering a refreshing theoretical perspective distinct from prevailing statistical and uncertainty-based methods.\n2. The theoretical underpinning is compelling, outlining why the proposed dynamics-based approach naturally differentiates between InD and OOD data through steady-state solutions and basin boundaries.\n3. The method can be integrated smoothly with other advanced OOD generalization techniques, adding to its practical utility and adaptability.\n\nWeaknesses:\n1. The method requires the simultaneous estimation of complex PDE solutions, potentially resulting in increased GPU memory usage and reduced computational efficiency, especially in very large-scale or resource-constrained environments.\n2. While some hyperparameter analyses are presented, a deeper understanding of the sensitivity and stability related to PDE discretization parameters, regularization strengths, or solver accuracy would significantly enhance the method’s clarity and reproducibility.\n3. The experimental evaluation is limited to relatively standard feature-extraction architectures, specifically ResNet and ViT, leaving the effectiveness of the approach on more diverse network architectures or modalities (e.g., text or multimodal data) unexplored.\n\nQUESTIONS:\nPlease refer to Weaknesses.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a novel physics-inspired framework called Collective Behavior Dynamics (CBD) to address out-of-distribution (OOD) detection and generalization. It conceptualizes high-level features as charged particles evolving under a self-consistent electric field, modeled via the Vlasov–Poisson system, and defines the “basin of attraction” as the region where in-distribution (InD) features converge to a steady state. The authors show that OOD samples can be identified as those falling outside this basin, while model generalization can be enhanced by enlarging the basin through dispersion relation regularization. According to evaluation results, CBD achieves competitive performance across multiple OOD detection and generalization benchmarks, and is compatible with existing methods for further performance gains. This approach bridges dynamical systems theory with deep learning, offering both theoretical insights and practical benefits for robust model behavior under distribution shifts.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n- Treating high-level features as particles in a dynamical system offers a new paradigm for OOD detection/generalization grounded in physical systems rather than statistical heuristics.\n- The method supports both OOD detection and generalization using the same underlying principles, and defines clear, interpretable loss functions (Poisson, Vlasov, and dispersion losses) tied directly to physical laws.\n- Code is provided for reproducibility purposes.\n\nWeaknesses:\n\n- This paper lacks a comprehensive comparison between physics-based and statistical approaches for OOD detection and generalization. While the proposed method is rooted in a novel physics-inspired framework, the authors do not provide sufficient discussion on how it fundamentally differs from or improves upon traditional statistical methods. Specifically, it remains unclear why modeling high-level features as particles under self-consistent fields offers a more effective or principled solution compared to well-established statistical techniques such as energy-based models, density estimation, or confidence-based scoring. A deeper theoretical and empirical analysis comparing the strengths, limitations, and use-case suitability of both perspectives would significantly strengthen the motivation and positioning of the proposed approach.\n- The framework assumes that high-level features behave like charged particles in a self-consistent field and reach a steady state. While this is an elegant abstraction, it lacks empirical or theoretical grounding to show that this analogy meaningfully holds for deep neural networks.\n- The limitation of the proposed theoretical framework is not discussed. In particular, this framework doesn’t address conditions under which the Vlasov–Poisson-based formulation might fail or be unstable, especially in highly non-linear or high-dimensional feature spaces.\n- The method is built around visual features extracted by CNNs or ViTs, and it's unclear whether the approach generalizes well to non-image modalities (e.g., text, graphs, time series).\n- The writing is overly complex and lacks clear organization, which makes it challenging to fully grasp the core concepts of CBD, particularly its application to OOD detection and generalization, as well as the accompanying theoretical analysis.\n\nQUESTIONS:\n- What is the theoretical or empirical justification for modeling high-level features as charged particles governed by the Vlasov–Poisson system, as opposed to using conventional statistical methods? It is beneficial if the authors provide clearer rationale and comparative discussion that contrasts this physics-inspired approach with established statistical paradigms (e.g., energy-based models, density estimation, confidence scoring). What unique modeling capabilities or interpretability does the proposed framework offer?\n- Are there specific cases where CBD fails to detect OOD or generalize well? What are the limitations in terms of types of shifts or datasets?\n- Can the authors evaluate CBD in additional domains (e.g., time series, tabular data) or on more realistic OOD scenarios (e.g., long-tailed or adversarial settings)?\n\nLIMITATIONS:\n- The experimental design is limited to imaging data. Generalization beyond vision tasks is not discussed, leaving unclear how well the method transfers to domains like healthcare, finance, or natural language, where OOD robustness is also critical.\n- The proposed approach introduces multiple MLP branches (for learning potential and distribution functions), PDE-based losses, and Fourier-domain regularization, all of which significantly increase computational and memory overhead.\n- Several derivations (e.g., use of plane wave decomposition, homogeneous steady state) rely on simplifying assumptions (e.g., uniform ion background, constant velocities) that may not capture the full complexity of real-world feature distributions.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-27"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a novel physics-inspired framework named Collective Behavior Dynamics (CBD) to tackle out-of-distribution (OOD) problems. The core idea is to treat high-level features from a neural network as charged particles interacting within a self-consistent electric field, and collective behavior of these particles is modeled using the Vlasov-Poisson system. In-distribution data is assumed to correspond to initial states that converge to a steady state within this system, and the set of all such initial states forms a \"basin of attraction\". OOD detection is then framed as determining whether a new input falls within this basin. For OOD generalization, the goal is to expand the basin of attraction, making the model robust to a wider range of perturbations. The authors achieve this by analyzing system stability through a dispersion relation and introducing a regularization loss to suppress unstable modes.\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\nNovelty: The paper's main strength lies in its novel perspective of bridging concepts from physics (the Vlasov-Poisson system) with deep learning. This provides an interpretable model for understanding OOD phenomena, moving beyond purely statistical approaches.\n\nStrong Empirical Performance: The proposed CBD method achieves state-of-the-art results on multiple benchmarks for both OOD detection and OOD generalization. This demonstrates the practical effectiveness of the physics-inspired approach.\n\nUnified Approach: The framework addresses both OOD detection and generalization within a single conceptual model. The basin of attraction serves as a unifying concept for identifying outliers and for quantifying and improving model robustness.\nCompatibility: The proposed method is a modular addition to existing network architectures. The experiments show that it can be combined with other advanced OOD generalization techniques (like SAM and SAGM) to yield further performance improvements.\n\nWeakness:\n1.The paper's entire theoretical foundation is based on treating feature vectors as charged particles and describing their behavior with the Vlasov-Poisson system. However, the paper does not sufficiently justify how much deviation will this approximation induce and why using this specific model.\n\n2.The Vlasov-Poisson system is difficult to handle in high-dimensional spaces. The paper applies this model to the high-dimensional feature space generated by deep networks, but it does not explicitly address the challenges posed by the \"curse of dimensionality.\"\n\n3.The framework introduces several new and non-standard hyperparameters, such as the loss weights (α, β), the wavevector scaling factor (σ), and the wavenumber (N). Hyperparameter analysis is required.\n\nQUESTIONS:\nRegarding In-Distribution Structure: The mathematical implementation of the paper (Equation 4-8) seems to build only one steady-state solution and one corresponding basin of attraction. This presupposes that the dynamic behavior of in-distribution (In-D) data is unimodal. However, real-world datasets are often highly multimodal. How to bridge this gap?\n\nRegarding the Model Choice: How crucial is the specific choice of the Vlasov-Poisson system? Could simpler dynamical systems or energy-based models capture the essential dynamics of InD vs. OOD data?\n\nRegarding steady state: The entire theory relies on the assumption that a steady state exists. However, during Stochastic Gradient Descent (SGD) training, the underlying electric field actually changes drastically at each step due to data being fed in mini-batches. It is questionable whether the concepts of steady state can still strictly hold in a constantly changing field.\n\nRegarding assumption: The paper assumes that high-level features behave like charged particles with uniform initial velocities. How sensitive is the model's performance to this assumption? Have the authors explored alternative physical analogies or initial conditions?\n\nLIMITATIONS:\nSee weakness and questions", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces a novel physics perspective on out-of-distribution detection by treating high-level data features as particles in a field. These particles evolve under the influence of a learned potential field, with in-distribution samples converging toward a steady-state region or “basin of attraction.” The boundary of this basin is then used as a decision surface for detecting OOD inputs. The authors support their proposal with theoretical results involving partial differential equations and evaluate their approach on standard OOD benchmarks.\n\nSTRENGTHS AND WEAKNESSES:\n*Strengths*\n- The idea of interpreting feature dynamics via a physical system governed by a PDE and identifying the basin of attraction as an OOD boundary is original and interesting\n- The authors attempt to rigorously ground their model in physics-inspired PDE theory, including steady-state solutions and stability analysis \n- The approach appears to be usable in a post-hoc setting, potentially making it broadly applicable to existing trained models (though this is not clearly communicated in the main text).\n- The authors speculate that model robustness may correlate with the size of the basin of attraction, which, if substantiated, could offer a new direction for designing new methods.\n- The approach achieves supposedly SotA performance for OOD detection and generalisation (however, I was not able to reach sufficient clarity on how this method produces scores for an individual input point, and how exactly the networks are trained to confidently interpret these results, see weakness below)\n\n*Weaknesses*\n- Key terms like \"collective behavior,\" \"self-consistent electric field,\" \"macroscopic properties,\" and \"perturbation\" are not clearly defined early in the paper, making it very hard to appreciate clearly without several passes\n- Many technical statements are vague or confusing (e.g., “Plane wave modes” as an x-axis label in a figure; unclear phrasing such as “measure its boundary” without formally clarifying what \"its\" refers to).\n- The flow of theoretical principles (e.g., Principles 1 and 2) lacks sufficient intuitive grounding and logical coherence (i.e. \"thus\" is used despite it being unclear how the two principles are necessary or sufficient for the subsequent statement).\n- Several figures (e.g., Figure 1 and Figure 2) are confusing or potentially mislabeled, weakening the explanatory power of the paper.\n- There is an over-reliance on jargon without providing accessible interpretations early in the paper, making the work difficult to follow even for an expert audience familiar with OOD literature.\n- It’s not transparent from the main body how the method is actually used to compute OOD scores. Only by reading the appendix does it become evident that the method is post-hoc (\"post-hoc\" is not even mentioned anywhere in the paper, nor the fact that the F and phi functions are learned with gradient descent using held out InD data; my experience of reading this paper was that I like the idea but I felt continuously unclear what the method itself actually is until reading the appendix--I should not need to read the appendix to appreciate the actual algorithm)\n- The use of \"batch\" in the pseudocode is ambiguous -- it's not clear whether the method assumes access to a test-time batch or operates on individual points, it's not clear whether the batch is used just to fit the F and phi, but then at test time use only a singleton input point, or if the intended use is to use batches at test time.\n- “we posit that network robustness improves as the basin’s range expands.” → “How can we enlarge basin of attraction’s boundary to enhance model generalization?” This is an interesting idea but I don’t like that they went from an idea to a question that presumes the idea is good and operationalises it. It is not clear that what they posit is indeed true, so it feels like a big leap to then start already seeking to maximize it.\n- Notation in Theorem 2 (e.g., $L_1$, $L_\\infty$, $n_i(z)$, $\\delta(v−v_0)$) is introduced without definition.\n- The physical analogy (particles, mass, steady state) is inconsistently applied and appears more illustrative than foundational e.g. (\"mass\" appears once in the paper, but no definition or intuition).\n- Modulo my lack of clarity on the exact evaluation setting (e.g. what is the \"batch\" in the pseudo-code, how many particles lie in R^z for an individual input point (is this $N$?)) the results seem compelling, but confidence intervals are provided in the tables without any explanation for what they represent and how they are constructed.\n\n*Small points*\n- Figure 1 shows only a single particle, despite the paper’s emphasis on collective particle dynamics. Consider revising to reflect the collective behavior.\n- The x-axis label of Figure 2 “Plane wave modes” is confusing and lacks explanation. Also, fix the typo “solusion.”\n- In the sentence “as illustrated in Figure 6,” it seems you meant Figure 2 instead.\n\nQUESTIONS:\nPlease help me address the weaknesses above. In particular, can you explain the full training and testing procedure for your models?\nAdditionally, what hyperparameter tuning was performed for your method? (e.g. how did you choose the MLP architectures etc.)\n\nNote that I am willing to raise my score upon reaching more clarity on the above.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-02"}