arXiv:2605.15965v1 Announce Type: new Abstract: Variational Autoencoders (VAEs) often exhibit a polarised regime in which latent variables separate into active, passive, and mixed subsets. Existing criteria for identifying active dimensions depend on a Gaussian prior, limiting their applicability to variational models and specific priors. We propose a simple information-theoretic classification of the polarised regime based on the entropy of the mean representation. We show theoretically how this entropy couples to KL minimisation through entropy--variance bounds, and we relate the resulting criterion to Bonheme's active/passive conditions. We also clarify a key limitation: entropy of the mean alone cannot reliably distinguish active from mixed dimensions without additional signals from the variance representation. Empirically, we evaluate the entropy criterion on $\beta$-VAEs, identifiable VAEs, Least-Volume Autoencoders, and L2-regularised autoencoders, and find that it consistently recovers a polarised regime when such a regime is present across the model classes studied. Finally, we show that passive dimensions can yield small but consistent improvements on downstream tasks when latent codes are appropriately normalised, suggesting that collapse is often a matter of scale rather than absolute information removal.
Science Journals
arXiv:2605.15788v1 Announce Type: new Abstract: Proactive autoscaling for containerized workloads depends on knowing the provisioning delay, i.e., the time between a scaling decision and the moment new capacity is ready to serve traffic. In practice, this cold-start duration can vary substantially across environments and even across consecutive scale-out events. We present ADAPT (Adaptive Duration Approximation for Predictive Timing), an online EWMA estimator that tracks coldstart duration at runtime. ADAPT feeds a dynamic planning horizon, FH-OPT, into a Model Predictive Controller (MPC) that optimizes replica counts over a rolling window. Together, these components form a closed-loop proactive autoscaling design that adapts its lookahead based on measured provisioning delay. Evaluated across three policies (MPC+LSTM, MPC+Prophet, HPA) and six workload archetypes with five random seeds, MPC+LSTM achieves below 5% SLA violation on all workloads, compared with 7-19% for reactive HPA and up to 28.7% for MPC+Prophet on bimodal traffic.
arXiv:2605.15671v1 Announce Type: cross Abstract: Multimodal 3D MRI brain tumor segmentation is a pivotal step in radiotherapy target delineation, surgical planning and post-treatment assessment. Existing methods often assume artifact-free MRI images. However, inevitable patient motion during scanning introduces artifacts and blur that degrade boundary and texture features, leading to poor segmentation performance. To bridge this gap, we introduce Degradation-Aware Blur-Segmentation Net (DABSeg), a synchronous deblurring 3D multimodal MRI segmentation network that unifies blur removal and accurate segmentation. Specifically, we propose a feature-domain motion-deblurring stem to compensate for blur and rebalance intensity. Concurrently, the backbone network embeds a blur-aware cross-modal cross-attention module and multi-scale residual aggregation to yield effective modality complementarity. Notably, we optimize a joint loss that combines weighted Dice with a clear-reference reconstruction term, where imbalanced weights are applied to small targets to boost learning intensity and predictive stability for small lesions and border regions. Systematic comparisons and ablation experiments on the BraTS2020 dataset under both clear and degenerative conditions consistently demonstrate that DABSeg surpasses state-of-the-art methods in tumor Dice score and boundary precision. These results validate the effectiveness of degenerative-aware cross-task collaborative learning in improving the robustness and clinical utility of multi-modal 3D brain tumor segmentation under realistic degenerative conditions. The source code is available at https://github.com/YuchunWang24/DABSeg_ICPR
arXiv:2601.15818v3 Announce Type: replace-cross Abstract: Advances in accelerator technology have led to significant improvements in the quality of muon beams over the past decades. Investigations of the muon and muonium enable precise measurements of fundamental constants, as well as searches for new physics beyond the Standard Model. Furthermore, by utilizing muon beams with high intensity and polarization, studies of the dynamics of the muon and muonium within atomic level can offer valuable insights into materials science. This review presents recent progress and prospects at the frontiers of muon beams and high-precision muonium physics. It also provides an overview of novel methods and detection techniques to achieve high sensitivities in different areas, including particle physics, nuclear physics, materials science and beyond.
arXiv:2604.12750v2 Announce Type: replace-cross Abstract: We study how exact Solvability Complexity Index (SCI) statements should be formulated for families of computational problems rather than for single problems. While the equality \(\mathrm{SCI}_G (\mathcal P)=k\) is unambiguous for an individual computational problem \(\mathcal P\), the family setting requires one to distinguish family-pointwise exactness, witness-space sharpness, and worst-case exactness. We formalize this trichotomy, prove that witness-space sharpness coincides with worst-case exactness but is, in general, strictly weaker than family-pointwise exactness, and give a canonical source-family example witnessing the strictness. We then establish two positive upgrade theorems: an abstract pullback principle and a concrete finite-query criterion guaranteeing that witness-space sharpness upgrades to family-pointwise exactness. Next, we introduce a decoder-regular finite-query transport preorder on SCI computational problems, prove that it is a preorder, derive a transport-saturation sufficient criterion extending the principal-source package, and show that the associated transport degrees need not form a lattice in full generality. We analyze the natural decoder classes \(\mathscr R_{\mathrm{cont}}\) and \(\mathscr R_{\mathrm{Bor}}\): on the full class the corresponding quotients are not upper semilattices, while on the nondegenerate subclass the preorder is upward and downward directed. Finally, we exhibit two natural positive families realizing the principal transport mechanism: exact integration on compact intervals and a fixed-window spectral decision family obtained by block-diagonal stabilization.
arXiv:2605.14236v2 Announce Type: replace Abstract: Pairwise Ranking Prompting (PRP) elicits pairwise preference judgments from an LLM, which are then aggregated into a ranking, usually via classical sorting algorithms. However, judgments are noisy, order-sensitive, and sometimes intransitive, so sorting assumptions do not match the setting. Because sorting aims to recover a full permutation, truncating it to meet a call budget does not produce a dependable top-K. We thus reframe PRP reranking as active learning from noisy pairwise comparisons and show that active rankers are drop-in replacements that improve NDCG@10 per call in the call-constrained regime. Our noise-robust framework also introduces a randomized-direction oracle that uses a single LLM call per pair. This approach converts systematic position bias into zero-mean noise, enabling unbiased aggregate ranking without the cost of bidirectional calls.
arXiv:2605.15787v1 Announce Type: new Abstract: Why does a Transformer that has memorized its training set wait thousands of steps before it generalizes? Existing accounts locate this delay in norm minimization, feature emergence, or the late discovery of sparse subnetworks. These explanations capture important parts of the transition, but ignore a constraint unique to attention-based models: if attention discards an informative token, no bounded downstream computation can recover it. We formalize attention as an implicit Bayesian posterior over the task dependency graph and prove that generalization requires two separable conditions: a familiar Goldilocks bound on MLP capacity, coinciding with norm-based theories of grokking, and a novel Bayesian structural condition requiring attention to place sufficient mass on every informative token. This decoupling explains delayed generalization as delayed structural inference. Early in training, the MLP memorizes through unaligned features, drives the cross-entropy loss near zero, and thereby starves attention of structural gradient. Weight decay must then erode memorization before the missing graph becomes learnable, yielding the known inverse-weight-decay delay, which we derive as a structural waiting time. We then prove that this explaining-away delay can be bypassed by a KL-based structural intervention, yielding an inverse-intervention-strength scaling law for the grokking time. Experiments on algorithmic sequence tasks isolate structure from capacity and show that this Bayesian ticket matches or outperforms lottery-ticket transfer.
arXiv:2605.16225v1 Announce Type: new Abstract: The study of optimal preemption policies for status update systems has been a recurring topic in the age of information (AoI) literature, where threshold-based structures have been shown to be optimal under a generate-at-will update generation model under certain assumptions. In this work, we study the effectiveness of threshold-based policies for a system with random update arrivals. In this regard, we introduce an analytical framework for evaluating the AoI of multi-threshold preemption policies and present interesting characteristics of the structure of the optimal preemption policy. We show the effectiveness of these threshold-based policies over the traditional probabilistic preemption policies and single-threshold policies, where we observe that significant gains in terms of AoI can be obtained by utilizing both the age of the packet and the age of the system when designing these preemption policies.
arXiv:2605.15848v1 Announce Type: new Abstract: Conversational interfaces powered by large language models (LLMs) are widely used for ideation and analysis, yet their linear structure limits exploration of alternatives and management of long-running interactions. We present CanvasConvo, a conversational interface concept that transforms linear chat into a branching conversation tree embedded in a spatial canvas. CanvasConvo enables users to explore what-if scenarios by branching directly from conversational content, supporting parallel development of alternative directions. These branches are visualized on a canvas while remaining integrated with a familiar chat interface, allowing users to switch between linear and non-linear interaction. Features such as timeline-based navigation, automatic tagging and summarization, and context-aware controls (e.g., goals, reusable prompts) support structured interaction and continuity. We evaluated CanvasConvo in a 5-7 day field study with 24 participants. Our findings highlight how non-linear conversational structures support exploratory workflows and different interactions in LLM-based work.
arXiv:2605.16222v1 Announce Type: new Abstract: Aphasias, selective language impairments which can arise from brain damage, reveal the functional organization of human language by providing causal links between affected brain regions and specific symptom profiles. Drawing on this literature, we introduce an aphasia-inspired technique to characterize the emergent functional organization of language models (LMs). We ``lesion'' (zero-out) model parameters and measure the effects of this intervention against clinical aphasia symptoms, as diagnosed by the Text Aphasia Battery (TAB). When applied to 112,426 outputs from five 1B-scale LMs, the full range of evaluated symptoms surface, but in distributions largely distinct from those of humans. Our method uncovers broad symptom-profile differences between attention components (query, key, value, output) and feed-forward components (up, gate, down), with weaker evidence for differences among components within the same mechanism. We also find an effect of depth, where lesions in early layers disproportionately cause syntactic and semantic symptoms while late-middle layers yield higher rates of phonological and fluency deficits. Although some LM lesions induce quantitatively more similar profiles to some human aphasia types than others, qualitative differences in symptom patterns between LMs and humans suggest that aphasia syndromes are heavily influenced by the details of learning and processing rather than being a domain-invariant consequence of disrupted language processing.
arXiv:2605.16126v1 Announce Type: new Abstract: For a fixed flow-based generative model under a small inference budget, sample quality can depend strongly on where the sampler spends its few function evaluations. Flow matching and Schr\"odinger bridges define probability paths, yet their inference grids are usually heuristic or inherited from one-endpoint diffusion. We derive a conditional-marginal entropy-rate objective for bridge-aware discretization, separating endpoint-conditioned bridge geometry from marginal flow evolution, and use it to build a training-free entropic inference-time scheduler from first principles. For Gaussian Brownian bridges this rate is closed-form and U-shaped, motivating boundary-heavy nonuniform grids. On trained two-dimensional bridge/flow models, the estimated profile recovers the predicted shape and improves 10-step ODE-Heun MMD over linear by 18.1%, with a paired 22.7% SDE-Heun improvement in the same low-NFE sweep. On EDM/CIFAR-10, the entropic time-discretization gives the best tested five-step FID (186.3 \pm 4.0 versus 200.5 \pm 2.9 for linear and 238.0 \pm 5.3 for cosine). On AlphaFlow protein generation, entropic conditional-marginal (cond-marg) scheduling shows advantage in low-NFE regimes on both CAMEO22 and ATLAS benchmarks. These results support entropy-rate scheduling as a practical low-budget allocation signal for high-dimensional bridge and flow samplers.
arXiv:2605.15705v1 Announce Type: new Abstract: World models aim to improve robotic decision making by predicting the consequences of actions. However, in practice, their predictions often become unreliable once the robot encounters states outside the training distribution, limiting their effectiveness at deployment. We observe that execution itself provides a natural but underutilized signal: after each action, the robot directly observes the true next state, revealing the mismatch between predicted and actual outcomes. Building on this insight, we propose feedback world model, a new paradigm that closes the loop between prediction and observation at inference time. Instead of treating the world model as a static open-loop predictor, our method maintains a lightweight feedback state that is updated online to iteratively correct future predictions, compensating for model errors using real-time observations without additional training data or parameter updates. We show that this process can be interpreted as a latent-space observer and admits convergence guarantees under mild conditions. We further introduce action-aware guidance to better translate corrected predictions into control by emphasizing action-controllable components while suppressing irrelevant variations. Experiments on LIBERO-Plus, Robomimic, and real-world manipulation tasks demonstrate that our method substantially improves both prediction accuracy and policy performance under distribution shift. In particular, it reduces world model prediction error by up to 76.4% and improves out-of-distribution (OOD) success rate by 30%. These results show that incorporating real-time feedback at inference time provides a simple yet powerful alternative to static world modeling.
arXiv:2605.15695v1 Announce Type: new Abstract: Fueled by the ability to mine real-world graph data, GNN applications have experienced phenomenal growth. Sparse Matrix-Matrix Multiplication (SpMM) is a critical operator in GNNs. However, existing SpMM designs for GNNs struggle to adapt to diverse input characteristics. In this paper, we first conduct a comprehensive analysis of existing SpMM optimizations, revealing their limitations through statistical and empirical evidence. Based on this analysis, we introduce ParamSpMM, a parametric approach for highly adaptive and efficient SpMM computation in GNNs. It incorporates a new data structure, the Parameterized Compressed Sparse Row (PCSR), to flexibly integrate existing optimization techniques. ParamSpMM enables the configuration of these optimization techniques according to various input characteristics. Furthermore, we complement ParamSpMM with an ML-based SpMM-decider that predicts optimal configurations based on carefully crafted input features. Our evaluations demonstrate that ParamSpMM outperforms Nvidia cuSPARSE with an average speedup of 1.92x, significantly enhancing GNN training efficiency.
arXiv:2605.15786v1 Announce Type: new Abstract: We present a new strategic voting model where we use uncertainty representation to model preferences. Specifically, we use probability sets as uncertainty representations, together with lower and upper expected utility gains to take strategic decisions. Focusing on belief functions in particular, we demonstrate that this very expressive model includes in one sweep many existing models based on probabilities, sets or incomplete preferences. Additionally, we generalize several well-known convergence results from the literature to this broader representational setting. Furthermore, we illustrate how this model can capture more realistic scenarios for practical applications but also raises theoretical challenges.
arXiv:2605.16219v1 Announce Type: new Abstract: Differential privacy changes the effective sample size governing CVaR learning. For tail mass $\tau$, the privacy-relevant sample size is not $n$, but $n\tau$; equivalently, the effective private tail sample size is $\epsilon n\tau$. Private CVaR excess risk decomposes into ordinary tail-risk statistical error and a privacy price. This decomposition is complete for scalar estimation and finite classes: scalar estimation has rate $\Theta(B \min\{1,(n\tau)^{-1/2}+(\epsilon n\tau)^{-1}\})$, and finite classes of size $M$ have rate $\Theta(B \min\{1,\sqrt{\log(2M)/(n\tau)}+\log(2M)/(\epsilon n\tau)\})$. These complete rates hold under pure DP, and their lower bounds extend to approximate DP in the stated small-$\delta$ regimes. For convex Lipschitz learning, modular upper and lower reductions show that the CVaR-specific privacy term necessarily scales as $1/(\epsilon n\tau)$, with dimension dependence inherited from private stochastic convex optimization. Together, these results identify ordinary private learning on $\Theta(n\tau)$ informative tail records as the canonical hard subproblem inside private CVaR learning.
arXiv:2605.15701v1 Announce Type: new Abstract: Memory data are ubiquitous in Large Language Model (LLM)-based agents (e.g., OpenClaw and Manus). A few recent works have attempted to exploit agents'memory for improving their performance on the question-answering (QA) task, but they lack a principled mechanism for effectively modeling how memory data evolves over time and retrieving memory data effectively, leading to poor performance in memory utilization. To fill this gap, we present H-Mem, a novel memory mechanism via a hybrid structure that can not only effectively model the evolution of agent memory over a long period of time, but also provide an efficient memory retrieval approach. Particularly, H-Mem builds a temporal and semantic tree structure that allows the short-term memory data to evolve progressively into long-term memory data, where the latter provides summarized information about the former, while simultaneously constructing a knowledge graph to capture the relationships between entities in memory. Moreover, it offers an effective memory retrieval approach by exploiting the hybrid structure of the tree and graph structures. Extensive experiments on three agent memory benchmarks show that H-Mem achieves state-of-the-art performance on the QA task.
arXiv:2505.21535v4 Announce Type: replace Abstract: While transformers dominate modern vision and language models, their attention mechanism remains poorly suited for in-memory computing (IMC) devices due to intensive activation-to-activation multiplications and non-local memory access, leading to substantial latency and bandwidth overhead on ReRAM-based accelerators. To address this mismatch, we propose FAR, a Function-preserving Attention Replacement framework that substitutes all attention in pretrained DeiTs with sequential modules inherently compatible with IMC dataflows. Specifically, FAR replaces self-attention with a multi-head bidirectional LSTM architecture via block-wise distillation to retain functional equivalence while enabling linear-time computation and localized weight reuse. We further incorporate structured pruning on FAR models, enabling flexible adaptation to resource-constrained IMC arrays while maintaining functional fidelity. Evaluations on the DeiT family demonstrate that FAR maintains comparable accuracy to the original attention-based models on ImageNet and multiple downstream tasks with reduced parameters and latency. Further analysis shows that FAR preserves the semantic token relationships learned by attention while improving computational efficiency, highlighting its potential for energy-efficient transformer inference on IMC-based edge accelerators.
arXiv:2605.15736v1 Announce Type: new Abstract: Biomedical Vision--Language Models (VLMs) have shown remarkable promise in few-shot medical diagnosis but face a critical bottleneck: \textit{fragility to prompt variations}.Existing adaptation frameworks typically optimize visual and textual prompts as independent streams, relying on ideal ``Golden Prompts''. In clinical reality, where descriptions are often noisy and heterogeneous, this modality isolation leads to unstable cross-modal alignment. To address this, we propose BiomedAP, a vision-informed dual-anchor framework with gated cross-modal fusion.BiomedAP enforces synergistic alignment through two mechanisms: (1) Gated Cross-Modal Fusion, which enables layer-wise interaction between modalities, acting as a dynamic noise regulator to suppress irrelevant textual cues; and (2) a Dual-Anchor Constraint that regularizes learnable prompts toward stable semantic centroids derived from both expert templates (High Anchors) and few-shot visual prototypes (Low Anchors). Extensive experiments across 11 benchmarks demonstrate that BiomedAP consistently surpasses baselines, achieving competitive few-shot accuracy and markedly enhanced robustness under prompt perturbations. Our code is available at: https://github.com/tongdiedie/BiomedAP. Keywords: Vision-Language Models; Prompt Learning; Parameter-Efficient Fine-Tuning; Few-shot Learning
arXiv:2605.16167v1 Announce Type: new Abstract: Ransomware recovery in critical manufacturing infrastructure is not only a backup-restoration problem. Production capability depends on coupled information-technology, operational-technology, physical-process, quality, logistics, identity, and supplier systems. After ransomware, a plant may rebuild servers yet remain unable to schedule work, authenticate operators, trust engineering workstations, release product, reconnect OT assets, or coordinate suppliers. This paper reframes manufacturing ransomware recovery as a critical-infrastructure continuity and interdependency problem. We conduct a PRISMA-guided multivocal review of academic literature, standards and government guidance, threat frameworks, public incident material, and verified full-text/source-page evidence anchors. The review identifies nine evidence-backed recovery failure modes: dependency blindness, untrusted restore point and backup over-trust, identity trust collapse, lack of proof-of-recovery, unsafe OT reconnection, segmentation assumption failure, capability mismatch, unmanaged degraded operation, and supplier dependency failure. We then introduce Minimum Viable Factory Recovery (MVF Recovery): the smallest safe, trusted, and operationally meaningful production capability that can be resumed under current dependency, evidence, identity, data, network, OT, and supplier constraints. MVF Recovery is an analytical objective rather than a claim of full recovery, implementation, or safety certification. The paper derives a recovery lifecycle and benchmarking directions as secondary outputs. The contribution is an evidence-calibrated foundation for capability-centric ransomware recovery in critical manufacturing infrastructure.
arXiv:2605.15704v1 Announce Type: new Abstract: Serverless computing has emerged as a promising computing paradigm for edge computing. However, adopting the event driven model in highly dynamic, heterogeneous, and distributed edge systems poses significant challenges in request placement and resource management. Efficiently allocating requests to containers is therefore critical to reduce resource over provisioning and unnecessary data movement. This paper proposes Scale, a Service Level Objective aware container scheduling and resource allocation framework designed for serverless edge computing. Scale employs a policy based deep reinforcement learning algorithm to balance system stability and performance under dynamic workloads. The design jointly incorporates SLO constraints, end to end latency, and data locality into the scheduling decision process. Extensive simulations using large scale real world datasets from Huawei Cloud demonstrate that Scale achieves solutions within a factor of 1.11 to 1.15 of a state of the art Integer Linear Programming solver, while reducing decision making time by up to 99%.
arXiv:2605.15729v1 Announce Type: new Abstract: Despite recent progress in constructing generalizable parallel algorithm portfolios (PAPs), no general-purpose approach is yet available for multi-objective binary optimization problems (MOBOPs). To fill this gap, this paper proposes domain-agnostic co-evolution of parameterized search for multi-objective binary optimization~(DACMO), which features two technical innovations. First, we propose a neural instance representation architecture that decouples domain-invariant and instance-specific features, enabling class-consistent instance generation across varying dimensions without problem-specific instance generators. Second, we introduce LLM-based automatic search operator generation into PAP construction, extending the search space from parameter tuning of predefined templates to operator-level algorithm design. We evaluate DACMO on four representative MOBOP classes to demonstrate its effectiveness as a general-purpose PAP construction method: the multi-objective match max problem~(MMMP), the multi-objective knapsack problem~(MKP), the multi-objective contamination control problem (MCCP), and the multi-objective complementary influence maximization problem~(MCIMP). Experimental results show that DACMO can be directly applied to all four problem classes without modification, outperforms PAPs built from classic MOEA templates, and achieves performance comparable to a privileged state-of-the-art baseline that relies on manually designed problem-specific instance generators, while outperforming it on two of the four evaluated problem classes.
arXiv:2509.01685v2 Announce Type: replace-cross Abstract: We consider sampling from a Gibbs distribution by evolving finitely many particles. We propose a preconditioned version of a recently proposed noise-free sampling method, governed by approximating the score function with the numerically tractable score of a regularized Wasserstein proximal operator. This is derived by a Cole--Hopf transformation on coupled anisotropic heat equations, yielding a kernel formulation for the preconditioned regularized Wasserstein proximal. The diffusion component of the proposed method is also interpreted as a modified self-attention block, as in transformer architectures. For quadratic potentials, we provide a discrete-time non-asymptotic convergence analysis and explicitly characterize the bias, which is dependent on regularization and independent of step-size. Experiments demonstrate acceleration and particle-level stability on various log-concave and non-log-concave toy examples to Bayesian total-variation regularized image deconvolution, and competitive/better performance on non-convex Bayesian neural network training when utilizing variable preconditioning matrices.
arXiv:2605.15851v1 Announce Type: new Abstract: This paper presents a data-driven framework for uncertainty propagation under unmeasured or statistically unmodeled (unstructured) disturbances. We consider residual disturbances, which consolidate all unstructured disturbances into a single quantity that can be estimated from data. Under mild assumptions, the resulting stochastic predictor is causal and distributionally consistent, enabling efficient uncertainty quantification through polynomial chaos expansions and higher-order Chebyshev inequalities. The proposed method is validated using experimental data from a smart home in Norway.
arXiv:2605.15733v1 Announce Type: new Abstract: Humans abstract experiences into structured representations to facilitate pattern inference and knowledge transfer. While the hippocampal-entorhinal (HPC-MEC) circuit is known to represent both spatial and conceptual spaces, the mechanisms for concurrently extracting abstract structures from continuous, high-dimensional dynamics remain poorly understood. We propose a brain-inspired hierarchical model that simultaneously infers latent transitions and constructs a predictive visual world model. Our architecture employs an inverse model for structural extraction alongside an HPC-MEC coupling model that dissociates relational structures (MEC) from integrated episodic scenes (HPC). Using primitive transformation dynamics as a benchmark, we demonstrate the model's capacity for structural abstraction. By leveraging velocity-driven path integration, the framework enables robust prediction and structural reuse across diverse contexts, thereby achieving structural generalization. This work provides a novel computational framework for understanding how brain-inspired, self-supervised learning of world models facilitates the acquisition of reusable abstract knowledge.
arXiv:2605.16211v1 Announce Type: new Abstract: Traditional scientific modeling typically begins with fixed, instance-wise effective equations and then carries out equation-specific analysis and computation, a procedure that becomes exceptionally challenging in complex applications such as multiscale systems. We propose an alternative paradigm by learning mesoscopic dynamics within a mathematically constrained hypothesis class. Building upon a generalized Onsager principle, we introduce a unified framework encompassing both dissipative and conservative mesoscopic dynamics. We establish uniform and a priori theoretical guarantees, including global well-posedness, asymptotic stability, unique factorization identifiability, and discrete energy dissipation, applicable to all spatio-temporal evolution equations within this hypothesis class prior to all learning stages. Data from each problem instance is then used to guide the identification of members within our hypothesis class, giving rise to accurate, robust and interpretable dynamical models. We empirically validate this framework on both data from continuum PDE models as a check, and on data arising from microscopic chain models for which exact meso-scale models are unknown. The proposed approach not only acts as an effective dynamics learner, but also offers vital interpretable diagnostics of the underlying physics.