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01.
arXiv (CS.CV) 2026-06-16

Pixel-TTS: Image based Text Rendering for Robust Text-to-Speech

Recent advances in pixel-based text modeling show that representing text as images enables models to exploit visual cues for language understanding. Grounding text in its visual form allows structurally similar characters with different Unicode encodings to produce similar embeddings, benefiting cross-lingual and zero-shot scenarios. Conventional text-based approaches treat each character independently, limiting generalization to unseen characters and requiring embedding expansion during cross-lingual adaptation. We propose Pixel-TTS, the first framework for visually grounded speech synthesis. It renders text as images and projects them through a 2D convolutional layer to generate embeddings. This design eliminates embedding matrix expansion during fine-tuning while improving robustness to unseen characters and orthographic variations. Extensive experiments show Pixel-TTS achieves competitive performance with strong baselines, faster convergence and robust zero-shot generalization.

02.
arXiv (CS.CL) 2026-06-16

SAAS: Self-Aware Reinforcement Learning for Over-Search Mitigation in Agentic Search

Agentic search enables LLMs to solve complex multi-hop questions through iterative reasoning and external search. Despite the effectiveness, these systems often suffer from a critical limitation in practice: agents fail to recognize their own knowledge boundaries, blindly triggering searches when internal knowledge suffices and failing to terminate search even when adequate evidence has been collected. The lack of self-awareness leads to severe over-search, incurring substantial inference latency and prohibitive computational cost. To this end, we propose SAAS, a novel RL framework designed to cultivate dynamic self-awareness that precisely regulates search behavior without compromising accuracy. SAAS introduces three key components: (i) a search boundary modeling mechanism, which identifies the search boundary under the evolving policy by contrasting search-disabled and search-enabled rollouts; (ii) a boundary-aware reward module, which translates this boundary awareness into trajectory-level penalties, suppressing unnecessary and redundant searches; and (iii) a stage-wise optimization strategy, which leverages a sequential curriculum to prioritize reasoning over search regularization, thereby avoiding reward hacking. Extensive experiments demonstrate that SAAS substantially reduces over-search, while maintaining accuracy. Our code and implementation details are released at https://github.com/XMUDeepLIT/SAAS.

03.
arXiv (CS.AI) 2026-06-15

Optimizing Agentic Reasoning with Retrieval via Synthetic Semantic Information Gain Reward

arXiv:2602.00845v3 Announce Type: replace Abstract: Agentic reasoning enables large reasoning models (LRMs) to dynamically acquire external knowledge, but yet optimizing the retrieval process remains challenging due to the lack of dense, principled reward signals. In this paper, we introduce InfoReasoner, a unified framework that incentivizes effective information seeking via a synthetic semantic information gain reward. Theoretically, we redefine information gain as uncertainty reduction over the model's belief states, establishing guarantees, including non-negativity, telescoping additivity, and channel monotonicity. Practically, to enable scalable optimization without manual retrieval annotations, we propose an output-aware intrinsic estimator that computes information gain directly from the model's output distributions using semantic clustering via bidirectional textual entailment. This intrinsic reward guides the policy to maximize epistemic progress, enabling efficient training via Group Relative Policy Optimization (GRPO). Experiments across seven question-answering benchmarks demonstrate that InfoReasoner consistently outperforms strong retrieval-augmented baselines, achieving up to 5.4% average accuracy improvement. Our work provides a theoretically grounded and scalable path toward agentic reasoning with retrieval. The code is available at https://github.com/dl-m9/InfoReasoner

04.
arXiv (CS.LG) 2026-06-15

Uncertainty Estimation and Generalization Bounds for Modern Deep Learning

arXiv:2606.13818v1 Announce Type: new Abstract: This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning systems. While neural networks achieve remarkable predictive performance, their ability to generalize and to quantify uncertainty remains only partly understood. This thesis approaches this challenge from both methodological and theoretical angles: unifying Bayesian inference, function-space modeling, and large-deviation theory under a common probabilistic perspective. On the methodological side, the thesis introduces the Deep Variational Implicit Process (DVIP), a scalable Bayesian framework that extends implicit processes to deep architectures. Complementing this, two post-hoc methods – the Variational Linearized Laplace Approximation (VaLLA) and the Fixed-Mean Gaussian Process (FMGP) – are proposed to equip pretrained deterministic networks with calibrated uncertainty estimates. The theoretical contributions focus on one of the central open questions in modern machine learning: why do large, over-parameterized neural networks generalize so well? To address this, the thesis develops a unified probabilistic framework that connects three key mechanisms – diversity, smoothness, and stochasticity – within the language of PAC-Bayesian and large-deviation theory.

05.
arXiv (CS.LG) 2026-06-16

Agent trajectories as programs: fingerprinting and programming coding-agent behavior

arXiv:2606.16988v1 Announce Type: cross Abstract: Benchmark scores tell you what an agent got right; they do not tell you how it got there. In this work, we introduce methods for comparing agents procedurally in different contexts, where the model, tasks, and approaches vary. We compare ten agents and find that they are identifiable by their behavioral habits, which we define as fingerprints: a probe over these procedural signatures attributes an unseen trajectory to the correct agent at 85.7% accuracy, controlling for leakage across tasks. We develop procedural representations for agent problem-solving procedures with an emergent vocabulary induction technique that is meant to be maximally compressive to avoid surface-level variation while being expressive enough to unveil the quirks of the models' patterns. We apply our framework to the software engineering evaluation dataset SWE-Bench to study the structural distinctness of agent trajectories and find that behavior is most similar between models from similar release periods and those that are distilled from one another (e.g., a distilled student model and its teacher have a Jensen-Shannon divergence of 0.25, about half the distance between other model pairs). As more models saturate evaluations, we believe that it will be important to probe model behavior along more holistic dimensions than success rates alone. We introduce ProcGrep, a library for auditing and evaluating agents for how they approach tasks at a procedural level given their traces in a top-down fashion. We believe this work has a range of applications to help developers work with and program coding agents, such as task-aware model routing, agent monitoring, and finer-grained cost analysis.

06.
arXiv (math.PR) 2026-06-15

Semiclassical limit of Polyakov-Liouville measure and Q-Curvature Uniformization on evev-dimensional manifolds

arXiv:2606.14443v1 Announce Type: new Abstract: We study the semiclassical limit of the Polyakov-Liouville measure $\boldsymbol{\nu}_\gamma$, which is a non-Gaussian measure on $H^{-\eps}(M)$ that has recently been extended from Riemann surfaces to general Riemannian manifolds $(M,g)$ of even dimension. We show that under an appropriate rescaling in the semiclassical limit as $\gamma\to0$, the normalized Polyakov-Liouville measure $\Q_\gamma$ concentrates on the unique smooth weight $u$ for which the conformal metric $e^{2u}g$ on $M$ has constant $Q$-curvature.

07.
arXiv (CS.LG) 2026-06-17

INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities

arXiv:2606.18032v1 Announce Type: cross Abstract: We propose a new weak-form Physics-Informed Neural Network approach (named INI-VPINN). INI-VPINN naturally incorporates Neumann boundary and interface conditions into the variational formulation. It removes the need for additional loss terms or multiple subdomain networks. This framework employs compact support weighting functions and integration by parts to implicitly impose flux and continuity constraints. In this way, it implicitly ensures physical consistency across material boundaries. The proposed method is tested on Poisson and Laplace problems with sharp interfaces and complex geometries. Results show that, compared with several other Physics Informed Neural Networks-based formulations, the INI-VPINN consistently achieves higher accuracy, smoother and faster convergence. The proposed framework provides a general approach for solving multimaterial problems with complex geometries and mixed Neumann-Dirichlet boundary conditions using neural networks. The implementation is publicly available in a GitHub repository.

08.
arXiv (quant-ph) 2026-06-19

Steady-state entanglement of spin qubits mediated by nonreciprocal and chiral magnons

arXiv:2509.13094v3 Announce Type: replace Abstract: We propose a hybrid quantum system in which a magnet supporting non-reciprocal magnons, chiral magnons, or both mediates the dissipative and unidirectional coupling of spin qubits. By driving the qubits, the steady state of this qubit-qubit coupling scheme becomes the maximally entangled Bell state. We devise a protocol where the system converges to this entangled state and benchmark it including qubit decay and dephasing. The protocol is numerically tested on a hybrid system consisting of nitrogen-vacancy (NV) centers coupled to magnon surface modes of an yttrium iron garnet (YIG) film. We show that the dephasing time of the NV centers forms the bottleneck for achieving the entanglement of NV centers separated by a distance within the magnon coherence length. Our findings identify the key technological requirements and demonstrate a viable route toward steady-state entanglement of solid-state spins over distances of several microns using magnonic quantum networks, expanding the toolbox of magnonics for quantum information purposes.

09.
arXiv (CS.LG) 2026-06-12

Mirror Descent on Riemannian Manifolds

arXiv:2603.17527v2 Announce Type: replace-cross Abstract: Mirror Descent (MD) is a scalable first-order method widely used in large-scale optimization, with applications in image processing, policy optimization, and neural network training. This paper generalizes MD to optimization on Riemannian manifolds. In particular, we develop a Riemannian Mirror Descent (RMD) framework via reparameterization and further propose a stochastic variant of RMD. We also establish non-asymptotic convergence guarantees for both RMD and stochastic RMD. As an application to the Stiefel manifold, our RMD framework reduces to the Curvilinear Gradient Descent (CGD) method proposed in [26]. Moreover, when specializing the stochastic RMD framework to the Stiefel setting, we obtain a stochastic extension of CGD, which effectively addresses large-scale manifold optimization problems.

10.
arXiv (CS.CV) 2026-06-15

HPSv3++: Scaling Reward Models Across the Full Spectrum of Diffusion Model Capabilities

Reward models guide text-to-image (T2I) systems toward outputs aligned with human preferences. However, typical reward models such as HPSv3 are trained on pre-annotated data from earlier T2I models, without accounting for quality discriminative shifts arising from evolving model capabilities and reinforcement learning (RL) iterations, limiting their broader applicability. In this work, we propose HPSv3++, a reward model framework that elevates the HPSv3 model for varying T2I model capabilities and their RL iteration changes across the full capability-iteration spectrum. Specifically, we first introduce HPDv3++, a 212K dual-dimension preference dataset annotated for text fidelity and aesthetic quality using a recent high-capability (Qwen-Image) model with human supervision. We then propose a two-stage training framework. Stage 1 employs data-aware orthogonal gradient projection to incorporate diverse aesthetic perception from HPDv3++ while preserving the original effective human preference knowledge in HPSv3. Stage 2 further leverages unlabeled data from T2I models spanning different capability levels and RL iterations, and introduces a joint capability-iterations conditioned signal for the reward model together with a standard deviation-driven unsupervised guidance mechanism, strengthening reward model across the capability-iteration spectrum. HPSv3++ achieves state-of-the-art preference prediction, outperforming HPSv3 9.8% on HPDv3, 5.5% on GenAI-Bench, while achieving 79.1%/88.1% on our proposed HPDv3++. When used for T2I RL training, it consistently improves GenEval scores across diverse T2I models, demonstrating its wide-range capabilities. The code is available at https://github.com/PlantPotatoOnMoon/HPSv3-PlusPlus.

13.
arXiv (CS.CV) 2026-06-16

PROSE: Training-Free Egocentric Scene Registration with Vision-Language Models

Registering two captures of the same indoor space taken at different times underpins persistent spatial memory for robots and AR systems, yet the realistic version of this task is egocentric and its most scalable form is RGB-only. Head-mounted cameras yield blurry, fast-moving, partially overlapping views from which dense geometry is hard to recover. Classical registration leans on exactly the clean point clouds this setting lacks, while learned scene-graph methods require a pre-built or annotated graph and a trained matcher that we find brittle under egocentric data. We take a different route, using a pretrained vision-language model as the source of both scene understanding and cross-scan matching. Our method, PROSE (Prompted Scene rEgistration), lifts each RGB sequence into an object-level 3D scene graph using off-the-shelf foundation models for geometry, segmentation, and language, then prompts the same VLM to match object instances across the two RGB sequences. To make this matching tractable and reliable, we leverage object heights as a prior and verify each proposed match with a paired same/different query, then solve for the rigid transform by hypothesizing a candidate per matched object and selecting the one with the strongest geometric consensus. PROSE adds no learned parameters and requires no depth sensor, training, or annotated graph. On the egocentric Aria Digital Twin and Aria Everyday Activities benchmarks, it outperforms both geometric and learned scene-graph baselines in registration accuracy, on ground-truth and RGB-reconstructed point clouds alike, and the scene graph it produces transfers directly to downstream tasks.

14.
arXiv (CS.AI) 2026-06-17

Counterfactual Optimization of Baseball Pitch Sequences and Estimation of Its Impact on Season-Level Statistics

arXiv:2606.17345v1 Announce Type: cross Abstract: Although pitch sequencing is a central topic in baseball analytics, previous studies have primarily focused on optimizing the final pitch within a single plate appearance, leaving the role of preceding setup pitches and their impact on long-term season-level performance insufficiently examined. To address these issues, this study conducted counterfactual analyses using MLB Statcast data. A Transformer-based machine-learning model was trained to predict whether a target pitch would result in an in-play outcome or swing-out. Counterfactual pitch sequences were then generated by replacing either the final pitch or the preceding setup pitch with alternative pitch types and locations while keeping the surrounding contextual information fixed. Optimal counterfactual selections were defined as those that minimized the predicted in-play probability, and their expected effects on pitchers' seasonal statistics were estimated using regression models linking model outputs to season statistics. The results suggest that the optimization of both final and setup pitches may substantially influence season-level performance, including improvements of more than 1.0 in K/9. The analyses also provided several practical insights, including velocity-band-specific effective locations, the importance of pitch commands, and the expansion of pitch-selection options through middle-velocity pitches. These findings quantitatively support the strategic importance of pitch sequencing in baseball.

15.
arXiv (CS.CV) 2026-06-18

ROSA-TFormer: A Radar-Optical Sensor-Aware Temporal Transformer for Pinus sylvestris Plantation Classification in Northern Shaanxi Using GEE-Derived Sentinel-1/2 Time Series

Accurate identification of Pinus sylvestris var. mongolica plantations is important for monitoring afforestation quality and ecological restoration in northern Shaanxi. This paper proposes ROSA-TFormer, a radar-optical sensor-aware temporal Transformer for P. sylvestris classification using Sentinel-1/2 time-series data generated on Google Earth Engine. The model integrates separate SAR and optical embedding branches, a sensor-aware gate, and temporal attention pooling to capture multi-source seasonal features. Experiments on monthly and half-month point-level datasets show that ROSA-TFormer achieves strong classification performance, with 99.67% overall accuracy, 99.56% macro F1, and 98.91% P. sylvestris F1 on the HalfMonth-dataBig dataset. Spatial block validation and ablation results further indicate the effectiveness of radar-optical temporal fusion and sensor-aware modeling. The results demonstrate the potential of ROSA-TFormer for point-level P. sylvestris plantation classification, while broader wall-to-wall validation remains necessary.

16.
arXiv (CS.CV) 2026-06-18

DART: A design-aware microfluidic chip paradigm for real-time live-cell image analysis

High-throughput microfluidic live-cell imaging generates rich single-cell data. Yet semi-automated procedures for locating regions of interest (RoIs), each containing one cell population, and removing surrounding microfluidic structures from recorded images, scale with the number of RoIs. This prevents real-time image analysis and delays time-to-insight by hours to days. We introduce the Design-Aware and Real-Time capable (DART) paradigm for microfluidic cultivation chips, which aligns the CAD blueprint with the physical chip and thereby enables throughput-independent localization of all RoIs and fully automated image processing across diverse RoI geometries and chip layouts. DART establishes this alignment through embedded fiducial markers and deep-learning-based marker detection. We validate DART using the Swiss Army Knife chip, which combines eight structurally distinct RoI designs across 1164 RoI locations. DART localizes all RoIs in five minutes, removes microfluidic structures from raw microscopy images in 40 ms, and performs fully automated image analysis, including cell segmentation, in under 1.1 s per image. Together, these capabilities establish DART as an end-to-end hardware-software paradigm with real-time-capable analysis that paves the way toward closed-loop and outcome-driven smart microscopy.

17.
arXiv (CS.LG) 2026-06-18

QUIVER: Cost-Aware Adaptive Preference Querying in Surrogate-Assisted Evolutionary Multi-Objective Optimization

arXiv:2605.04267v2 Announce Type: replace Abstract: Interactive multi-objective optimization systems face a budget allocation dilemma: one can spend resources on expensive objective evaluations or on eliciting decision-maker preferences that identify the relevant region of the Pareto set. Moreover, preference elicitation itself spans modalities with different information content and cognitive burden, ranging from cheap, noisy pairwise preference statements (PS) to richer but costlier indifference adjustments (IA). We study cost-aware optimization under an unknown scalarization and introduce QUIVER (Query-Informed Value Estimation for Regret), a surrogate-assisted evolutionary multi-objective optimizer that adaptively chooses between objective evaluations and heterogeneous preference queries. At each step, QUIVER selects the next action by maximizing the expected decision-quality improvement per unit total cost. Across DTLZ and WFG benchmarks under synthetic decision-maker models, QUIVER achieves the lowest final utility regret on challenging WFG problems (utility regret of 2.14 on WFG4, 2.82 on WFG9: a 25% improvement over baselines), outperforming all single-modality baselines. We analyze how the optimal mix of PS and IA adapts to problem difficulty: on easy problems (DTLZ2), QUIVER selects 80\% PS queries; on hard problems (WFG9), it shifts to 35% IA queries. This adaptive modality selection demonstrates cost-aware preference learning in action.

18.
arXiv (CS.AI) 2026-06-16

Mask-Proof: An LLM-based Automated Data Curation Pipeline on Mathematical Proofs

arXiv:2606.15258v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly capable of mathematical problem solving and can even assist with research-level proofs, yet we still lack a scalable and reproducible way to measure step-level reasoning in long proofs across diverse sources. This evaluation gap limits trustworthy AI assistance in proof-certified scientific progress. Existing evaluations often emphasize final answers or rely on costly expert grading, while end-to-end proof generation remains open-ended and hard to verify automatically. We introduce Mask-Proof, a pipeline that turns real proofs into automatically checkable masked-step tasks. It masks key formula steps, provides the necessary surrounding context, and evaluates model reconstructions with an LLM-based equivalence judge using repeated votes for stability. The resulting Mask-ProofBench contains 292 curated problems across diverse research areas. Experiments with 17 models show that reasoning-enhanced models outperform standard models by 12% to 27%. Our evaluator achieves 96.8% agreement with expert annotators, enabling faithful, reproducible, and comparable measurement of step-level mathematical reasoning. Benchmark, annotations, and code are available at https://github.com/weating/Mask-Proof.

19.
arXiv (CS.AI) 2026-06-16

How to Detect and Measure the AI Dangers to Democracy

arXiv:2606.16054v1 Announce Type: cross Abstract: Research on artificial intelligence and democracy has grown quickly over the last decade. A shared conclusion in this literature is that AI does not create new democratic problems so much as it makes old ones worse. We now see this across information ecosystems, in elections, and in public administration. However, despite growing evidence, we lack a clear way to prioritize risks in this area, compare them across domains, and identify where democratic control is most likely to break down. So, our problem is: How can we systematize the problems that AI systems pose to democratic processes? This paper argues that principal agent theory may fit the task. In many phases of democratic systems, principals delegate key functions to AI systems and their providers without really being able to monitor how these systems operate or the outputs they produce. Treating AI as a delegation problem helps identify accountability gaps and other governance failures. Most importantly, as we shall illustrate, it provides metrics for empirical assessments of AI impact on democracy. As a second analytical element, we draw on the NIST AI Risk Management Framework and its seven characteristics of trustworthy AI, which supply substantive criteria for evaluating delegated tasks. Operationalized across the three domains through measurable indicators and domain specific trustworthiness criteria, we propose an analytical framework that centers on institutional assessability as the central condition for democratic control over AI. However, we stress that how severe a harm is, and how much risk is acceptable, are evaluative judgments that current methodologies neither acknowledge nor operationalize. This becomes acute when such evaluative judgments are (silently) delegated to private vendors. We identify this as a strong limitation left for future work.

20.
arXiv (CS.LG) 2026-06-17

Discovering Functionally Selective Brain Regions with a Deep Topographic Multimodal Model

arXiv:2606.09770v2 Announce Type: replace-cross Abstract: Nearby neurons in cortex share similar response profiles, producing systematic spatial organization across sensory and cognitive systems. Recent topographic models reproduce aspects of this structure but remain unimodal and spatially constrain each layer separately, yielding fragmented maps that capture neither the contiguity of cortical processing streams nor their integration across modalities. We introduce Topo-Omni, a topographic multimodal model in which visual, auditory, and language/cognitive processing share a single contiguous in-silico sheet. Built by fine-tuning a pretrained foundation model with a spatial smoothness objective, this architecture develops clusters across modalities that are consistent with human neuroimaging, from sensory to cognitive systems. Driving or suppressing a cluster selectively biases or impairs perception, paralleling human intervention studies. Finally, we use our model to screen for novel clusters in-silico and discover new natural landscape and animal networks which we validate in human data. A single spatial principle thus organizes representations across modalities and processing stages, yielding testable hypotheses about cortical organization.

21.
arXiv (quant-ph) 2026-06-17

Optimal Probe State for Phase Estimation Under Covariant Measurement

arXiv:2606.18169v1 Announce Type: new Abstract: We study the optimization of input states for phase estimation under covariant measurements. Building on Holevo's framework, which provides the optimal covariant measurement for a fixed input state, we further optimize over the input state itself. For a general even $2\pi$-periodic cost function with non-negative Fourier coefficients, we derive a necessary and sufficient condition for the optimal input state: Its Fock coefficients are determined, up to arbitrary phases, by the eigenvector corresponding to the largest eigenvalue of a Toeplitz matrix defined by the cost function. This characterization yields an explicit expression for the attainable lower bound of the average cost under optimal covariant measurements and shows that this bound asymptotically approaches zero in the infinite-energy limit. For the specific cost function $W(\theta,\tilde{\theta})=4\sin^2[(\theta-\tilde{\theta})/2]$, we obtain the optimal input state and the corresponding minimum average cost in closed form, demonstrating Heisenberg scaling with respect to the mean photon number.

22.
Nature Biotechnology 2026-06-22

Affordable centimeter-scale 3D microscopy with submicrometer resolution

作者: 未知作者

Submicrometer-resolution three-dimensional (3D) imaging of large samples has been constrained by the short working distance, high cost and inflexible design of immersion objectives. We developed hybrid solid–liquid optics (HySIL) — a refractive framework with index-matched components — for submicrometer-resolution 3D imaging of centimeter-scale samples in various immersion media using inexpensive air objectives.

23.
arXiv (quant-ph) 2026-06-19

Proposal of quantum arrival-time measurement with a Bose-Einstein condensate

arXiv:2606.20278v1 Announce Type: new Abstract: This work shows how a Bose-Einstein condensate of ultracold atoms could be used to address a long-standing question in quantum theory: how much time does it take for a particle to reach a detector? To this end, we propose a realistic experimental setup, whose key idea is not to measure arrival times directly, but the arrival flux on the detector as a function of its position. This novel approach not only solves practical issues with having a detector close to the system, but also results in signals that allow to unambiguously distinguish different theoretical predictions. This proposal raises prospects for resolving the decades-old debate on this fundamental issue.

24.
arXiv (CS.CL) 2026-06-18

Enhancing Multilingual Reasoning via Steerable Model Merging

Model merging is an effective technique for composing the capabilities of a multilingual model and a reasoning model. It has achieved promising generalization in multilingual reasoning tasks by aligning feature spaces of different models. However, the merged single model often fails to address the conflicts between source models, leading to suboptimal performance. In other words, the one-size-fits-all merging strategy may not align with the characteristics of different inputs which may require prioritizing certain models over others. To this end, we propose a Steerable Model Merging (ST-Merge) framework to modulate the contribution of each source model. To realize this idea, we introduce a gated cross-attention mechanism to weight or filter the two attended source models in an adaptive manner. Extensive experiments demonstrate that ST-Merge consistently outperforms multiple strong baselines on four multilingual reasoning benchmarks across 21 different languages.

25.
arXiv (quant-ph) 2026-06-15

Tamed Feynman-Kac diffusion processes: Killing-branching intertwine

arXiv:2605.07824v2 Announce Type: replace-cross Abstract: Relaxation to equilibrium of a drifted Brownian motion is quantified by a transition probability density function, whose main (multiplicative) entry is an inferred Feynman-Kac kernel of the Schr\"{o}dinger semigroup operator. Although seemingly devoid of a natural probabilistic significance (except for its explicit path integral definition), the pertinent kernel relaxes to equilibrium as well. The implicit Feynman-Kac potential ${\cal{V}}(x)$, continuous, confining and bounded from below, may take negative values. If positive, ${\cal{V}}(x)$ can be interpreted as the killing rate of the decaying diffusion process. In case of relaxing F-K kernels the killing effects are tamed (often overcompensated). The taming inavoidably appears in conjunction with the existence of the negativity subdomains of ${\cal{V}}(x)$ in $R$. If locally ${\cal{V}}(x) < 0$, its sign inversion $- {\cal{V}}(x)$ can be interpreted as the branching (cloning, alternatively bifurcation) rate in the course of the other wise free random motion. The arising killed diffusion processes with branching, we interpret as the possible path-wise background of tamed (relaxing) Feynman-Kac diffusions. We present acomputer-assisted path-wise arguments, towards a consistency of the killing/branching taming scenario, for a number of nonlinear model systems in one space dimension. Special attention is paid to Feynman-Kac potential shapes in the double well form, where an analytic access to eigenvalues and eigenfunctions is scarce. Throughout the paper the dynamics refers to the positive real time. Since the Newton-type equations of motion for admissible classical trajectories have a Euclidean form (due to the sign inverted force term), we give a brief resume of a couple of their explicit solutions, without recourse to the Euclidean time intuitions, and the instanton lore of related quantum model systems.