arXiv:2607.05612v1 Announce Type: new Abstract: Language model (LM) perplexity (PPL) has historically been used as a proxy for automatic speech recognition (ASR) word error rate (WER), with prior work reporting an approximately linear relation in log-log space. Modern end-to-end ASR systems challenge this assumption because they already contain internal language modeling capacity, are often evaluated without external language models, and can now be combined with neural LMs and large language models (LLMs) through different recognition strategies. This paper revisits the relation between PPL and WER for modern ASR systems. We study whether external LMs still improve current end-to-end ASR systems, whether the PPL-WER relation remains linear in log-log space, how encoder context length affects this relation, and how LLM perplexities fit into the trend observed for standard neural LMs. We further investigate internal language modeling (ILM) in attention-based encoder-decoder systems and show that ILM subtraction changes the observed PPL-WER relation, indicating that the decoder's internal LM must be considered when interpreting the effect of external LM quality.
Science Journals
arXiv:2607.05679v1 Announce Type: new Abstract: Language models (LMs) exhibit problematic biases, such as stereotypes. Effectively analyzing and mitigating such biases requires accurate and generalizable evaluation methods of the underlying associations. Some existing approaches focus on downstream metrics that analyze associations in generated text. Since generated text content can vary drastically across LMs, such metrics often require specialized evaluation datasets, which limits the generalization of such downstream metrics. In contrast, upstream metrics examine LMs at the fundamental level of embeddings or continuation probabilities, enabling principled association analyses across LMs. Yet, to date, no upstream metric for generative LMs has uncovered a strong relationship with real-world associations, including those measured in generated text. To address this gap, we introduce the Relative Probability Association Metric (RPAM), an association evaluation metric for generative LMs. For three LMs of different quality of language generation and purpose (Mistral-7B-Instruct, Mistral-7B, and GPT-2) and well-studied evaluation datasets (WEAT-WS, Bellezza, WS-353, and SST2), we find a strong relationship between upstream RPAM measurements and corresponding implicit and explicit associations observed in humans, as well as biases measured downstream with LM-specific tasks, outperforming prior record values where applicable.
arXiv:2607.05708v1 Announce Type: new Abstract: Recent LLM-based agent systems continuously accumulate context across multi-turn interactions, tool invocations, and cross-session workflows. Replaying the full history for every request quickly becomes impractical: long contexts increase prefill cost, may exceed context limits, and often bury task-relevant evidence in irrelevant content, degrading both serving efficiency and output quality. We propose Akashic, a low-overhead memory system built around MemAttention, which organizes context into bounded chunks and models semantic relationships across chunks, preserving cross-chunk evidence without repeatedly rewriting the full history. Akashic further applies hardware-software co-designed memory placement to co-locate likely co-retrieved chunks, reducing retrieval fragmentation and I/O overhead. Across four representative workloads and three model sizes, Akashic improves task accuracy by up to 10.2 points, throughput by up to 1.21x, and sustainable request rate by up to 1.88x over strong prior memory baselines.
arXiv:2607.05877v1 Announce Type: new Abstract: The concept of Digital Twin (DT) consists of a physical asset, a digital asset, and their bidirectional data exchange, differing the DT from concepts with lower level of integration. Availability of the bidirectional interconnection not only enables monitoring of system states but also allows automated control of the system. Leveraging the DT concept, this paper presents a practical implementation of an electric drive DT by means of a permanent magnet synchronous machine (PMSM) in a test lab environment. The approach aims to virtually sense the disturbance variable, here the acting load torque. By integrating an observer controller into the PMSM control loop, the DT enables compensation of the disturbance variable, which is not measurable in many applications. The results of the DT implementation recorded on the test bench demonstrate an effective disturbance compensation of the acting load torque by the observer controller. However, the results still show a deviation between the observed and measured load torques, indicating room for further refinement. This work serves as a first step towards further practical applications of the DT in the electric drive testing environment.
arXiv:2607.05994v1 Announce Type: new Abstract: Human-Object Interaction (HOI) video generation aims to synthesize realistic videos of humans manipulating diverse objects, serving as a promising avenue for AI-driven live streaming e-commerce. A primary obstacle in this domain lies in the complexity of modeling fine-grained physical dynamics and the intricate spatial-temporal coordination between human hands and objects. Existing approaches to this problem typically rely on dense temporal guidance, e.g., frame-wise hand-object pose sequences, to strictly control the interaction process. However, such dense guidance incurs high annotation costs and affects motion synthesis diversity. To overcome these limitations, we introduce SparseCtrl-HOI, a novel sparse temporal control framework for HOI video generation. It requires only a few keyframes that capture interaction states at designated timestamps. Specifically, we employ a Time-Controlled Rotary Positional Embedding (TiRoPE) mechanism to temporally anchor these keyframes while preserving their spatial integrity. Subsequently, to govern the dynamics across intermediate frames, we propose a Motion Prior Injection Module that leverages Multimodal Large Language Models (MLLMs) to extract high-level motion priors. This empowers the model to hallucinate logically and physically plausible transitions. Furthermore, we build SparseHOI-5K, a high-quality and richly annotated dataset for HOI video generation with sparse temporal control. Comprehensive evaluations confirm that our method substantially reduces annotation overhead while synthesizing superior live-streaming e-commerce videos. Both our code and dataset are publicly available at https://mpi-lab.github.io/SparseCtrl-HOI.
arXiv:2607.05883v1 Announce Type: new Abstract: In dual-arm dexterous teleoperation, cross-platform generalization of motion retargeting and interactivity of grasping are crucial. However, the heterogeneity of robotic architectures and the wide variety of grasping objects pose significant challenges to achieving precise motion retargeting and compliant grasping in dual-arm dexterous teleoperation. To address these challenges, a dual-arm dexterous teleoperation system (DexTele) is proposed based on motion retargeting and adaptive force control. First, a vision-based motion retargeting module is designed to generate preliminary robot motions from human images. In this module, a motion-graph encoder and latent optimization are proposed for precise and convenient cross-platform motion retargeting. Second, an adaptive grasping module is designed to achieve compliant grasping. This module combines a vision-language model (VLM) with model predictive control (MPC), allowing the system to predict the required grasping force for a target object and perform gradient-based online optimization. Finally, extensive experiments demonstrate that the DexTele achieves precise motion retargeting and compliant grasping with generalization across multiple robot platforms.
arXiv:2607.05934v1 Announce Type: new Abstract: Efficient model order reduction for many-port resistor-capacitor (RC) networks is essential in post-layout circuit simulation. Existing high-accuracy elimination-based methods have certain limitations, such as fixed frequency points, large reduced-order models, or high reduction cost. This paper proposes FlexRC, a flexible multi-point model order reduction method for many-port RC networks. FlexRC starts from the same elimination step as previous methods, and then constructs a nonorthogonal projection basis by a modified block rational Arnoldi process to generate a sparse banded reduced model. FlexRC features three adjustable components: user-specified frequency points, a tolerance-controlled port-reduction technique for the internal subsystem, and an optional sparsity-control strategy. We discuss passivity under port-reduction perturbations, analyze moment matching, and provide a conservative error estimate for port reduction. Numerical experiments on industrial RC examples and IBM power-grid examples demonstrate the effectiveness of FlexRC in terms of reduction time and transient simulation time.
arXiv:2607.06036v1 Announce Type: new Abstract: Late interaction models have shown strong generalization capabilities, often outperforming much larger dense embedding models. One challenge to their widespread deployment is the large number of token vectors they produce per document and the associated storage and memory costs. Pooling tokens at inference time has shown great promise to reduce the vector count with limited effects on retrieval accuracy. Large-scale pooling-aware training has demonstrated even more impressive results at high compression rates. We propose lightweight fine-tuning as a practical alternative and find that even minimal pooling-aware training with k-means yields broad gains over inference-only pooling, shows evidence of transfer across pooling methods and datasets, and - with multi-factor training - produces a single model effective across different compression levels. Our strongest model outperforms the unpooled baseline on BEIR SciFact across pool factors 1-6, implying a vector compression rate of 83% at no cost to retrieval accuracy.
arXiv:2607.06039v1 Announce Type: new Abstract: High-integrity systems, such as autonomous vehicle fleets and large-scale energy infrastructures, rely on structured assurance cases to justify safety claims. To remain valid under evolving operational conditions, such cases must be examined against potential challenges, known as defeaters. While large language models (LLMs) can support the scalable generation of candidate defeaters, assessing their quality remains largely manual and subjective process. This paper presents an automated approach for supporting the assessment of LLM-generated defeaters using natural language processing techniques. The method combines structural features from assurance case graphs with semantic embeddings and meta-classifiers trained on expert-assessed defeater annotations. We evaluate the approach through two case studies in the automotive and energy domains. The results show substantial human reviewer dissensus, with Cohen's kappa values below 0.442, highlighting the difficulty of consistent manual assessment. Against this background, the proposed classifiers achieve an average F1-score of 0.84 in validation and show improved alignment with individual expert ratings. The findings suggest that automated assessment can help reduce subjective variance and provide scalable decision support for assurance case review, while leaving final judgment to domain experts.
arXiv:2607.06043v1 Announce Type: new Abstract: Several programs for marginalized young people have been intentionally designed to increase the diversity in STEM careers; however, the participation of racially and ethnically minoritized individuals continued to be underrepresented in STEM disciplines. Using discipline-based STEM identity theories and drawing data from an NSF-funded survey of 1,134 participants, these regression analyses examine the impact of prior educational experiences on STEM identity (i.e., seeing oneself as a STEM person) and career aspirations among individuals attending Minority Serving Institutions (MSIs). The study's findings indicate that although positive reinforcement positively correlates with the STEM identity construct, the efforts are not always supportive enough to predict STEM career aspirations for minoritized individuals. It underscores the importance of explicitly designing appropriate interventions to support STEM identity formation and STEM career pursuit.
arXiv:2607.06085v1 Announce Type: new Abstract: The multiobjective optimization of electric machines always involves a trade-off caused by various competing objectives such as performance and cost. A suitable design is usually determined by comparing variants from the Pareto front, which has been generated by a large number of simulation runs. This paper addresses the efficient generation of the Pareto front using a continuation method based on a homotopy method that exploits second-order derivative information to achieve superlinear convergence, enabling the fast generation of new Pareto-optimal points within only a few iterations. A key contribution is the derivation of formulas to compute the Hessian with respect to geometry parameters and shape, thus enabling direct modifications of the motor geometry in the context of Isogeometric Analysis. We apply our method to nonlinear 2D magnetostatic simulations of a permanent magnet synchronous motor and demonstrate its effectiveness by optimizing the cost, mean torque and torque ripple of the motor. Compared to a first-order optimization method, this approach reduces the number of iterations and function evaluations needed, making the pareto optimization fast and efficient.
arXiv:2607.06211v1 Announce Type: new Abstract: We analyze a balls-and-bins game against an adaptive adversary that sequentially deletes bins. Starting with $n$ balls distributed across $n$ bins, the adversary deletes a bin in each step, forcing the algorithm to redistribute its balls to surviving bins. We prove that after $n/2$ rounds, uniform random redistribution yields optimal $O(n)$ recourse and $O(\frac{\log n}{\log \log n})$ maximum load. Furthermore, we show that applying the ``power of two choices'' reduces the maximum load to $O(\log \log n)$ while maintaining linear recourse. We also consider a variation of this game where the balls from the deleted bin are partitioned evenly among $d \ll n$ random bins rather than being redistributed independently. We demonstrate that keeping the balls together ($d=1$), which gives small maximum load and recourse against an oblivious adversary, fails against an adaptive adversary. Nevertheless, we show that splitting the balls into just two groups ($d=2$) is sufficient to recover linear recourse and efficient load balancing in the adaptive setting.
arXiv:2607.06234v1 Announce Type: new Abstract: Generating CT volumes from MRI and CBCT can improve treatment planning in adaptive radiotherapy while avoiding additional radiation exposure. However, direct regression of CT intensities is challenged by the inherently high dynamic range and long-tailed distributions, thereby averaging out sparse yet clinically important structures. To alleviate this issue, we reformulate the regression target into multiple windowed representations, leveraging the inductive prior that CT intensities are structure-deterministic and window-separable. These windowed views exhibit smoother distributions and admit structured fusion back to the full-range CT. Building on this reformulation, we introduce WING, a WINdow-prior-based Generative network comprising: 1) a new Gated Inception Generator to produce multi-window predictions, enabling multi-shape kernel interactions to capture cross-modality correspondence; 2) a Fuse-and-Refine Transformer to aggregate the windowed outputs and learn residuals for detail refinement; and 3) a joint adversarial training objective to enhance window-conditioned realism. Extensive experiments demonstrate that our compact WING achieves state-of-the-art performance on the MRI-to-CT and CBCT-to-CT benchmarks, while supporting multi-anatomy synthesis with a single model.
arXiv:2607.06238v1 Announce Type: new Abstract: Magnetic resonance imaging (MRI) super-resolution is vital for improving diagnostic accessibility, yet most methods treat it as a deterministic mapping from a fixed low-resolution input to a high-resolution target. This overlooks a key property of MRI acquisition physics: spatial resolution and signal-to-noise ratio (SNR) are inherently coupled, making any given low-resolution scan merely one of many possible realizations under varying acquisition trade-offs. We rethink MRI super-resolution as a physics-aware reconstruction problem, in which the goal is to identify the optimal resolution-SNR configuration and then super-resolve it to obtain high-quality MRI results. A key implication of this formulation is that MRI resolution becomes dynamic rather than fixed. To handle such resolution-heterogeneous inputs, we adapt 2D Gaussian Splatting (2D GS) to MRI by formulating reconstruction as a coordinate-based, resolution-agnostic rendering problem. To further enhance fidelity, we introduce three innovations: (1) a prior-aware Gaussian representation that combines an Anatomical Structure Prior for tissue-specific kernel initialization with an Imaging System Prior that captures hardware characteristics via a covariance dictionary; (2) a physics-constrained signal modeling scheme that predicts intrinsic tissue parameters (proton density rho and effective relaxation rate R2) and synthesizes intensities through governing physical equations, ensuring biophysically plausible contrast; and (3) a meta-learning framework that alleviates paired-data scarcity by pretraining on simulated data and adapting to real-world conditions. Extensive experiments on dynamic-resolution datasets and standard benchmarks demonstrate that our method achieves state-of-the-art performance, highlighting its strong potential for clinical deployment.
arXiv:2607.06248v1 Announce Type: new Abstract: Validation of robotic systems critically depends on the operating conditions under which they are assessed. Scenario selection and variation are often manual, experience-driven, and difficult to scale, which harms reproducibility and weakens validation conclusions. We propose a scenario-based methodology that models scenarios compositionally and formalizes how these dimensions are varied, instantiated, executed, and interpreted. Building on this, we introduce RoboVAST, a framework that realizes declarative campaign specifications, plugin-based scenario generation, and scalable containerized execution with integrated result analysis. We demonstrate the approach with a navigation dataset comprising 5480 scenario configurations and over 100000 execution runs across five indoor maps with varied paths, sensor noise, software parameters, and obstacle settings, totaling more than 1800 hours of simulated operation and 1873 km traveled. Twenty repetitions per configuration allow us to distinguish systematic failures from stochastic anomalies.
arXiv:2607.05824v1 Announce Type: new Abstract: High-throughput holotomography often relies on long-working-distance, multiwell-compatible optics that reduce illumination numerical aperture (NA) and limit access to high spatial frequencies. Here we present ResShift-ODE, a deterministic diffusion-prior framework that transfers low-NA refractive-index (RI) tomograms to high-NA-equivalent volumes without modifying the acquisition hardware. We formulate low-NA-to-high-NA transfer as a diffusion-prior inverse problem under an explicit NA-limited Fourier-domain forward operator, distinct from suppressing artifacts within an already measured passband. The method extends residual-shifting diffusion to volumetric RI data and reformulates the reverse process as a probability-flow ordinary differential equation, enabling reproducible inference in five denoiser evaluations. On held-out emulated-pair test volumes, inferred volumes matched high-NA references with RI errors of 0.002-0.003 for >99% of voxels, while Fourier analysis confirmed measurement-anchored lateral-band recovery without filling the axial missing cone. 3D ResShift-ODE required five denoiser evaluations per volume, incurring ~5.8x the cost of a 3D U-Net while remaining ~166x faster than a 1000-step 3D denoising diffusion probabilistic model.
arXiv:2607.05421v1 Announce Type: new Abstract: Precision agriculture, smart breeding, and agricultural robotics require accurate and automated plant modeling. These models provide high-fidelity three-dimensional (3D) representations of plant architecture. They provide the geometric foundation for simulations of water and nutrient transport, light interception, structural loading, and crop lodging. Unlike static plant modeling pipelines, procedural modeling frameworks not only generate accurate 3D plant geometries but also support the generative modeling of crop diversity and the dynamic modeling of plant growth. While terrestrial laser scanning, LiDAR, photogrammetry, and neural reconstruction-based approaches have made 3D plant reconstruction possible, the resulting data are typically in the form of point clouds, which cannot be directly utilized for high-fidelity simulations. We present an automated volumetric procedural modeling framework for plant branching structures that generates analysis-suitable hexahedral meshes from input skeletons or 3D point clouds. The input skeleton is first converted into a rooted graph representation that captures the plant branching topology. Each graph edge is then represented by a smooth centerline B-spline curve, around which a cylindrical tensor-product B-spline volume is constructed. At each junction, incident B-spline volume control lattices are joined using blending operations. The resulting volumetric parameterization is evaluated to generate a smooth and conforming hexahedral mesh of the whole plant. We demonstrate the framework on three diverse plant datasets, namely mung bean, tomato, and walnut trees, generating meshes with both uniform and spatially varying branch radii. The framework also supports dynamic mesh generation suitable for modeling plant growth by locally updating newly added branches without reconstructing the full plant geometry.
arXiv:2607.05501v1 Announce Type: cross Abstract: Pipe diagrams have emerged as a powerful framework for flexible lattice surgery compilation and spacetime optimization for the surface code. In contrast, analogous compilation techniques for color code architectures remain largely unexplored, despite the color code's favorable properties, including reduced qubit overhead and transversal single-qubit Clifford gates. In this work, we develop a pipe diagram representation for the triangular color code on the 6.6.6 lattice and establish its correspondence to ZX-diagrammatic descriptions of computation. We present distance-independent constructions of color code pipe diagrams together with explicit realizations of correlation surfaces, stabilizers, and syndrome extraction circuits. This framework enables both macroscopic optimization of logical computations in spacetime and microscopic compilation to executable syndrome extraction circuits. We demonstrate the potential for compact spacetime embeddings with the color code's geometry. These results provide a foundation for automated lattice surgery compilation and diagrammatic optimization in color code architectures.
arXiv:2607.06408v1 Announce Type: new Abstract: Robust remote verification of identity documents relies on analyzing faint, transparent security features like Optically Variable Devices (OVDs), or "holograms", within user-captured videos under uncontrolled conditions. Current systems, however, face critical limitations: existing methods often treat video frames in isolation, neglecting the intrinsic dynamic nature of OVDs and leaving systems vulnerable to swapping attacks, or focus on general holographic presence and lack the ability to verify specific OVD types. Moreover, the economic infeasibility of frame-by-frame video annotation makes supervised training impractical. In this work, we introduce two novel approaches for verifying the dynamic behavior of transparent OVDs protecting the holder's portrait, specifically designed for open-set scenarios where attack types are unknown during training. We demonstrate that these approaches can be trained without any attack samples in a self-supervised setting, surpassing previous state-of-the-art methods on public datasets while adhering strictly to industrial constraints. Our results confirm that modeling temporal dynamics is essential for defeating sophisticated attacks under realistic conditions, and underscores the promise of sequence modeling and anomaly detection for OVD verification. Code is available at https://github.com/EPITAResearchLab/pouliquen.26.icdar.
arXiv:2607.05620v1 Announce Type: new Abstract: In many decision-making settings, new interventions are acceptable only if they do not reduce outcomes below some established threshold. For example, in clinical medicine, new treatments are often acceptable only if they do not worsen outcomes relative to an established standard of care. Safe Bayesian optimization maximizes an objective subject to safety constraints. In the setting that we consider here, safety is defined relative to a known baseline policy whose outcomes are counterfactual and therefore unobserved. Thus, the counterfactual outcomes of the baseline policy must be estimated and those (uncertain) estimates must be used to safely optimize the objective. We address this estimation problem by using conformal prediction to construct valid uncertainty intervals for counterfactual baseline outcomes, and we show how these intervals can be integrated into safe Bayesian optimization to ensure that constraint violations occur at or below a user-specified rate. We also show how to adapt these conformal estimates to different kinds of covariate shift. We provide a safety proof, experimental evidence, and a sensitivity analysis.
arXiv:2607.06416v1 Announce Type: new Abstract: This paper systematically analyzes the relationships among the $dq$-domain, $\alpha\beta$-domain, and sequence-domain representations used in small-signal impedance modeling of voltage-source converters (VSCs). It is shown that the AC impedance matrix expressed with $dq$-complex and $\alpha\beta$-complex variables leads to different formulations in the sequence domain. The study demonstrates that asymmetric systems exhibit different physical phenomena in the rotating and stationary reference frames; therefore, the transformations between these frames are not physically consistent in such cases. It is also demonstrated that the so-called modified sequence-domain impedance is equivalent to the universal impedance model in the frequency domain. The analysis clarifies several notational inconsistencies found in the literature. Finally, a physical interpretation is presented highlighting the implications of using stationary and rotating reference frames for stability analysis of power converters.
arXiv:2607.06093v1 Announce Type: new Abstract: Hybrid electrolyzer systems combining alkaline water electrolysis and proton exchange membrane water electrolysis have been investigated in the literature motivated by the expectation that their contrary techno-economic characteristics compensate for the individual technical and economic restrictions of each technology, thereby improving the profitability of green hydrogen production. To reassess the economic potential of hybrid electrolyzer systems beyond these technology-specific assumptions, we independently vary two key characteristics, electrolyzer efficiency and investment cost, in a large-scale sensitivity analysis. For each generated parameter configuration, we performed a techno-economic optimization of a green hydrogen supply chain, including two electrolyzers. The resulting system design, cost objective, and dispatch behavior are subsequently analyzed. Consequently, hybrid electrolyzer systems are identified as optimal if they provide a cost benefit over single electrolyzer systems. The analysis reveals that hybrid electrolyzer systems represent the optimal solution in at most 5.0% of the investigated cases. Furthermore, the maximum cost benefit is 0.057 EUR/kgH2, which corresponds to only about 1% of the total green hydrogen production cost. Additional analyses considering variations in energy purchase prices, storage fees, availability of renewable energy, and baseline electrolyzer efficiency yield negligible changes to these results. Hence, considering that hybrid electrolyzer systems offer marginal cost benefits and prove economically optimal in very few cases, they seem more likely to represent an economic fallacy than a smart strategy.
arXiv:2607.06364v1 Announce Type: new Abstract: Mapping cloud security controls to technical metrics is currently a manual process. This paper proposes domain adaptation of Sentence Transformer models to automate it. We build a training corpus of 3,499 semantic pairs from five European security standards and a set of technical metrics, then expand it via back-translation and LLM-based paraphrasing to up to 13,996 samples across four scenarios. We fine-tune five architectures and evaluate their performance on two independent tasks: control-to-metric and cross-standard controls association. All fine-tuned models outperform their zero-shot baselines. On the control-to-metric task, the best model gains up to 23 nDCG@10 points, while on the cross-standard control task, \textit{multi-qa-mpnet-dot-v1} under back-translation reaches 0.870 nDCG@10. The results show that in-domain training data is a primary driver of performance for the considered case studies.
arXiv:2607.05811v1 Announce Type: new Abstract: We consider the numerical solution of the wave equation in materials with rapidly varying coefficients, and time harmonic sources. For these problems, direct discretization is prohibitively costly, and instead multiscale methods are used. There are several multiscale methods that directly discretize in the frequency domain. In this work we instead start in the time-domain and combine a finite difference Heterogeneous Multiscale Method (HMM) for the wave equation with the WaveHoltz method. Each WaveHoltz iteration marches the wave equation towards the time-periodic Helmholtz solution. The advantages of the WaveHoltz method relative to traditional Helmholtz solvers carry over directly to the multiscale problems considered here. Since, in addition, the time-domain solver does not artificially impose boundary conditions on the micro-scale problems, no boundary errors from the micro-scale problems are present in the homogenized frequency domain solution.
arXiv:2607.05815v1 Announce Type: new Abstract: The Minkowski functionals of a field's excursion sets -- area, boundary measure, and Euler characteristic -- describe its level-set morphology; the Euler characteristic is the cheapest handle on topology. We derive smooth Monte-Carlo estimators for all three of a continuous neural field, evaluated at scattered points via the co-area formula and Gauss-Bonnet, using only autodiff: no grid, no complex, no persistence. The estimator is accurate to 1-3% against exact topology in 2D and 3D, and costs about 3 ms per iteration where a persistent-homology (PH) loss on a cubical grid costs 650-1000 ms -- a 250x gap. We establish four design rules without which these losses silently fail: a dense level ladder (invariants are flat in the parameters away from transitions), a $C^2$ backbone (ReLU nets hide curvature in kinks), the full Minkowski vector (Euler characteristic alone is an alternating sum, gamed by debris-hole cancellation; pricing perimeter closes the channel), and sampling-scale coverage. In 2D the vector-valued cap is the only method in a controlled comparison that both repairs topology (3/3 seeds) and preserves fidelity -- uniform smoothing repairs at 11-17x the fidelity cost, and the Euler term alone repairs nothing. In 3D neural-SDF fitting, however, a failure mode we believe general to any sampled soft topology objective appears: gradient descent adversarially hides topological noise below the sampling density, where the estimator is blind -- spurious-feature counts are invariant to 4x more samples, and closing the window needs cubically many points, erasing the cost advantage. A grid-based PH baseline, whose complex is the evaluation resolution, solves the same benchmark ($4/9$ exact; median $b_1$ error 1 vs. ours above $10^4$). The 250x cost of persistence is, at present, the price of having no null space. We release estimators, receipts, and benchmarks.