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arXiv

Improving Performance of Spike-based Deep Q-Learning using Ternary Neurons

Aref Ghoreishee, Abhishek Mishra, John Walsh, Anup Das, Nagarajan Kandasamy

We propose a new ternary spiking neuron model to improve the representation capacity of binary spiking neurons in deep Q-learning. Although a ternary neuron model has recently been introduced to overcome the limited representation capacity offered by binary spiking neurons, we show that its performance is worse than that of binary models in deep Q-learning tasks, contradicting previous findings from recent studies. Through mathematical and empirical analysis, we hypothesize that gradient estimation bias during training is the underlying cause. The proposed ternary spiking neuron model mitigates this issue by reducing the estimation bias. We use the proposed ternary spiking neuron as the fundamental computing unit in a deep spiking Q-learning network, which we call the deep asymmetric ternary spiking Q-network (DATSQN), and evaluate the network's performance in seven Atari games from the Gym environment. The results show that the proposed ternary spiking neuron mitigates the performance degradation of ternary neurons in DQN tasks and improves the mean game score relative to the binary baseline under the evaluation settings used in this paper.

arXiv

Computational Algebra with Attention: Transformer Oracles for Border Basis Algorithms

Hiroshi Kera, Nico Pelleriti, Yuki Ishihara, Max Zimmer, Sebastian Pokutta

Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gröbner and Border bases are fundamental but suffer from high computational costs, which have motivated recent Deep Learning approaches to improve efficiency, albeit at the expense of output correctness. In this work, we introduce the Oracle Border Basis Algorithm, the first Deep Learning approach that accelerates Border basis computation while maintaining output guarantees. To this end, we design and train a Transformer-based oracle that identifies and eliminates computationally expensive reduction steps, which we find to dominate the algorithm's runtime. By selectively invoking this oracle during critical phases of computation, we achieve substantial speedup factors of up to 3.5x compared to the base algorithm, without compromising the correctness of results. To generate the training data, we develop a sampling method and provide the first sampling theorem for border bases. We construct a tokenization and embedding scheme tailored to monomial-centered algebraic computations, resulting in a compact and expressive input representation, which reduces the number of tokens to encode an $n$-variate polynomial by a factor of $O(n)$. Our learning approach is data efficient, stable, and a practical enhancement to traditional computer algebra algorithms and symbolic computation.

arXiv

Rule Extraction in Machine Learning: Chat Incremental Pattern Constructor

Caleb Princewill Nwokocha

Rule extraction is a central problem in interpretable machine learning because it seeks to convert opaque predictive behavior into human-readable symbolic structure. This paper presents Chat Incremental Pattern Constructor (ChatIPC), a lightweight incremental symbolic learning system that extracts ordered token-transition rules from text, enriches them with definition-based expansion, and constructs responses by similarity-guided candidate selection. The system may be viewed as a rule extractor operating over a token graph rather than a conventional classifier. I formalize the knowledge base, definition expansion, candidate scoring, repetition control, English-rule heuristics, and response construction mechanisms used by ChatIPC. I further situate the method within the literature on rule extraction, decision tree induction, association rules, interpretable machine learning, and sequence construction. The updated C++ code implementation of ChatIPC is also reviewed in detail: it parses an embedded dictionary, normalizes lexical keys, caches definition tokens and part-of-speech tags, computes Jaccard scores on bitsets, applies heuristic linguistic bonuses, and persists the knowledge base with a versioned binary format. The paper emphasizes mathematical formulation and algorithmic clarity, and it provides pseudocode for the learning, scoring, and construction algorithms.

arXiv

How to Verify Consistency of Probabilistic Claims

Orr Paradise, Oliver Richardson, Yoshua Bengio, Shafi Goldwasser

When a probabilistic predictor answers many conditional-probability queries, are its answers self-consistent, and can this be verified in polynomial time? This problem is of interest for AI safety, where safety is derived from honesty about probabilistic predictions of unwanted outcomes potentially caused by an AI action. We construct an interactive PCP as follows. Let a predictive model be specified by a probability circuit P and a circuit Q which outputs confidence in predictions. Together, P and Q implicitly specify exponentially many probabilistic claims. We show a protocol in which a polynomial-time verifier can verify the approximate consistency of (P,Q). The verifier is given the pair of circuits (P,Q), which it evaluates at only a few points; alongside them it is given a proof oracle, an encoding of a witnessing probability distribution allegedly consistent with the predictions of (P,Q), which it reads at a few locations while interacting with a single untrusted prover. En route, we must ensure the existence of a sparse witnessing distribution consistent with the model's predictions. To do so, we first consider witness distributions for the consistency of explicit probabilistic claims, rather than claims specified by a predictor: say m claims, each of the form Pr[Y = 1 | X = x] = p, over n Boolean variables. Building on work initiated by Nilsson (Artif. Intell., 1986), we place l_2-approximate probabilistic consistency of explicit claims in NP, with certificates of length O(mn + log B) in the input bit-precision B; we further show how a small additive completeness-soundness gap removes the dependence on B. Together these results provide a complexity-theoretic foundation for certifying the self-consistency of probabilistic predictors. We view our interactive PCP as a first step toward training predictive models to prove their own consistency.

arXiv

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex

Eric A. F. Reinhardt, Adam J. Hauser

The attention mechanism forms the foundation of many modern AI models such as the Transformer. In one subclass of problems where attention is used, inputs and outputs are bound to the probability simplex so that all outputs sum to one. In this setting, softmax attention admits an exact, component-by-component quantum realization. Attention scores are Hadamard-test statistics on block-encoded projections of amplitude-encoded inputs. The exponential softmax is the interior of a cosine-squared family generated by Born-rule measurement under an exact bijection, whose boundary expresses sparse attention with exact zeros at finite parameter values. The softmax temperature is a repetition count where post-selected measurement rounds realize discretized inverse temperature exactly. Value aggregation is a deterministic column-loading channel that dilates the column-stochastic value matrix. The gated residual is the preparation angle of a single ancilla, with the additive identity at a mixing angle of π/2. Every learnable parameter is a rotation-gate angle. The composed layer is exact in the infinite-shot limit with one measure-and-reload step per attention score; a fully-coherent variant is ε-approximate via quantum singular value transformation in the infinite depth limit. The algebraic core is machine-checked in Lean 4.

arXiv

Hierarchical Empirical-Bayes Naive Bayes: Minimax Smoothing and Calibration with AODE Extension

Nguyen Thai Anh, Truong Viet Vu, Tran Thien Thanh, Vo Nguyen Quoc Bao, Ngo Hoang Tu

The Naive Bayes (NB) classifier remains a standard choice for categorical data, yet its widely used smoothing rules, such as Laplace, Lidstone, Krichevsky-Trofimov, and the $m$-estimate, all prescribe a fixed smoothing strength that ignores feature cardinality, sample size, and class imbalance, inducing a non-vanishing bias on modern high-cardinality tabular data. We propose hierarchical empirical-Bayes Naive Bayes (HEB-NB), in which each class-feature conditional probability is smoothed by a Dirichlet prior whose concentration is learned data-adaptively via Type-II maximum likelihood, enabling principled information sharing across classes while retaining closed-form inference. We further introduce HEB average one-dependence estimators (HEB-AODE), showing that the adaptive smoothing transfers cleanly to structural relaxations of NB. Theoretically, we establish a non-asymptotic $\ell_1$ error bound for HEB-NB matching the empirical-distribution minimax rate plus a vanishing data-adaptive bias, together with a matching Laplace-tight lower bound that yields a finite-sample, risk-level strict separation from Laplace. We further derive a plug-in excess Bayes-risk bound via total-variation tensorization and a population top-1 expected calibration error (ECE) corollary. Empirically, across 31 UCI and OpenML benchmarks, HEB-NB attains the best average Friedman rank on probabilistic metrics, with up to 22.1% log-loss reductions on high-cardinality datasets and consistent improvements of HEB-AODE over vanilla AODE. Combining HEB-NB with mutual-information weighting reduces top-1 ECE by 41%-70%, demonstrating substantial gains in probabilistic accuracy and calibration.

arXiv

Conditional Independence Tests for Constraint-Based Causal Discovery: A Survey

Pavel Averin, Theodoros Moysiadis, Ioannis Katakis

Conditional Independence (CI) tests are the statistical engine of constraint-based causal discovery: in algorithms such as PC (Peter-Clark) and FCI (Fast Causal Inference), skeleton pruning and key orientations follow directly from CI decisions. This survey reviews CI testing with emphasis on assumptions, robustness, and scalability in high-dimensional and mixed-type settings common in biomedical domains. The survey organizes widely used CI methods into six families: partial-correlation, contingency-table, regression, nearest-neighbor, kernel, and machine-learning-based. Special emphasis is provided on the robustness layers that address the limitations of these families. For each family, the survey examines when CI decisions reflect the data-generating distribution and when they fail. By this, we link test-level properties, including power decay with conditioning set size and asymmetric type I/II error consequences, to graph-level errors in skeleton recovery and v-structure orientation. The survey also compares adoption across major R and Python libraries and summarizes open challenges, including mixed-type CI testing without discretization, small-sample error control, and strategies for improving scalability of CI-testing.

arXiv

DACRI: Decision-Aware Causal Intervention Ranking for Critical Supply Chains

Shiqi Huang, Jiani He, Dingyan Shang, Yihua Xu, Jize Li, Yan Lyu, Lashimi Muraleedharan Nair

Detecting or attributing a supply-chain disruption is not the same as selecting the intervention that maximizes recoverable net value. We present CriticalSCM-Bench v1, a controlled synthetic benchmark with causal ground truth, paired factual/counterfactual rollouts, and an explicit net-value objective. Relative to a full-information train-selected static benchmark, LambdaMART improves median normalized net value by 5.7--16.2\%, with paired statistical support on the semiconductor and critical-material archetypes but not on digital infrastructure. On digital infrastructure, a domain-informed constant-buffer policy remains stronger, showing that greater model complexity is not uniformly justified. Across partial and delayed settings, LambdaMART retains 33--75\% of full-clamp value. Stress tests further show that intervention fidelity, timing, cost, and held-out disruptions can alter policy ordering. Critical materials show the weakest out-of-distribution retention. Separately, a guarded explanation study over 540 generations preserves every fixed intervention decision after deterministic validation and template fallback, although exact wording remains unstable. Within this controlled setting, the results identify regimes in which adaptive ranking adds value and those in which simpler structural policies remain preferable.

arXiv

Scheduling Mixed RL Rollouts Beyond Prefix Locality

Zetao Hong, Song Yuan, Yuanhao Ding, Yibo Zhu, Daxin Jiang, Zhibin Wang, Chen Tian

Modern reinforcement learning (RL) post-training pipelines for large language models (LLMs) increasingly combine rollout workloads across multiple domains and feedback paradigms. Prefix-aware routing improves inference efficiency through cache reuse and load balancing, but it does not control how heterogeneous rollout sessions compete for KV-cache capacity. When reinforcement learning with verifiable rewards (RLVR), reinforcement learning from human feedback (RLHF), and agentic rollouts share an asynchronous inference service, their distinct sequence structures, interaction patterns, and KV-residency times create substantially different serving demands. Rollout scheduling must account for this heterogeneity without distorting the workload mixture specified by the trainer. We present MISA-T, a routing-layer admission policy for mixed rollout serving. MISA-T combines adaptive session admission, workload-aware KV-capacity allocation, and residency-time-aware KV accounting. In rollout-only ablations on Step3.7 and Qwen3.6-35B-A3B, MISA-T improves rollout throughput over a sweep-tuned cache-aware vLLM Router by 53.3% and 43.6%, respectively, while maintaining high prefix-cache hit rates. In a matched 50-iteration Step3.7 experiment, it increases rollout throughput by 35.6% and reduces mean iteration time by 22.8%, while keeping the consumed workload mixture close to the trainer target and achieving comparable task scores.

arXiv

A Recommendation System Approach for Interference-Robust Sensor Subset Selection

Kaan Buyukkalayci, Kyle Pak, Merve Karakas, Christina Fragouli

This paper develops a method for sensor-subset selection for tracking. Prior work showed that low-cost acoustic Received Signal Strength Indicator (RSSI) measurements can be used to recommend subsets of sensor nodes whose expensive sensing modalities, such as cameras, can achieve high tracking accuracy. While efficient, RSSI-based approaches are challenged by acoustic interference. We propose a recommendation-system-inspired framework that instead leverages frequency-band acoustic features and a Two-Tower Multi-Layer Perceptron (MLP) architecture to efficiently score candidate sensor subsets. Experimental results on outdoor vehicle-tracking deployments show that the proposed method can improve accuracy by around 20\% over the RSSI baseline while maintaining the low computational overhead required for real-time selective sensing.

arXiv

Two-stage Odd Residual Flows for Mean-Preserving Probabilistic Time Series Forecasting

Kiran Madhusudhanan, Christian Klötergens, Lars Schmidt-Thieme, Vijaya Krishna Yalavarthi

Probabilistic forecasting plays an essential role in risk-sensitive decision-making, particularly in long-horizon settings. However, existing approaches often face a fundamental trade-off between distributional flexibility and accurate mean prediction. Traditional parametric methods, such as Mean Variance Estimation (MVE), can suffer from degraded point accuracy when trained under joint Negative Log-Likelihood (NLL) objectives, while modern-flexible generative models, including Normalizing Flows and Diffusion Models, typically rely on costly Monte Carlo sampling and may yield suboptimal mean estimates. To address this limitation, we propose Two-stage Odd Residual Flows (TORF), a framework that decouples mean forecasting from uncertainty estimation. In the first stage, a pre-trained deterministic model is used to produce an accurate mean prediction. In the second stage, a Restricted Normalizing Flow, with strictly odd functions learns flexible residual distributions around the point forecast, guaranteeing mean preservation from the first stage without sampling. Experiments show that TORF achieves state-of-the-art deterministic accuracy (NMAE) while providing strong density estimation performance (CRPS) on short and long-horizon forecasting.

arXiv

Why Does CLAUDE.md Keep Growing? Catastrophic Remembering in Agentic Coding

Kushal Chakrabarti

Agentic coding READMEs like CLAUDE.md grow without bound in real repositories, stopping only when the repository retires or someone rewrites the file wholesale. We trace this to imperfect recall: appending an instruction is always cheap, but once an instruction's rationale is gone, deleting it without risking a correctness regression costs O(2^|D|) in a prompt of |D| instructions. We name the resulting divergence catastrophic remembering, the inverse of catastrophic forgetting around which continual learning is organized. First, we characterize this phenomenon across 247,694 instruction lifetimes in 1,867 repositories: agentic prompts grow without bound, more than tripling over their lifetime (+226%), gaining +4.9 net instructions every commit; further, the older an instruction gets, the less likely it is to be deleted (log-hazard -0.032/commit). Then, we show that prompt comments can halt the growth: inverting IFEval yields verifiable worlds whose optimal prompts are known, and there comments encoding latent reasoning remove 99.3% of excess instructions (+211.3% to +1.4%). Finally, applying the same inversion to WildIFEval, we show that prompt comments can improve real-world agentic instruction-following by up to 23.1%. If English is the new code, why don't we have comments yet?

arXiv

A Systematic Sample Size Analysis of ML-Based Path Loss Prediction for LPWAN

Robert Bitterling, Christian Nettersheim, Jörn Hees, Michael Rademacher

Low Power Wide Area Networks like LoRa are increasingly deployed for smart city applications, requiring accurate path loss prediction for effective network planning. Traditional (empirical) propagation models often exhibit limited accuracy in these scenarios. We investigate machine learning models for LoRa path loss prediction, systematically analyzing how prediction accuracy scales with training set size using real-world measurements from an urban deployment. Our approach employs a Random Forest with LiDAR-derived terrain features and k-Nearest Neighbors with coordinate data, comparing their performance against established empirical models and specialized LPWAN models. Under random pooled splits, both ML models consistently outperform the considered baseline models across the evaluated training-set sizes. At maximum training size, they achieve RMSE values below 6.5 dB compared to 9.7 dB for the best baseline, indicating accurate within-deployment interpolation. A leave-one-gateway-out check qualifies this result: RF shows placement-dependent transfer to held-out gateways, with moderate degradation for several gateways but larger errors for others, whereas coordinate-only k-NN degrades substantially when the gateway location is unseen

arXiv

Batch Size or Negatives? A Selection Rule for Memory-Constrained Recommender Training

Artyom Sabitov, Daniil Volkov, Alexey Zaytsev

Large-scale neural recommender systems are typically trained with a softmax cross-entropy objective over the full item vocabulary. For a typical large number of possible items $K$, the final classification layer dominates memory, requiring $O(nK)$ logits and gradients to materialize for a batch of $n$ examples. Sampled softmax reduces this cost by restricting the objective to only $k \ll K$ candidate negative items, resulting in an $O(nk)$ memory. However, for a fixed budget $B = n k$, it remains unclear whether one should prioritize larger batches or the inclusion of more negative items. We address this question by analyzing sampled-softmax training under a fixed memory constraint. Under standard smoothness and variance assumptions, our theoretical evidence suggests that the fastest convergence arises from an $ n \sim B, k \sim 1$ allocation. So, an actionable rule is to include as many objects as possible given computational constraints. Our theory is supported by controlled synthetic and synthetic and four real sequential recommendation benchmarks, including MovieLens-20M. The suggested configuration achieve faster convergence and better final recommendation quality than imbalanced alternatives within the same memory constraint. These findings provide a theoretical and empirical foundation for configuring memory during the training of recommender systems. Code, reproducibility materials, and all scripts for generating figures are available at https://anonymous.4open.science/r/LimitedMemoryRule-BBFB

arXiv

Uncertainty-Aware Deep Learning for Genomics Applications: Insights from an Empirical Study

Sepideh Saran, Mahsa Ghanbari, Uwe Ohler

Deep learning models have emerged as the standard computational tool for a wide range of applications in genomics. Yet, uncertainty quantification (UQ) -- and more specifically, the reliability of different uncertainty estimates in this domain -- has received little systematic attention. This work presents an empirical analysis of UQ in deep learning models, focusing on genomics applications. In a series of experiments, we contrast Deep Ensembles, Bayesian Neural Networks, and Monte Carlo-dropout methods. We assess their ability to quantify uncertainty in different scenarios, accounting for common dataset characteristics in two genomic application areas and modalities: sequence-to-activity models, and single-cell expression analysis. Our systematic comparison framework provides guidelines for the applicability and reliability of UQ methods in genomics, highlighting their strengths and limitations in different scenarios. We show that Bayesian Neural Networks are better at capturing uncertainty caused by strong class imbalance and out-of-distribution data in genomics, despite their computational disadvantages. Moreover, we show how uncertainty scores can be used to select high-quality predictions in protein-RNA interactions.

arXiv

Efficient Hypergradient Descent for Inverse Reinforcement Learning

Nikita Sevriukov, Anna Barabanova, Uliana Gagarina, Karina Ivanova, Sofiia Kasaeva, Ilya Levin, Marina Sheshukova

Inverse reinforcement learning (IRL) aims to recover a reward function under which the resulting policy reproduces the behavior observed in expert demonstrations. A natural approach is to formulate IRL as a bilevel optimization problem, in which the inner level corresponds to policy optimization under the learned reward and the outer level measures the discrepancy between the induced policy and expert data. However, this formulation is computationally challenging in practice because the outer update requires a hypergradient involving an inverse-Hessian-vector product for the inner objective. We address this challenge by showing that, at the inner optimum, the Hessian of the inner objective is proportional to the Fisher information matrix of the policy, yielding a structured Fisher-based hypergradient closely related to Natural Hypergradient Descent. To address the resulting scalability bottleneck associated with large Fisher matrices, we approximate the required inverse-Fisher-vector product using a streaming spectral sketch, avoiding explicit construction of the Fisher matrix. We evaluate our approach against a first-order stochastic bilevel baseline across discrete- and continuous-control environments. The results demonstrate competitive policy performance and strong reward-ranking quality, while Fisher sketching reduces curvature-storage complexity and can improve computational efficiency relative to an explicit Fisher solver.

arXiv

SCOUT: Symmetric Consensus Outlier Detection for Failure Localization in LLM Pre-Training

Zhuang Wang

In LLM pre-training, synchronization propagates rank-local stalls, slowdowns, and numerical errors into job-wide symptoms, obscuring their origin. Existing diagnosis often relies on in-process monitors that cannot report after the trainer blocks or terminates, or on post-mortem logs that preserve only synchronized symptoms; offline health tests lose the workload and operating conditions that triggered the failure. We present SCOUT, a unified runtime failure-localization framework built on one design principle: identify outliers through strict-majority consensus among equivalent replicas. SCOUT aligns replica progress, timing, and numerical evidence, then uses its Consensus Collective Communication (C3) abstraction to identify ranks whose compact signatures disagree with their peers. An out-of-band CPU observer remains responsive when training hangs, whereas in-situ replay exercises recurring stragglers and silent data corruption (SDC) beside the live job with its model state, kernels, allocations, communication path, and thermal and memory pressure present. Collective fingerprints expose rank-local protocol divergence. Clean replay coverage certifies checkpoint numerical integrity, preventing recovery from selecting state corrupted by SDC. SCOUT integrates with PyTorch, TorchTitan, Megatron-Core, and DeepSpeed without training-loop or framework-source modifications. SCOUT is open source at https://github.com/LMResiliency/lm-resiliency.

arXiv

Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond

Maciej J. Mikulski, Tadeusz Uhl

We systematically investigate finite-difference (FD) derivative computation in Physics-Informed Neural Networks (PINNs) as an alternative to automatic differentiation (AD). On three benchmark PDEs we show that, with a properly calibrated step size, FD matches AD in accuracy on every problem while running faster across the full tested batch-size range and using substantially less GPU memory, and that a stochastic variant we propose outperforms AD on a stationary problem. We further show that for neural architectures with inter-sample dependencies (e.g. BatchNorm, self-attention) the standard PyTorch autograd idiom is silently incorrect; the correct per-sample alternative is computationally infeasible at PINN-relevant batch sizes, while FD provides a forward-only approximation that is empirically an order of magnitude closer to the true per-sample derivative.

arXiv

DEFT: Data-Efficient Frequency-domain Top-k Sampling via Inverse Discrete Fourier Transform for Spatiotemporal Dynamical Systems Modeling

Hengbo Xiao, Jiale Liu, Jiahao Song, Guannan He

Modeling spatiotemporal dynamical systems governed by partial differential equations (PDEs) poses two major challenges: it either requires expensive physics-based simulators that entail iterative numerical solving at high computational cost, or it depends on abundant training data, yet purely data-driven models often generalize poorly to downstream dynamic operating conditions. We propose DEFT, a frequency-domain data sampling method that identifies the dominant Fourier modes of a physical system and systematically varies the corresponding amplitudes and phases to generate physically consistent training data via the inverse discrete Fourier transform. In addition, we derive a generalization bound of this method. We note that it also provides a theoretically principled criterion for selecting $K$. We evaluate the proposed method through three sets of experiments, each targeting a distinct aspect of its utility. First, we validate the framework on canonical PDEs solving demonstrating that it outperforms traditional methods when the system is dominated by a few prominent frequency components. Second, we employ DEFT as a data-value filter on the diffusion--sorption and Burgers equations of PDEBench, showing that it reduces data requirements by $40\%$ while sacrificing less than $2\%$ in predictive accuracy. Third, to evaluate DEFT for more challenging and practically relevant problems, we validate it in the battery degradation PDE system, achieving consistently high predictive accuracy across various test datasets with $R^2$ values exceeding $0.99$. Moreover, the learned frequency-domain features transfer to other battery chemistries with only $20\%$ of the fine-tuning data. These results demonstrate that DEFT is an effective data-sampling method for efficient operator learning.

arXiv

Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithms

Florian Beier, Stephan Eckstein

Clustering is a fundamental class of data analysis techniques with the most important representatives being centroid-based methods like $k$-means. Such methods are strongly connected to quantization problems, which aim to approximate general probability measures with discrete ones. For example, $k$-means corresponds to quantization with respect to the Wasserstein distance. While Wasserstein quantization clusters points within a fixed space, this paper studies Gromov-Wasserstein (GW) quantization, which additionally aims at clustering the ambient geometry of the space. We show existence of solutions to the GW quantization problem and give a characterization that justifies an analogue to the $k$-means algorithm (Lloyd's algorithm) to approximate them numerically. We further calculate the quantization rate for usual Euclidean geometries that are used in the GW context, and relate it to standard Wasserstein quantization rates. Finally, numerical experiments show that GW quantization opens up many modeling possibilities beyond normal clustering methods (e.g., for geodesic distances of 3D shapes or structured pruning of neural networks) and that the introduced algorithm leads to useful numerical solutions with approximation quality often in line with theoretically optimal rates.

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