Papers

Large language models (LLMs) can generate BPMN process models from natural-language descriptions, yet supervised fine-tuning (SFT) limits their output quality to the patterns present in the training data. Reinforcement learning (RL) can optimize beyond this ceiling using external quality measures, but how the reward function should be designed when quality is multi-dimensional remains unexplored. We present a systematic investigation of reward function design for RL-based process model generation, training two LLM families (Llama~3.1 8B, Qwen~2.5 14B) under 48 configurations using Group Sequence Policy Optimization with rewards derived from an automated evaluation framework comprising 38 metrics across syntactic, pragmatic, and semantic quality. Three findings emerge. First, RL significantly improves pragmatic and syntactic quality while preserving semantic fidelity, reducing output variability by more than sixfold. Second, equal reward weighting consistently outperforms targeted weighting: emphasizing a specific dimension fails to improve it and can collapse the model into a low-quality mode. Third, design choices interact with model architecture in non-trivial ways: the invalidity penalty is essential for one model but irrelevant for the other, and SFT initialization is indispensable for one architecture but counterproductive for another. These results demonstrate that reward composition is a primary determinant of optimization outcomes, with effects as large as the decision to apply RL itself. The findings generalize to any structured generation task where quality is assessed along multiple automated dimensions. We release our implementation and experimental code at https://github.com/chlauer99/RL_for_process_modeling.

Foundation Models for Electronic Health Records (FEMRs) are pretrained on large-scale structured patient data, enabling them to convert longitudinal patient trajectories into generalizable representations for diverse clinical prediction tasks. Despite their effectiveness, FEMRs remain black-box models, raising concerns about bias, interpretability, and clinical trust. To address this, we propose the first token-level explainability approach for FEMRs. We train a Transformer-based surrogate model on input-output pairs from the FEMR across two prediction tasks, approximating its behavior while preserving temporal dynamics. We identify the most influential tokens, providing insights into how FEMRs leverage different aspects of patient history for predictions. To evaluate clinical relevance, we introduce a novel clinical alignment metric that quantifies the correspondence between the surrogate model's key tokens and clinically validated features. Our results demonstrate that the surrogate closely approximates FEMR predictions and that token-level explanations align well with clinical knowledge, offering a practical framework for interpretable and trustworthy clinical AI.

Generalization remains a pivotal challenge in deep learning, where traditional optimizers like Stochastic Gradient Descent (SGD) often converge to sharp minima, leading to overfitting and reduced performance on unseen data. Building on Sharpness-Aware Minimization (SAM), for seeking flat minima associated with improved generalization, we propose the Extragradient-Inspired Sharpness-Aware Minimization (EISAM), a novel optimizer that enhances generalization via the extragradient technique. EISAM uses a two-step update process: a prediction step investigating the geometry of the loss landscape and a perturbation step that refines updates with a base optimizer. This approach achieves better generalization performance than SAM. Crucially, EISAM reduces sensitivity to the perturbation radius, enhancing robustness, and simplifying the tuning across diverse settings. Extensive experiments on benchmark datasets demonstrate that EISAM consistently outperforms SGD, Adaptive Moment Estimation (Adam), and SAM in test accuracy and training efficiency across various architectures. Theoretical analysis further confirms that EISAM tightens the generalization bound by steering parameters toward flatter minima with reduced curvature. Accompanied by a thorough hyperparameter analysis, EISAM offers practical tuning guidance, establishing it as a robust, scalable, and broadly applicable optimization solution that advances both the theory and practice in deep learning.

Reliable seam segmentation is essential for autonomous robotic welding in construction, where harsh illumination, specular reflections, and thin weld geometries often degrade segmentation performance. This study proposes a reflection-robust seam segmentation framework that enhances a BiSeNetV2 backbone through transfer learning and a hybrid Cross-Entropy–Lovász loss. Rather than increasing architectural complexity, the proposed framework improves reflection robustness through learning-stability-oriented optimization. Experimental results show that the proposed method achieves 81.76% Joint IoU and 90.73% mIoU, improving Joint IoU by +22.36 percentage points over the OHEM-based baseline while maintaining identical FLOPs, parameter count, and inference speed. The proposed approach also recovers 96.33% of severe zero-IoU failure cases under reflective conditions. Comparative experiments across BiSeNetV2, DeepLabV3+, UNet, and SegFormer further demonstrate that the proposed optimization strategy is particularly effective for lightweight real-time segmentation architectures. Qualitative analyses additionally show improved seam continuity and reflection robustness in challenging welding environments. These findings suggest that the proposed framework provides a practical and lightweight perception solution for robotic welding applications involving reflective metallic surfaces.

Multi-Pool Chemical Exchange Saturation Transfer (CEST) MRI provides valuable metabolic information but is clinically limited by long acquisition times. Although sparse sampling reduces scanning time, reconstructing high-resolution Z-spectra from limited data remains an ill-posed inverse problem. Conventional interpolation and generic Implicit Neural Rep-resentations (INRs) often lack physical constraints, leading to spectral artifacts and physically invalid signals. To address this, we propose Lorentz Encoding (LE), a physics-informed framework that formulates CEST reconstruction as a self-supervised reconstruction task via implicit continuous coordinate learning. Unlike generic positional encodings, LE regularizes the continuous spectral mapping by projecting sparse coordinates into a physically constrained space governed by a combination of parametric Lorentzian profiles with learnable basis functions. This mechanism effectively reduces noise and enforces consistency with physical models. Experiments on in vivo human brain data demonstrate that LE significantly outperforms state-of-the-art methods. Specifically, under a 39-point sampling strategy, LE achieves a PSNR of 57.58 dB and an SSIM of 0.9994. Furthermore, the learned physics-informed encodings form a continuous, geometrically ordered trajectory in the latent space, ensuring accurate quantitative metabo-lite mapping (APT, NOE, MT).

The increasing energy demand of software systems is raising concerns about their environmental impact and associated costs. Reasoning on energy usage early in the development flow has the potential to significantly reduce the overall energy usage of a software system, as it allows developers to make informed design and refactoring decisions before inefficiencies propagate. However, assessing energy usage without repeated profiling and direct measurement is difficult, which limits early reasoning in practice. This study investigates the limits of method-level energy prediction in Java, examining whether static source code metrics complemented with method-level execution time can estimate the energy consumption of Java methods. We profile 2,786 Java methods to extract 33 static features and measure execution time and energy, then train and compare eleven regression models. Our findings show that static source code metrics alone yield poor predictive performance, with average R2 values close to zero. Incorporating execution time as a lightweight dynamic input significantly improves accuracy, raising R2 to as high as 0.46. Execution time, internal method calls, and cyclomatic complexity consistently emerge as the strongest predictors of energy consumption.

In next-generation networks, communication systems will no longer be limited to data transmission and will be expected to acquire awareness of the surrounding environment. This leads to the concept of integrated sensing and communication (ISAC), where the same wireless infrastructure is used for both communication and environmental sensing. Thus, ISAC enables the system to transmit information efficiently and observe and interpret channel variations and user behavior. Motivated by this capability, this work focuses on detecting an active attacker in an urban environment scenario, where the attacker intentionally manipulates beamforming directions to increase interference and mislead the transmitter into allocating the main lobe of beam toward itself instead of legitimate users. We apply game-theoretic approaches to model the interaction between legitimate users and the attacker, and integrate the resulting utility-based formulation into a reinforcement learning (RL) framework. Simulation results demonstrate that the proposed method effectively addresses security challenges in dynamic 6G ISAC systems.

Diffusion and flow matching models generate high-quality samples, but their ODE samplers often need tens to hundreds of neural function evaluations (NFEs). This remains a practical challenge for released checkpoints, since many accelerators require additional design choices and training cost through retraining, distillation, or trajectory redesign. We investigate a different route based on $x$-prediction. During sampling, standard affine probability paths already expose $x_0$ information: an intermediate state and its path velocity determine a principled estimate of the clean sample. We formalize this property as endpoint decodability and show that the decoder is the minimum-MSE estimator $\mathbb{E}[x_0\mid x_t]$ under the usual $\ell_2$ objective. This yields Truncated Jump Sampling (TJS): stop the ODE at an early-exit time $t^*$ and return the decoded $x_0$. TJS requires no retraining, distillation, or architecture change. Across SDXL, SD3.5M, Z-Image-Turbo, and three class-conditional benchmarks, it reduces NFEs by 20–70% with near-matched quality. The analysis also shows why endpoint prediction can work without straightening the trajectory, providing inference acceleration without trajectory redesign.

A cyber-physical system (CPS) can enter a faulty state that is individually normal on every sensor and reconstructs accurately, yet is improbable under normal joint operation. This exposes the central weakness of reconstruction-based detection: reconstruction measures whether a state can be reproduced (reachability), not whether normal operation is likely to occupy it (probability). We model CPS normal behavior as a union of many imbalanced operating regimes, ten assumptions we call Massive, Implicit, Imbalanced Multimodality (MIIM). Our detector, LatAD, jointly learns a latent and a Gaussian-mixture clustering of these regimes (VaDE) and scores anomalies by density rather than reconstruction. Because a CPS is an assembly of coupled subsystems, we factorize that density over correlation-community subsystems and combine per-community surprises by a cohesion-weighted, sparsity-adaptive statistic, concentrating a local fault a global density dilutes. Evaluated with raw point-wise metrics and a difficulty split isolating the stealthy faults a per-channel threshold misses, LatAD attains the best AUROC on three real CPS benchmarks (WADI 0.862, HAI 0.949, SWaT 0.993) and leads the difficult subset of all three, notably on HAI (0.849; a significant +0.09 over the next-best baseline, 95% CI [0.046, 0.160]); the reconstruction-based USAD and TranAD fall to 0.30-0.48 on these reconstructable-but-improbable faults.

Intelligent systems should not only solve tasks but also adapt under real-world constraints. Autonomous adaptation via self-supervised learning, sequential adaptation via online learning, and memory-efficient implementation via perturbation-based learning are important requirements for such systems. However, these requirements are generally in tension for high-dimensional systems, because perturbation-based learning suffers from variance that grows with the dimension of the perturbed variables. In this study, we focus on echo state networks (ESNs), where this tension naturally arises in large reservoirs. We propose a perturbation-based learning rule for online self-supervised learning in ESNs. The proposed rule is derived from an orthogonal decomposition of the self-supervised learning cost, which separates an input-dependent component from a redundant component determined by the fixed ESN parameters. By perturbing only the input-dependent component, the effective perturbation dimension is reduced from the reservoir dimension to the input dimension. Thus, the proposed method preserves self-supervised adaptation, online learning, and scalar-feedback perturbation learning, while avoiding reservoir-size-dependent variance growth. This suggests a design principle for scalable and hardware-compatible learning: online learning should be restricted to the dynamically necessary low-dimensional component of the objective.

Eco-acoustic monitoring generates vast volumes of audio data, making active learning a promising approach for reducing annotation effort while efficiently training reliable biodiversity classifiers. This report presents CARE-DPP, a batch active-learning acquisition method submitted to BioDCASE Active Learning for Bioacoustics 2026 challenge. The method combines class-balanced predictive uncertainty with embedding-space novelty, while a determinantal point process (DPP) objective selects a high-quality and non-redundant acquisition batch. The uncertainty-novelty balance is annealed over the annotation budget: early cycles emphasize geometric coverage, whereas later cycles increasingly exploit classifier uncertainty. To mitigate unreliable early scores, the DPP candidate pool mixes top-quality candidates with a decreasing proportion of random exploration. An adaptive acquisition schedule uses smaller batches early and larger batches later. Evaluated over five repeats on the BirdSet HSN, POW and UHH subsets and on ATBFL, CARE-DPP obtains a mean development AULC of 0.50 for macro mAP, compared with 0.46 for the official CoreSet baseline. Ablations identify DPP batch diversification and the adaptive acquisition schedule as the largest contributors.

We aim to identify scattering network architectures that maximize the separation capacity on data with low intrinsic dimension. The networks we consider employ a fixed monomial nonlinearity and no pooling, so that the only design variable is the frame generated by the network filters. For data modeled as rectifiable sets, we first characterize and bound the separation capacity of general feature extractors in terms of the geometry of the dataset. We then particularize to scattering networks and obtain two design criteria: (i) the filters should meet the data on sufficiently many frequencies, and (ii) the matrices coupling the frame to the geometry of the data should be well-conditioned.

A shared electrocardiogram (ECG) is itself a biometric fingerprint that can re-identify a patient and reveal personal information. Recent ECG anonymizers transform the signal before sharing to reduce privacy leakage. However, existing methods still face a privacy–utility trade-off, in which preserving privacy often compromises utility while preserving utility reveals personal information. We propose REAN (REconstruction-aware ECG ANonymizer), a raw ECG signal anonymizer, to address this privacy–utility trade-off. REAN reconstructs the signal using a 1-D U-Net trained with losses from frozen privacy and utility classifiers to reduce privacy leakage while preserving utility. The privacy and utility gradients are near-orthogonal ($\approx$93.8$^\circ$), so reducing privacy leakage leaves utility almost unchanged. On four public PhysioNet databases, REAN achieves the strongest privacy–utility balance among raw ECG signal baselines. It drives re-identification to chance (0.96$\to$0.00), keeps arrhythmia macro-AUROC at the clean level (Clean 0.9982 vs.\ REAN 0.9991), and maintains re-identification protection under unseen privacy-classifier architectures.

We present a novel isogeometric deep learning method, termed SplineNet, for the seamless design and analysis of shell structures with complex geometries. The proposed approach is built upon watertight spline representations, e.g., analysis-suitable unstructured T-splines, and features exact geometric descriptions of Computer-Aided Design (CAD) models in neural networks. Bézier extraction is used to build the network architecture, where Bernstein polynomials serve as the nonlinear activation functions. SplineNet can be applied in a data-free or data-driven way. In the data-free case, energy-based formulations can be naturally incorporated as loss terms, which fulfill the need of Computer-Aided Engineering (CAE) and can be accurately calculated. In particular, the Kirchhoff–Love (KL) model is adopted to solve for the mechanical behaviors of shell structures. This way, CAD and CAE can be tightly integrated in a deep neural network without the time-consuming model/data exchange process. In the data-driven case, SplineNet can be used as the trunk net of Deep Operator Networks (DeepONet) to provide interpretability. Given such a trained network and unseen input data, results can be immediately obtained without retraining the network or repeatedly performing the traditional workflow for analysis. In the end, a variety of numerical examples are studied to demonstrate the effectiveness of the proposed method, especially when real-world complex geometries are involved.

We study a human-AI service system in which tasks arrive sequentially and are processed through a two-stage architecture: an automated chatbot followed, when necessary, by a human agent. We consider $T$ sequentially arriving tasks, each belonging to one of $K$ heterogeneous types. For each task the decision maker chooses how many resources to allocate to the chatbot, whose type-dependent success probabilities are initially unknown. Tasks not resolved by the chatbot enter type-dependent human-service queues, where they are processed by a human agent with unknown service rates. This model captures a central tradeoff in hybrid service systems: relying more on automation reduces human congestion but increases chatbot costs, while insufficient automation may overload the human agent. We propose the UCB-DPP policy, which combines Upper Confidence Bounds with Drift-Plus-Penalty control to learn the unknown parameters of the system while making queue-aware decisions. We prove that UCB-DPP achieves regret $\widetilde{\mathcal{O}}(K\sqrt{T})$ and guarantees mean-rate stability of the human-service queues. Simulations on synthetic instances show that the proposed policy outperforms natural baselines.

Adaptive gradient methods can favor max-margin separators that differ from gradient descent, yet a fixed positive numerical stability constant eventually changes the update geometry again. This paper studies the rate-controlled middle case for full-batch linear classification on separable data. For memoryless stability-annealed smoothed-sign descent with weighted exponential loss, we prove that the normalized iterates converge to the minimizer of a convex Burg-type barrier over a margin slice. The proof rewrites the dynamics exactly as entropic mirror ascent on a concave dual objective, controls the dual gap by a KL recursion, and yields an explicit S_t^{-1/2} normalized-iterate envelope. The static barrier geometry is fully characterized, including KKT conditions and both endpoint limits. Experiments validate the exact dual identities to floating-point error, illustrate the predicted path and rate diagram, and show an empirical fixed-epsilon crossover scaling in cumulative time. We further report robustness and boundary diagnostics for logistic tails, fixed-epsilon crossover, and adaptive-method variants, delineating the scope of the proved smoothed-sign theory.

Attributing code to the large language model that produced it is essential for provenance, licensing, and misuse accountability, yet no deployed watermark meets this need. Generation-time schemes require access to the producing model and cannot be applied to third-party code, while post-hoc schemes work on any code but carry at most 4 bits of payload, far too few to distinguish the many deployed model configurations. We present multi-channel spread-spectrum watermarking, the first post-hoc, training-free code watermark with a 24-bit payload and formal robustness guarantees. The scheme encodes bits in variable naming conventions and in eight pairs of semantically equivalent code patterns, and a keyed pseudo-random permutation maps every site to a codeword bit so that each bit receives multiple independent votes. Majority voting absorbs distributed corruption, while an outer Reed-Solomon code recovers the identifier when concentrated channel attacks defeat the vote, yielding provable robustness bounds for formatting, syntactic, and structural attacks. Across 1,750 Python files from CodeNet and from GPT-4.1 and Llama-4 generations, the watermark achieves 100% clean-detection accuracy with zero false positives. Under 17 attack types, it recovers the identifier at 97.6% accuracy under 8 variable renames and 94.1% under 10% random per-site corruption, while the strongest post-hoc baseline collapses to 0% under any single-transform attack. Embedding and detection together take under 200 ms on CPU without training data or GPU.

We propose a novel approach to mine patterns in spatio-temporal event data based on discovering frequent closed embedded sub-Directed Acyclic Graphs (DAGs). In our method, event instances are represented as nodes labelled by event types, while edges capture spatio-temporal following relationships. We formally define the considered class of patterns and provide the rationale for focusing on closed sub-DAGs as compact and non-redundant representations of recurring interaction patterns. We implement the DigDag algorithm for mining such patterns and experimentally compare its efficiency with two related approaches: propagation pattern mining using the SLEUTH algorithm and Cascading Spatio-Temporal Pattern mining using the CSTPM algorithm. The experimental results demonstrate that our approach is substantially more efficient while operating under comparable parameter settings. Finally, we present a qualitative analysis of selected discovered patterns.

Recovering the exact directed acyclic graph (DAG) in linear non-Gaussian acyclic models with latent confounders (LvLiNGAM) remains a challenging problem. Although LvLiNGAM is identifiable only up to an observational equivalence class, each equivalence class is characterized by a unique sparsest DAG. Recovering the sparsest DAG from finite samples, however, remains difficult. Although existing methods are asymptotically consistent, they do not provide an explicit finite-sample procedure for recovering the unique sparsest DAG, nor do they handle models with an arbitrary number of latent confounders. In this paper, we propose a finite-sample method for recovering the sparsest DAG without imposing any restriction on the number of latent confounders. Simulation studies and real-data analyses demonstrate that the proposed method achieves superior finite-sample performance compared with existing approaches.

Sentiment analysis with frozen pre-trained language model (PLM) backbones has become a common paradigm, yet the practical benefit of explicit domain adaptation remains unclear, particularly when backbones encode varying degrees of target-domain knowledge. We present a preliminary case study evaluating a controlled family of frozen embedding backbones (Qwen3-Embedding 0.6B, 4B, 8B), alongside RoBERTa-base and FinBERT. We train a lightweight MLP adapter on consumer reviews using Domain-Adversarial Neural Networks (DANN), Maximum Mean Discrepancy (MMD), and Supervised Contrastive Learning (SCL), and evaluate transfer to movie reviews (SST-2) and a heavily restricted subset of financial news (Financial PhraseBank). Within this constrained sample, we observe two distinct transfer patterns. On SST-2, domain adaptation provides negligible gain regardless of scale. On the financial subset, explicit domain adaptation appears to recover substantial performance for small general-purpose backbones. Notably, we find that adversarial alignment (DANN) is associated with degraded performance for domain-specialized backbones like FinBERT, consistent with erosion of pre-existing domain-specific structure, whereas supervised contrastive loss appears to preserve it. These preliminary findings suggest that the efficacy of explicit domain adaptation is highly contingent on whether the frozen backbone already possesses target-domain coverage.

Integration of web APIs is a cornerstone of modern software systems, yet writing correct web API invocation code remains challenging due to complex and evolving API specifications. Although LLMs are increasingly used for code generation, previous work has empirically shown that their ability to generate correct web API integrations is limited. At the same time, mitigation techniques and their effectiveness for this setting remain insufficiently understood. In this paper, we propose and systematically evaluate retrieval-augmented generation (RAG) and constrained decoding (CD) as two complementary approaches to improving LLM-generated web API invocation code. For RAG, we design a retriever that processes OpenAPI specifications and retrieves compact endpoint representations to inject into model prompts. For CD, we introduce an automatic translation from OpenAPI specifications to regex-based constraints enforced during generation. We evaluate both approaches on WAPIIBench's existing synthetic dataset and on a new real-world dataset derived from GitHub repositories. Our results show that RAG reduces hallucinations and improves correctness when generating full API invocations but reduces it when the endpoint is already provided as it encourages the generation of unnecessary parameters. In contrast, CD reliably prevents illegal URLs, HTTP methods, and arguments and substantially improves overall correctness for both starter codes.

Dynamic Voltage Frequency Scaling (DVFS) on resource-constrained embedded GPU platforms is essential for energy-efficient small language model (SLM) fine-tuning, as privacy- and personalization-driven adaptation increasingly requires local execution and involves repeated forward-backward optimization over many mini-batches, making it substantially more time- and energy-intensive than single-pass inference. To this end, 1) we first characterize the fine-tuning behavior of representative encoder-only SLMs of BERT variants, and autoregressive decoder-only SLMs of Pythia variants on GLUE benchmarks. In addition to the characterizations, 2) we propose a simple yet effective ML-based model selection that selects energy-optimal GPU DVFS settings on resource-constrained embedded platforms. Our results on NVIDIA Jetson AGX Orin demonstrate average 13.11% energy savings (up to 26.73%) over MAXN Mode 0, which has no explicit power cap.

Real-world data distributions evolve over time, inducing temporal distribution shift that can substantially degrade the reliability of deployed machine learning systems. However, the extent to which architectural choices and their associated inductive biases affect temporal robustness remains insufficiently understood. We present a systematic empirical comparison of temporal robustness across three heterogeneous, time-indexed domains encompassing image classification, multi-label text classification, and text regression tasks. Using a unified evaluation framework based on temporal drift matrices, we train models on cumulative historical data and evaluate their performance on both earlier and later time periods, thereby quantifying cross-temporal generalization. Our study spans model families ranging from simple multilayer perceptrons and convolutional networks to recurrent networks and pretrained Transformer-based encoders. Collectively, the results show that architectural inductive biases systematically shape temporal robustness: models whose inductive biases lead them to exploit localized, highly discriminative features attain the highest in-distribution accuracy, yet those features are often the ones that change most over time, so these models degrade fastest, while pretrained encoders that draw on coarser, more stable representations drift more gradually. These observations offer practical guidance for selecting architectures for real-world systems subject to temporal drift.

Training a language model against its own reference-free judgments (the premise of self-rewarding, self-play, and LLM-as-a-judge pipelines) assumes a model's verdict on a shown answer tracks correctness. We show it fails structurally: conditioned on a candidate, a judge scores plausibility, not correctness, leaving false-positive basins a policy learns to exploit. We measure this with a hidden-anchor audit: a held-out, cross-source exact-match check the judge never sees. On GSM8K with Qwen3 policies, self-play drives the judge's pass rate from 0.72 to 0.94 while true accuracy stays at 0.20 (three seeds). This reward hacking is not white-box gaming: the errors transfer across judge families (Qwen, Llama, Gemma) and scales, a strict three-judge ensemble still accepts 55% of them, and no plausibility-scoring defense closes the basin. The decisive variable is whether the judge commits an answer of its own before using the candidate: committing first drops the false-positive rate from 0.719 to 0.012, blind solving lifts discrimination to 0.96, and used as the training reward the de-anchored channel keeps false positives at zero, preventing the basin rather than only detecting it. A falsifiable bound (the gap is at most 1 - accuracy) predicts which regimes are exposed. The full arc replicates without training under best-of-N selection in code and competition math, and with a Gemma policy.

We present K-ABENA (K-Adaptive Backpropagation with Error-based N-exclusion Algorithm), a selective gradient computation framework that reduces per-iteration training cost by excluding a fraction of low-loss ("minor") observations from the backward pass. Its canonical form (v3) combines a defensive-mixture sampling design over the minor set with Horvitz-Thompson inverse-probability reweighting, yielding a design-unbiased Horvitz-Thompson gradient estimator (Lemma 2) and whose self-normalized practical variant carries a bias of order O(1/m) with an explicit constant (Lemma 3). We prove an O(1/sqrt(T)) non-convex convergence guarantee for SGD under the estimator, with an additive term that quantifies the residual bias (Theorem 1). We further prove that uncompensated loss-based selection - a family that includes OHEM, SBP, and the two earlier K-ABENA variants - admits no stationary point at any minimizer where its selection bias is bounded away from zero (Proposition 2), and we quantify this failure empirically: at 0.17% class imbalance, uncompensated variants reach test AUC 0.53-0.62 versus 0.9998 for full-batch SGD, while the compensated estimator attains 0.9991 at identical 28.4% compute savings. On real datasets (Breast Cancer, Digits, Wine, Diabetes) the compensated estimator is statistically indistinguishable from full-batch SGD (paired permutation tests, p >= 0.5; Section 7) while saving 28-54% of per-epoch gradient computation. A biased "regularized mode" (the earlier half-domain variant) is retained as an option with a proven exact bias decomposition (Lemma 5) and quantified contraindications: it collapses to 0.386 accuracy under 40% label noise (baseline: 0.832) and to 0.53 AUC under extreme imbalance. Every advantage and every limitation reported in this paper is either proved or measured; all experiments are CPU-scale (NumPy/scikit-learn) and their scope is stated explicitly.

Evaluating whether unlearning algorithms truly remove training data influence remains an open challenge. We propose a practical auditor that computes data-dependent lower bounds on the unlearning parameter $\varepsilon$ using membership inference attacks. Evaluating multiple unlearning algorithms, we find a sharp separation: algorithms with rigorous guarantees, such as model clipping and rewind-to-delete, achieve very small $\varepsilon$ bounds that do not falsify their unlearning guarantees, whereas empirical methods such as Hessian-based unlearning, interleaved ascent-descent, ascent on the forget set, and fine-tuning on the retain set exhibit large bounds, indicating poor unlearning. Our auditor provides a practical tool for empirically falsifying unlearning claims through a hypothesis-testing framework, and we validate it on CIFAR-100 and Shakespeare text.

When analyzing a manifold learning algorithm for data lying on a smooth, compact, connected Riemannian submanifold $(\mathcal{M}, g)$ of $\mathbb{R}^d$, a key estimate for the geodesic distance $d_g$ is that there exists $K > 0$ such that $0 \leq d_g(p, q)^2 - \|p-q\|^2 \leq K d_g(p, q)^4$ for all $p, q \in \mathcal{M}$. We observe that more generally, when $\mathcal{M}$ is equipped with a smooth symmetric divergence $D$ satisfying a non-degeneracy condition and $g$ is given by $g_p := \frac{1}{2}\mathrm{Hess}_p(D(p, \cdot))$ for all $p \in \mathcal{M}$, there exists $K > 0$ such that $\left| D(p, q) - d_g(p, q)^2 \right| \leq K d_g(p, q)^4$ for all $p, q \in \mathcal{M}$. We demonstrate that this is sufficient for the pointwise convergence of graph Laplacians constructed with $D$ and discuss examples where $D$ is given by the Sinkhorn divergence on a family of probability measures parametrized by a manifold.

Coreset selection aims to identify a small and highly representative subset of a massive dataset for efficient model training. The problem remains challenging even in the few-shot knowledge distillation (KD) setup, where a full-scale pre-trained teacher informs the student network. Typical sample selection strategies often struggle to surpass the random selection baseline. In this paper, we showcase few-medoids, an embarrassingly simple coreset selection strategy that chooses the samples closest to the centroid (average image) of each class. We present extensive KD experiments on four datasets, covering a wide range of image classification problems, and three teacher-student model pairs, comprising both convolutional and transformer networks. Although the proposed method is embarrassingly simple, our empirical results indicate that few-medoids is able to consistently surpass the random selection baseline, as well as the other coreset selection strategies. We therefore consider that few-medoids can be used as a drop-in replacement for commonly-used baselines (e.g. herding or k-center Greedy), in future research on coreset selection. To reproduce the reported results, we publicly release our code at https://github.com/CemilAndreiDilmac/Few-Shot-KD-Coreset.

Memory-efficient optimizers such as GaLore train large language models by projecting gradients onto a rank-r subspace recomputed every T steps, assuming this subspace is a slowly drifting object that can be tracked. We show that beyond a small reproducible core, there is no such object. Two estimates of the top-r subspace computed at the same step from disjoint minibatches disagree as much as estimates computed T steps apart (0.73 vs 0.74 of the maximal chordal distance sqrt(2r), at Pythia-160M with r=128): the apparent rotation at each refresh is dominated by estimator noise. This holds across four model families in three architecture classes from 70M to 6.9B parameters, strengthening with scale, and more weakly in a vision transformer. Only ~39 of 128 directions are reproducible across minibatches, and averaging cannot recover the rest: under N-fold averaging the gradient's spectral tail shrinks as N^(-1/4) rather than the N^(-1/2) of pure noise, so no averaging budget makes the subspace well defined. What helps instead follows from treating each refresh as a change of coordinates for Adam's state. Carrying the second moment blindly is provably about (r-k*)/2 worse than the best rotation-blind estimator, while the first moment transports exactly through the rotation, the optimal linear map under isotropic gradients and the rule LDAdam uses. At 1B over 40k steps (3 seeds), full LDAdam reaches 18.7 perplexity at beta2=0.999, beating untransported GaLore after its best beta2 fix (19.3); shortening the second-moment memory to beta2=0.99 helps the refreshing optimizers, though for canonical GaLore the effect is small and a full-rank control reverses it. One measurable fact, subspace non-identifiability, clarifies why GaLore works, which patches work, and what to check before trusting a low-rank assumption: the reproducible rank k*.

Under a fixed privacy budget, the utility of differentially private (DP) training is ultimately determined by its optimization efficiency. Standard first-order DP optimizers such as DP-SGD rely solely on local gradients and ignore the underlying loss curvature. This geometric blindness causes severe zigzagging in ill-conditioned landscapes, squandering precious privacy budgets on inefficient iterations. Practitioners are thus trapped in a bind: either stop training prematurely or inject massive per-step noise, both of which critically compromise final model utility. Natural Gradient Descent (NGD) resolves this by preconditioning gradients with curvature, aligning updates with the loss geometry and extracting more efficient signal from every noisy step, offering a principled pathway to break the privacy-utility bottleneck. Despite its theoretical appeal, directly integrating NGD with DP introduces fundamental challenges: curvature estimation itself consumes prohibitive privacy budgets, isotropic DP operations conflict with the anisotropic scaling of NGD, and the inverse curvature catastrophically amplify parameter updates in flat directions, causing training instability. We propose DP-NGD, a practical framework that systematically addresses these obstacles by decoupling curvature estimation from private data, reconciling isotropic DP constraints with anisotropic second-order optimization via a whitened-space mechanism, and dynamically clamping the curvature to stabilize training. Extensive experiments on standard benchmarks demonstrate that DP-NGD achieves state-of-the-art accuracy, breaking through the utility ceilings of first-order baselines while delivering up to a $10\times$ convergence speedup under the same privacy budget.