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General Machine Learning · Methodology

Inés Castilla Rieso

Topological Machine Learning provides strong discriminative power for classification tasks through the use of Topological Data Analysis, and more particularly, Persistent Homology. Although it has strong theoretical appeal, it remains underused by the broader Machine Learning community; criticism often targets the reliance on synthetic data and the absence of shared experimental standards, which makes reported results difficult to compare. Indeed, current empirical evaluations lack a consistent framework for assessing methods: the construction of topological signatures is often opaque, statistical significance testing to validate reported gains, computing times and robustness to perturbations-such as missing data or noise-are often omitted. We assert that **progress in Topological Machine Learning depends on establishing clear and consolidated experimental standards that support meaningful comparison across methods**, articulated through a transparent and reproducible empirical framework including data processing and performance evaluation. We review current practices, highlight their limitations, and propose a set of principles for conducting rigorous and comparable empirical evaluations. Adopting these standards will enable trustworthy studies, clarify the gains of new methods, and ultimately support the broader adoption of Topological Machine Learning by the Machine Learning community.

Applications · Chemistry, Physics, and Earth Sciences

Zhaoxin Yu, Nan Xu, Kun Chen, Jiahao Zhao, Lei Wang, Wenji Mao

With the continuous advancement of reasoning abilities in Large Language Models (LLMs), their application to scientific reasoning tasks has gained significant research attention. Current research primarily emphasizes boosting LLMs' performances on scientific QA benchmarks by training on larger, more comprehensive datasets with extended reasoning chains. However, these approaches neglect the essence of scientific reasoning process -- logicality, which is the rational foundation to ensure the validity of reasoning steps leading to reliable conclusions. In this work, we make the first systematic investigation into the internal logicality underlying LLM scientific reasoning, and develop a scientific logicality enriched methodology, including a set of assessment criteria and data sampling methods for logicality-guided training, to improve the logical faithfulness as well as task performance. Further, we take physics, characterized by its diverse logical structures and formalisms, as an exemplar discipline to practise the above methodology. For data construction, we extract scientific problems from academic literature and sample a high-quality dataset exhibiting strong logicality. Experiments based on three different backbone LLMs reveal that: 1) the training data we constructed can effectively improve the scientific logicality in LLM reasoning; and 2) the enriched scientific logicality plays a critical role in solving scientific problems.

Deep Learning · Sequential Models, Time series

Shohaib Shaffiey, Massimiliano Pierobon

The fields of AI-based disease fingerprinting, drug discovery and repurposing are currently among the emerging frontiers of machine learning applied to medicine. One major challenge is to obtain robust $\textit{in-silico}$ modeling of disease progression while accounting for the vastly different time scales of biochemical interactions, from gene expression to protein abundance and metabolic flux. Discrete sequence models inadequately represent such multi-scale interactions, and standard Neural Ordinary Differential Equations (NODEs) often fail to train stably under stiffness (different time scales). To address this, in this paper a Tri-Scale Stiff NODE is introduced, defined by hierarchically coupled latent differential equations that model the causal flow from genes to proteins and metabolites, and optimized using reconstruction error and information-theoretic mutual information. This enables continuous-time modeling of cellular responses to identify not only disease dynamics, but also drug perturbations that act within narrow time windows, often invisible to discrete-time approaches. Lyapunov analysis provides a theoretical guarantee that the modeled trajectories remain stable and well-behaved even under extreme stiffness. The developed modeling methodology is tested upon a public dataset (STATegra B-cell differentiation) and utilized for a proof-of-concept drug repurposing pipeline.

Theory · Learning Theory

Andrea Della Vecchia, Damir Filipovic

This paper investigates theoretical and methodological foundations for stochastic optimal control (SOC) in discrete time. We start formulating the control problem in a general dynamic programming framework, introducing the mathematical structure needed for a detailed convergence analysis. The associate value function is estimated through a sequence of approximations combining nonparametric regression methods and Monte Carlo subsampling. The regression step is performed within reproducing kernel Hilbert spaces (RKHSs), exploiting the classical KRR algorithm, while Monte Carlo sampling methods are introduced to estimate the continuation value. To assess the accuracy of our value function estimator, we propose a natural error decomposition and rigorously control the resulting error terms at each time step. We then analyze how this error propagates backward in time-from maturity to the initial stage-a relatively underexplored aspect of the SOC literature. Finally, we illustrate how our analysis naturally applies to a key financial application: the pricing of American options.

Yonggan Fu, Lexington Whalen, Zhifan Ye, Xin Dong, Shizhe Diao, Jingyu Liu, CHENGYUE WU, Hao Zhang, Enze Xie, Song Han 等

Diffusion language models (dLMs) have emerged as a promising paradigm enabling parallel generation, but their learning efficiency lags behind that of autoregressive (AR) language models when trained from scratch. To this end, we study AR-to-dLM conversion, which transforms pretrained AR models into efficient dLMs that excel in speed while preserving AR models’ task accuracy. We achieve this by identifying limitations in the attention patterns and objectives of existing AR-to-dLM methods and then proposing methodologies and actionable insights for scalable AR-to-dLM conversion. Specifically, we first systematically compare different attention patterns and find that maintaining pretrained AR weight distributions is key to effective AR-to-dLM conversion. Accordingly, we introduce a continuous pretraining scheme with a block-wise attention pattern. We find that, in addition to block-wise attention’s known benefit of enabling KV caching, its block-wise causality better preserves pretrained AR models’ weight distributions, leading to a win–win in accuracy and efficiency. Second, to mitigate the training–test gap in mask token distributions (uniform vs. highly left-to-right), we propose a position-dependent token masking strategy that assigns higher masking probabilities to later tokens during training to better mimic test-time behavior. These studies lead to the Efficient-DLM model family, which outperforms state-of-the-art AR models and dLMs in accuracy–throughput trade-offs; for example, our Efficient-DLM 8B achieves +5.4\%/+2.7\% higher accuracy with 4.5$\times$/2.7$\times$ higher throughput compared to Dream 7B and Qwen3 4B, respectively.

General Machine Learning · Evaluation

Kabir Kang, Steve Mussmann

Standard classification treats all errors equally, but in content moderation, medical screening, and safety-critical applications, mistakes on clear-cut cases are far more costly than errors on ambiguous ones. We propose normalized excess cost (NEC), a metric that weights classification errors by per-example costs and reduces to standard error rate when costs are uniform. Costs can derive from annotator vote margins, distance from decision thresholds, or confidence ratings. Across text, image, and tabular benchmarks, we find that NEC is often substantially lower than error rate—models with 5% error rate can achieve 1.8% NEC—revealing that most mistakes concentrate on ambiguous, low-cost examples. However, incorporating costs into training via loss weighting, sampling strategies, or regression yields inconsistent benefits: improvements appear only when costs are predictable from input features, as in our synthetic control, while real-world datasets show mixed or negligible gains. Our framework provides a practical methodology for deriving and evaluating instance-level misclassification costs, even when cost-sensitive training offers limited benefit.

Social Aspects · Security

Zhao-Rong Lai, Xiwen Yuan, Jian Weng

Denoising diffusion sampling (DDS) is an emerging approach for generating new samples that have the same distribution as some training samples. However, it is vulnerable to adversarial attacks by even a Gaussian perturbation. In this work, we propose a complete set of adversarial attack and defense methodology for DDS. In the attack side, we propose to inject a perturbation to the sampling stage, which significantly worsen the performance of sample generation. In the defense side, we propose a local variation based regularization model for the potential function minimization, which effectively tolerates the adversarial perturbations. Moreover, we develop a conjugate gradient algorithm to solve the defense model, which integrates with a recently-developed zeroth order rejection sampling method that saves computational cost. Experimental results show that the proposed attack significantly worsen the existing state-of-the-art methods, but can be defended by the proposed local variation regularization.

General Machine Learning · Methodology

Junhyoung Chung, Euijong Song, Won Hwa Kim, Gunwoong Park

We introduce Convex Distance Operator Transport (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains by jointly preserving feature correspondence and intrinsic geometric structure. Specifically, CDOT employs an operator-based regularization that aligns aggregated distance structures by introducing distance and conditional expectation operators. Consequently, the proposed regularization improves the robustness to local geometric variations. We further prove that the resulting CDOT discrepancy is a valid pseudometric on the space of attributed compact metric-measure spaces. In addition, we characterize the relationship between CDOT and Gromov--Wasserstien (GW) through a new notion of dispersion gap, formally elucidating the geometric source of non-convexity in GW compared to the convexity of CDOT. In the finite-sample regime, we derive a non-asymptotic risk bound decomposed into optimization and statistical errors, establishing risk consistency under a globally convergent Frank--Wolfe algorithm. Experiments on synthetic point clouds, brain connectomes, and graph classification benchmarks demonstrate better performance over existing methods, with stable and reliable behavior in practice.

Jianhui Chen, Yuzhang Luo, Liangming Pan

Mechanistic Interpretability has successfully identified functional circuits in Large Language Models (LLMs), yet their causal origins in the training data remain poorly understood. We bridge this gap by introducing **Mechanistic Data Attribution (MDA)**, a scalable framework that traces the formation of specific interpretable units back to training samples using Influence Functions. Through extensive pre-training experiments on the Pythia family, we causally validate that removing a small fraction of high-influence samples significantly hinders the emergence of targeted heads, whereas augmenting them accelerates formation—effects that random interventions fail to replicate. Leveraging MDA, we reveal that highly repetitive structural data—such as LaTeX and HTML—acts as a "catalyst" that significantly accelerates the emergence of induction heads. Furthermore, we observe that interventions targeting induction head formation induce a concurrent change in the model’s in-context learning (ICL) capability. This provides direct causal evidence for the long-standing hypothesis regarding the functional link between induction heads and ICL. Finally, we propose a mechanistic data augmentation pipeline that builds upon these insights to consistently accelerate mechanistic convergence across diverse model scales, offering a principled methodology for understanding and steering the fine-grained development of LLM behaviors.

General Machine Learning · Methodology

Yang Zhao, Jungeun Lee, Jeong hwan Jeon, Sze Zheng Yong

We present a novel framework for embedding hard constraint satisfaction into neural network (NN) architectures, specifically feedforward neural networks and transformers, with input-dependent affine constraints of arbitrary cardinality. Traditional constraint enforcement approaches either rely on penalty-based soft constraints, which offer no guarantee of satisfaction, or on post-processing methods that enforce constraints after the NN is trained, which may lead to suboptimality. We introduce a trainable constraint-affine (CAffine) layer into NNs, yielding CAffNet, which goes beyond enforcing affine constraints via fixed orthogonal or parallel projections and enables joint optimization with network parameters. Moreover, we impose no restrictions on the constraint space dimensions and establish that our construction preserves the universal approximation properties of NNs, while providing provable guarantees on constraint adherence for all inputs. Experimental validation demonstrates robust performance across diverse domains requiring guaranteed constraint satisfaction.

Hanlin Zhang, Jikai Jin, Vasilis Syrgkanis, Sham Kakade

For deploying foundation models, practitioners increasingly need prescriptive scaling laws: given a pre-training compute budget, what downstream accuracy is attainable with contemporary post-training practice, and how stable is that mapping as the field evolves? Using large-scale observational evaluations with 5k observational and 2k newly sampled data on model performance, we estimate capability boundaries—high conditional quantiles of benchmark scores as a function of log pre-training FLOPs, via smoothed quantile regression with a monotone, saturating sigmoid parameterization. We validate the temporal reliability by fitting on earlier model generations and evaluating on later releases. Across various tasks, the estimated boundaries are mostly stable, with the exception of math reasoning that exhibits a consistently advancing boundary over time. We then extend our approach to analyze task-dependent saturation and to probe contamination-related shifts on math reasoning tasks. Finally, we introduce an efficient algorithm that recovers near-full-data frontiers using roughly 20% of evaluation budget. Together, our work releases the Proteus-2k, the latest model performance evaluation dataset, and introduces a practical methodology for translating compute budgets into reliable performance expectations and for monitoring when capability boundaries move.

Deep Learning · Generative Models and Autoencoders

Thorben Pieper-Sethmacher, Daniel Paulin

This paper introduces a rigorous framework for defining generative diffusion models in infinite dimensions via Doob's h-transform. Rather than relying on time reversal of a noising process, a reference diffusion is forced towards the target distribution by an exponential change of measure. Compared to existing methodology, this approach readily generalises to the infinite-dimensional setting, hence offering greater flexibility in the diffusion model. The construction is derived rigorously under verifiable conditions, and bounds with respect to the target measure are established. We show that the forced process under the changed measure can be approximated by minimising a score-matching objective and validate our method on both synthetic and real data.

Yanhao Jin, Krishna Balasubramanian, Debashis Paul

Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate random-effects linear models and study generalized ridge-regression based predictions. The statistical intuition of using generalized ridge regression in this setting is that the covariance structure of the random regression coefficients could be leveraged to make better predictions on new tasks. Accordingly, we first characterize the precise asymptotic behavior of the predictive risk for a new test task when the data dimension grows proportionally to the number of samples per task. We next show that this predictive risk is optimal when the weight matrix in generalized ridge regression is chosen to be the inverse of the covariance matrix of random coefficients. Finally, we propose and analyze an estimator of the inverse covariance matrix of random regression coefficients based on data from the training tasks. As opposed to intractable MLE-type estimators, the proposed estimators could be computed efficiently as they could be obtained by solving (global) geodesically-convex optimization problems. Our analysis and methodology use tools from random matrix theory and Riemannian optimization. Simulation results demonstrate the improved generalization performance of the proposed method on new unseen test tasks within the considered framework.

Social Aspects · Alignment

Tushita Jha, Rory Švarc, Mateusz Bagiński

The ML literature contains many distinct concepts falling under the heading of ‘AI alignment’. After noting three concepts of AI alignment and situating these ideals in the context of their corresponding research programs, we claim that realistic interventions may promote ‘AI alignment’ under one conception while being actively counterproductive from the perspective of others. We suggest that tensions between alignment ideals emerge due to differences in background threat-models, alongside differences in both methodological and normative orientations. In light of our analysis, researchers taking themselves to produce research aimed to further the goal of ‘AI alignment’ should do three things. First, they should distinguish between ‘AI alignment’ as a high-level ideal and the specific ‘alignment proxies’ used in empirical research. Second, they should use more granular concepts to identify the source in addition to the nature of possible AI harms/benefits. Third, they explicitly specify the non-technical background commitments motivating specific conceptions of ‘AI alignment’.

General Machine Learning · Representation Learning

Ali Kayyam

Whether deep vision models recognize objects primarily by shape or texture remains a central and unresolved question in computer vision. Early studies report a strong texture bias in convolutional neural networks (CNNs), while other work reports shape-biased representations. We argue that much of this apparent discrepancy reflects methodological confounds and a conflation of local contour sensitivity with genuine global shape understanding. Using minimal, tightly controlled stimuli, we directly compare cue-conflict and cue-suppression paradigms within a unified experimental framework. We show that standard CNNs consistently prioritize texture over global shape when cues compete, even when shape information is explicitly available. Evidence for shape bias typically reflects reliance on local fragments rather than invariant, relational representations of object structure. Our findings support the view that texture bias is fundamentally rooted in architectural inductive biases rather than data or optimization alone. This gap has direct consequences for robustness, safety, and generalization, and motivates the development of architectures that explicitly support global integration and relational reasoning, moving beyond incremental data-driven fixes.

Social Aspects · Accountability, Transparency, and Interpretability

Hilal Aka, Joe Kwon, Noam Kolt

AI models readily refuse explicitly unlawful requests, but real-world illegality often depends on context. We evaluate frontier models on contextual illegality across four corporate law domains in which routine actions—editing documents, trading stock, requesting payment, approving communications—become unlawful due to triggers such as pending investigations or bankruptcy filings. We study both chat and agentic settings and compare results to a human baseline. The best-performing models achieved near-zero compliance with illegal requests while maintaining high compliance with legal ones, though performance varied sharply by domain. We also identify distinct failure modes such as excessive refusal of legal requests and find improved performance from reasoning models and agentic environments. By utilizing the structure of contextual illegality to create controlled evaluations, our methodology provides empirical grounding for emerging research on law-following AI and extends naturally to additional legal domains.

Deep Learning · Other Representation Learning

Xiaolong Chen, Fuyuan Xiao, Xiaohong Zhang, Zehong Cao, Chin-teng Lin

Out-of-Distribution (OOD) detection requires accurately classifying In-Distribution (ID) samples while effectively distinguishing anomalous OOD data. However, existing methodologies predominantly rely on real-valued magnitude features, neglecting the semantic richness embedded in phase information, and often lack a systematic theoretical framework for quantitively modeling uncertainty. To address this dual limitation of incomplete feature representation and insufficient uncertainty modeling, the Trustworthy Quantum Evidence Neural Network (TrustworthyQENN) is proposed, a novel framework bridging complex-valued representation learning with Generalized Quantum Evidence Theory (GQET). Specifically, Supervised Complex-Valued Contrastive Learning (SCVCL) is proposed to synchronize amplitude distributions with phase correlations, thereby enforcing high intra-class compactness and inter-class separability for ID data. A quantum evidence generation mechanism based on GQET is subsequently devised, where the OOD state is formally grounded as the quantum empty set within a Hilbert space. Furthermore, the Generalized Quantum Evidential Combination Rule (GQECR) is leveraged to fuse multi-view evidence, thereby achieving trustworthy inference. Extensive experiments on the MSTAR, EuroSAT, and FUSAR-Ship benchmarks substantiate the superiority of TrustworthyQENN, which achieves a peak AUROC of 95.94% on the MSTAR dataset while consistently outperforming state-of-the-art methods across all evaluated scenarios.

General Machine Learning · Methodology

Terry Tong, Yu Feng, Surbhi Goel, Dan Roth

Large language models can solve algorithmic problems either through direct natural language (NL) reasoning or by generating executable code delegated to an external solver. However, little progress has been made on **understanding why**. Comparing NL reasoning and solver-based pipelines directly is ill-posed: they differ simultaneously in representation space and execution mechanism. We introduce a three-route framework that makes this comparison tractable by introducing an intermediary step---code generation with LLM-based execution. This enables our empirical analysis, which shows a statistically significant gap supporting code $>$ NL by +28.9\% across 48 different algorithmic tasks and 6 models. A statistical analysis indicates that natural-language reasoning does not provide additional decision-relevant information beyond what is already captured by code representations. Consequently, replacing NL traces with code traces incurs minimal performance loss while enabling deterministic execution. A systematic comparison of LLM-based reasoning and external execution further shows that execution, rather than trace representation, is the primary performance bottleneck.

Applications · Language, Speech and Dialog

Chenyang Shao, Jiahe Liu, Fengli Xu, Yong Li

Scientific illustration figures are essential for depicting research works' conceptual designs, methodology, and experimental workflows, playing a pivotal role in communicating complex academic insights. However, creating high-quality scientific illustrations remains a labor-intensive task for human scientists. While recent generative image models have advanced prompt-based editing, the synthesis of fully **editable** figures remains a fundamental challenge. Valid editability involves structured transformations of graphical elements, scales, attributes, and text, rather than simple pixel-level changes. Existing models generate raster outputs that do not support manual correction or layout adjustment, limiting their utility in scientific publishing, where editable vector figures are typically required for submission. To address this challenge, we introduce **LiveFigure**, an agentic framework driven by VLM agents that imitates the multi-step drawing workflow of human researchers. It first plans figure blueprints by drawing inspiration from high-quality references in previous works, then generates executable scripts that produce figures via the PowerPoint interface based on skills and experience, and finally refines the outputs with targeted visual diagnostics, producing fully vectorized, editable figures that meet publication standards. Extensive experiments demonstrate that LiveFigure generates inherently editable figures that are both visually clear and aesthetically appealing, achieving 80% publication-readiness within just 17 manual edits—far surpassing the 24% rate of the strongest baseline, NanoBanna. Human preference studies further validate this advantage, with LiveFigure securing a 60% win rate against NanoBanna. Our code is available at [https://anonymous.4open.science/r/LiveFigure](https://anonymous.4open.science/r/LiveFigure).

Deep Learning · Generative Models and Autoencoders

Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito, Arnulf Jentzen

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems. We learn the joint distribution of PDE parameters and solutions via a diffusion process in a latent space of scaled spectral representations, where Gaussian noise corresponds to functions with controlled regularity. This spectral formulation enables significant dimensionality reduction compared to grid-based diffusion models and ensures that the induced process in function space remains within a class of functions for which the PDE operators are well defined. Building on diffusion posterior sampling, we enforce physics-informed constraints and measurement conditions during inference, applying Adam-based updates at each diffusion step. We evaluate the proposed approach on Poisson, Helmholtz, and incompressible Navier--Stokes equations, demonstrating improved accuracy and computational efficiency compared with existing diffusion-based PDE solvers, which are state of the art for sparse observations. Code is available at https://anonymous.4open.science/r/PISD-32A0/.