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arXiv2026

KTO: Model Alignment as Prospect Theoretic Optimization

Kahneman & Tversky's $\textit{prospect theory}$ tells us that humans perceive random variables in a biased but well-defined manner (1992); for example, humans are famously loss-averse. We show that objectives for aligning LLMs with human feedback implicitly incorporate many of these biases -- the success of these objectives (e.g., DPO) over cross-entropy minimization can partly be ascribed to them belonging to a family of loss functions that we call $\textit{human-aware losses}$ (HALOs). However, the utility functions these methods attribute to humans still differ from those in the prospect theory literature. Using a Kahneman-Tversky model of human utility, we propose a HALO that directly maximizes the utility of generations instead of maximizing the log-likelihood of preferences, as current methods do. We call this approach KTO, and it matches or exceeds the performance of preference-based methods at scales from 1B to 30B, despite only learning from a binary signal of whether an output is desirable. More broadly, our work suggests that there is no one HALO that is universally superior; the best loss depends on the inductive biases most appropriate for a given setting, an oft-overlooked consideration.

cs.LG↗
arXiv2026

Small Molecule Optimization with Large Language Models

Molecular optimization, the process of designing molecules with desirable properties, represents a critical challenge in drug discovery. The recent advancements in large language models (LLMs) have opened new opportunities for their integration with traditional molecular optimization algorithms to improve performance. In this work, we propose Molecular Language Model powered Evolutionary Algorithm (Mol-E), an evolutionary algorithm that relies on the generative capabilities of LLMs trained on molecules and molecular properties. Scientific Contribution. Mol-E obtains the highest aggregate Top-10 AUC among the comparable full-23-task results considered here, scoring 17.500 in the task-agnostic regime, in which the oracle is treated strictly as a black box, and 20.551 in the task-informed regime, in which the optimizer receives a fixed semantic description of the objective. Mol-E also improves over the evaluated baselines on multi-property optimization with docking against DRD2, MK2, and AChE.

cs.LG↗
arXiv2026

The EM-algorithm and the Method of Moments in Softmax Mixture Models

Softmax Mixture Models (SMMs) are discrete $K$-component mixture models for the probabilities of selecting one of $p$ candidate feature vectors $X_1,\ldots,X_p\in\mathbb{R}^L$ in heterogeneous populations and are widely used in econometrics and scientific applications. Related softmax mixture mechanisms also appear in modern LLM architectures. We provide a theoretical and methodological study of SMMs, focusing on the Expectation-Maximization (EM) algorithm and the Method of Moments (MoM). We show that EM recovers the mixture atoms at the parametric rate, up to logarithmic factors, after $\mathcal{O}(\log N)$ iterations, provided atom separation is at least of order $\log K$. This improves on separation conditions in existing analyses of EM for high-dimensional Gaussian mixtures. We also develop MoM procedures for parameter and subspace estimation. Although MoM parameter estimates converge more slowly than EM and can deteriorate with $K$, they provide provable warm starts for EM and are useful for small $K$. For general $K$, we estimate the atom subspace via MoM and recommend running EM from multiple random initializations within this subspace. Finally, as $p\to\infty$, we show that SMMs approximate mixtures of exponential tilts of the feature distribution, yielding asymptotic identifiability.

stat.ML↗
arXiv2026

On Generalisation Error Bounds for Transformers

In this paper, we establish a collection of covering number bounds for linear function classes under various norm constraints on the inputs and matrices. We then combine these results with existing covering number bounds to derive improved estimates and, based on these estimates, develop generalization error bounds for single-layer Transformers. The resulting generalization bounds improve upon several existing results in the literature and, in particular, are independent of the input sequence length. Moreover, our generalization error bound decays at the rate $O(1/\sqrt{n})$, where $n$ denotes the sample size, thereby improving upon existing bounds that scale as $O((\log n)/\sqrt{n})$. Furthermore, our covering number analysis explicitly incorporates rank constraints on the underlying matrix classes, allowing us to characterize how low-rank structures affect the metric entropy and, consequently, the resulting generalization bounds for Transformer architectures.

stat.ML↗
arXiv2026

Projected Neural Differential Equations for Learning Constrained Dynamics

Neural differential equations offer a powerful approach for learning dynamical systems from data. However, they do not inherently respect known constraints, such as conservation laws, that should be obeyed by the learned dynamics. It is well known that enforcing constraints in data-driven models can enhance their generalizability and numerical stability. In this paper, we introduce projected neural differential equations (PNDEs), a method for constraining neural differential equations based on projection of the predicted velocities onto the tangent space of the manifold that fulfills the constraint. In tests on several examples from different fields, including chaotic dynamical systems and power grid models, PNDEs outperform existing methods for constraining learned dynamics, require fewer hyperparameters, and are computationally more efficient. The proposed approach demonstrates potential for enhancing the modeling of constrained dynamical systems, particularly in domains where accuracy and reliability are essential.

cs.LG↗
arXiv2026

A cautionary tale on the cost-effectiveness of collaborative AI in real-world medical applications

Federated learning (FL) has gained wide popularity as a collaborative learning paradigm allowing collaborative Artificial Intelligence (AI) in sensitive healthcare applications. Nevertheless, the practical implementation of FL presents technical and organizational challenges, as it generally requires complex communication infrastructures. In this context, consensus-based learning (CBL) may represent a promising alternative for collaborative learning, allowing the combination of local knowledge into a federated decision system, while potentially reducing deployment overhead. Nevertheless, a comprehensive assessment of the viability of consensus-based learning as a cost-effective and sustainable alternative to federated learning has not yet been conducted. In this work we propose an extensive benchmark of the accuracy, cost-effectiveness, and sustainability of a panel of FL and CBL methods in a wide range of collaborative medical data analysis scenarios. The benchmark includes 7 different medical datasets, encompassing 3 machine learning tasks, 8 different data modalities, and multi-centric settings involving 3 to 23 clients. Our results reveal that CBL is a cost-effective and more sustainable alternative to FL. When compared across the panel of medical datasets in the considered benchmark, CBL methods provide equivalent accuracy to the one achieved by FL. Nonetheless, CBL significantly reduces training time and communication cost (resp. 15 fold and 131 fold decrease) (p-value < 0.05). This study opens a novel perspective on the deployment of collaborative AI in real-world applications, whereas the adoption of cost-effective methods is instrumental to achieve sustainability and democratization of AI by alleviating the need for extensive computational resources.

cs.LG↗
arXiv2026

Fewer yet critical: Reducing Redundant Token Dependencies for Transformer-based Time Series Forecasting

Time series forecasting (TSF) is important in real-world applications. Recently, Transformer-based methods have achieved strong performance by modeling token dependencies through attention mechanisms. However, existing methods are usually trained mainly with prediction error losses, which may cause models to exploit both critical and redundant token dependencies. Such redundant dependencies can introduce irrelevant information and weaken generalization. To address this issue, we propose a simple yet effective token dependency selection strategy. Specifically, by jointly introducing the attention entropy constraint and prediction error constraint, the model can identify fewer but more critical inter-token dependencies and perform forecasting based on them, thus avoiding the interference of redundant dependencies. The proposed method can be easily extended to various Transformer-based TSF models. Experiments on multiple TSF datasets demonstrate its effectiveness.

cs.AI↗
arXiv2026

The Dynamics of Generalization in Deep Learning

We derive a differential equation that governs the evolution of the generalization gap when a model is trained by gradient descent-based methods. This differential equation is driven by two key quantities, a contraction factor that brings together trajectories corresponding to slightly different datasets, and a perturbation factor that accounts for them training on different datasets. The coupled decay of contraction and perturbation guarantees a controlled accumulation of generalization gap during training. We analyze this differential equation to show that the generalization gap is given by a quadratic form that consists of an ``effective Gram matrix'' that depends upon the training trajectory and a certain residual of the predictor at initialization. Our framework is applicable to general deep networks and smooth loss functions. In numerical experiments on different neural network architectures, datasets and sample sizes, we show that this quadratic form accurately captures the actual generalization gap. We also show how to instantiate our framework in a number of examples via analytical calculations. For example, for high-dimensional linear regression, our framework matches existing calculations of generalization gap in the literature exactly in under-parameterized, over-parameterized and critical regimes.

cs.LG↗
arXiv2026

How to Backdoor Image Knowledge Distillation

Knowledge distillation is widely used to transfer behavior from a large teacher model to a smaller student. It is often assumed to be safe when the teacher is clean, because classic backdoor attacks rely on poisoned labels and triggers in supervised training, whereas distillation trains the student to match a teacher's outputs. We show that this assumption can fail when the distillation dataset itself is poisoned. Our attack injects triggered and manipulated images that a clean teacher already predicts as an attacker chosen target label, which causes the student to learn a backdoor even though the teacher remains unaffected. We evaluate this threat across multiple manipulation strategies, including targeted adversarial perturbations and targeted GAN based class transitions, and study how distillation settings influence both accuracy and attack success. We show that the attack remains effective even at a 10% poisoning rates. The results demonstrate that a clean teacher alone is not a sufficient safeguard: poisoned distillation data can produce a strongly backdoored student while maintaining competitive performance on clean images. These findings show that the integrity and provenance of distillation data are part of the security boundary of data intensive KD pipelines, even when the teacher itself is trusted.

cs.CR↗
arXiv2026

A Theoretical Analysis of Provable Compositional Generalization in Neural Networks: A Necessary and Sufficient Condition

Compositional generalization$\unicode{x2013}$the ability to systematically process novel combinations of known components$\unicode{x2013}$is a hallmark of human intelligence; however, its theoretical foundation in neural networks is not yet well understood. This paper establishes a necessary and sufficient condition for provable compositional generalization, precisely characterizing its boundary. Conceptually, the condition consists of two principles: (i) structural alignment, where a model's computational graph aligns with a task's true compositional hierarchy, and (ii) unambiguous minimized representations, where each component encodes adequate but not redundant information on the training data. The result is fully proved and machine-verified in Lean 4 and holds even in few-shot and one-shot regimes. The necessity direction establishes that provable compositional generalization cannot circumvent these requirements, while the sufficiency direction yields a unified inductive bias that jointly governs architectural design, training data properties, and regularization strategies. Building on this condition, we develop an example algorithmic approach, illustrate it through a controlled minimal example, and further demonstrate the condition on the SCAN jump task. All conclusions are derived mathematically without reliance on empirical validation. Our work provides a theoretical characterization of provable compositional generalization.

cs.LG↗
arXiv2026

Clustering and Pruning in Causal Data Fusion

Data fusion, the process of combining observational and experimental data, can enable the identification of causal effects that would otherwise remain non-identifiable. Although identification algorithms have been developed for specific scenarios, do-calculus remains the only general-purpose tool for causal data fusion, particularly when variables are present in some data sources but not others. However, approaches based on do-calculus may encounter computational challenges as the number of variables increases and the causal graph grows in complexity. Consequently, there exists a need to reduce the size of such models while preserving the essential features. For this purpose, we propose pruning (removing unnecessary variables) and clustering (combining variables) as preprocessing operations for causal data fusion. We generalize earlier results on a single data source and derive conditions for applying pruning and clustering in the case of multiple data sources. We give sufficient conditions for inferring the identifiability or non-identifiability of a causal effect in a larger graph based on a smaller graph and show how to obtain the corresponding identifying functional for identifiable causal effects. Examples from epidemiology and social science demonstrate the use of the results.

stat.ML↗
arXiv2026

ControlTac: Scaling Tactile Data with Physically Controlled Tactile Image Generation

Vision-based tactile sensing is widely used in perception, reconstruction, and robotic manipulation, yet collecting large-scale tactile data remains costly due to diverse sensor-object interactions and inconsistencies across sensor instances. Existing approaches to scaling tactile data---simulation and free-form tactile generation---often yield unrealistically rendered signals with poor transfer to highly dynamic real-world tasks. We propose \name, a two-stage controllable tactile image generation framework that generates realistic tactile images conditioned on a single reference tactile image, contact force, and contact pose. By grounding generation in these important physical priors, \name synthesizes realistic samples across different sensors while effectively capturing task-relevant variations. Across a series of downstream tasks and real-world experiments, such as object insertion, imitation learning, and object weighting, the augmented datasets using our approach consistently improve performance and demonstrate practical utility in dynamic real-world settings. Project page: https://dongyuluo.github.io/controltac.

cs.CV↗
arXiv2026

NoLoCo: No-all-reduce Low Communication Training Method for Large Models

Training large language models is generally done on clusters containing thousands of accelerators, communicating over a high-bandwidth interconnect. Scaling up these clusters is expensive and can become impractical, imposing limits on the size of models that can be trained. Several recent studies have proposed training methods that are less communication intensive, avoiding the need for compute clusters with extremely high interconnect speeds. These low communication training methods still employ a global synchronization step for model parameters, which can be too costly with a high number of participants, as the communication cost scales quadratically with group size. In this work, we propose a novel optimization method, NoLoCo, that does not explicitly synchronize all model parameters during training and does not require any collective communication. NoLoCo implicitly synchronizes model weights via a novel variant of the Nesterov momentum optimizer by partially averaging model weights within randomly selected subgroups. We provide both a theoretical convergence analysis of our optimizer and empirical results from language model training. Our method requires significantly less communication than fully sharded data parallel training and DiLoCo, a widely used low-communication baseline. Moreover, our method avoids global blocking communication, thereby reducing accelerator idle time. Our experiments show that NoLoCo is more communication-efficient than DiLoCo, improving final perplexity by up to $4\%$ and converging up to $4\times$ faster in wall-clock time across a range of worker counts, model sizes, and communication bandwidths.

cs.LG↗
arXiv2026

SloMoDeblur: A Large-Scale Smartphone Image Deblurring Dataset

Motion blur remains one of the most common and visually disruptive degradations in real-world smartphone imaging, yet existing deblurring benchmarks are often limited in scale, resolution, or domain relevance. This gap is especially pronounced for smartphones, where rolling shutter, small sensors, and ISP processing produce blur statistics that differ from GoPro/DSLR-based benchmarks. We introduce a large-scale smartphone-oriented deblurring dataset constructed from 240~fps slow-motion video. To approximate exposure-time radiance integration, we synthesize blur by temporally averaging a fixed window of $N=30$ consecutive frames, which corresponds to an effective exposure of $T=1/8$~second, and we select the temporally centered frame as the sharp ground truth. The resulting benchmark contains 42,045 paired blur--sharp images at $1920\times1080$ resolution spanning 843 distinct scenes, with a train/test split of 37,841/4,204 pairs. We benchmark multiple state-of-the-art deblurring models using PSNR and SSIM and observe consistent performance degradation relative to the baseline similarity between the input blurry images and ground truth, underscoring the realism and difficulty of the proposed data. We release the dataset and generation scripts via HuggingFace to facilitate the development and evaluation of robust, deployment-oriented deblurring methods.

cs.CV↗
arXiv2026

MILAAP: Mobile Link Allocation via Attention-based Prediction

Channel hopping (CS) communication systems must adapt to interference changes in the wireless network and to node mobility for maintaining throughput efficiency. Optimal scheduling requires up-to-date network state information (i.e., of channel occupancy) to select non-overlapping channels for links in interference regions. However, state sharing among nodes introduces significant communication overhead, especially as network size or node mobility scale, thereby decreasing throughput efficiency of already capacity-limited networks. In this paper, we eschew state sharing while adapting the CS schedule based on a learning-based channel occupancy prediction. We propose the MiLAAP attention-based prediction framework for machine learning models of spectral, spatial, and temporal dependencies among network nodes. MiLAAP uses a self-attention mechanism that lets each node capture the temporospectral CS pattern in its interference region and accordingly predict the channel occupancy state within that region. Notably, the prediction relies only on locally and passively observed channel activities, and thus introduces no communication overhead. To deal with node mobility, MiLAAP also uses a multi-head self-attention mechanism that lets each node locally capture the spatiotemporal dependencies on other network nodes that can interfere with it and accordingly predict the motion trajectory of those nodes. Detecting nodes that enter or move outside the interference region is used to further improve the prediction accuracy of channel occupancy. We show that for dynamic networks that use local CS sequences to support relatively long-lived flow traffics, the channel state prediction accuracy of MiLAAP is remarkably ~100% across different node mobility patterns and it achieves zero-shot generalizability across different periods of CS sequences.

cs.NI↗
arXiv2026

On the Effectiveness of the z-Transform Method in Quadratic Optimization

The z-transform of a sequence is a classical tool used within signal processing, control theory, computer science, and electrical engineering. It allows for studying sequences from their generating functions, with many operations that can be equivalently defined on the original sequence and its $z$-transform. In particular, the z-transform method focuses on asymptotic behaviors and allows the use of Taylor expansions. We present a sequence of results of increasing significance and difficulty for linear models and optimization algorithms, demonstrating the effectiveness and versatility of the z-transform method in deriving new asymptotic results. Starting from the simplest gradient descent iterations in an infinite-dimensional Hilbert space, we show how the spectral dimension characterizes the convergence behavior. We then extend the analysis to Nesterov acceleration, averaging techniques, and stochastic gradient descent.

cs.LG↗
arXiv2026

Detecting and explaining clinical-omics inconsistencies to improve patient cohort stratification: an application to Parkinson's disease

Discrepancies between clinical diagnoses and omics profiles within a characterized cohort may reflect misdiagnosis, hidden subgroups or prodromal disease states. We propose MLASDO, a tool to detect and characterize such discrepancies before downstream analyses. MLASDO (1) detects outliers using two unsupervised methods, thereby flagging potential poor-quality samples; and (2) identifies and characterizes anomalous samples (ASs), i.e., individuals whose molecular profile resembles the opposite clinical class. We applied MLASDO to the Parkinson's Progression Markers Initiative (PPMI) and Parkinson's Disease Biomarkers Program (PDBP) Parkinson's disease (PD) cohorts. In PPMI, it detected 26 outliers and 12 ASs: 5 anomalous healthy controls (AHCs) and 7 anomalous PD cases (APDs). AHCs exhibited higher cerebrospinal fluid (CSF) A\b{eta}1-42 levels than controls (P < 0.0396), suggesting resistance to cognitive decline. AHC-specific genes were enriched for the MAPK pathway (P<0.0145), implicated in PD pathogenesis. One AHC later received a different neurological disorder, three months after enrollment. In PDBP, it identified 10 outliers and 8 ASs: 2 AHCs and 6 APDs. One AHC exhibited 24 clinical features consistent with a PD-like phenotype, including severe motor impairment. Results are compiled in an interactive report for inspection and querying, highlighting clinically meaningful individuals otherwise overlooked in conventional analyses.

cs.LG↗
arXiv2026

Dynamical stability for dense patterns in attractor neural networks

Recurrent neural networks are canonical models of biological memory. In these models, memories are represented by distributed patterns of neural activity that are stored in the recurrent connections between neurons, such that they become attractors of the network's dynamics. During memory recall, network dynamics thus converge toward one of these memory patterns when started from a noisy or partial cue. Therefore, memory performance critically hinges on the dynamical stability of the stored patterns. However, previous theoretical approaches only studied dynamical stability under highly restrictive conditions that do not readily apply to biological neural circuits. Here, we develop a theory of the local stability of discrete fixed points in a broad class of networks with graded neural activities and in the presence of noise. Using methods from random matrix theory, we analyze the bulk and outliers of the eigenvalue spectra of the Jacobians that characterize network dynamics around fixed points. We show that either all fixed points are stable or all of them are unstable, depending on whether their number is below a ``critical load for stability'', which is distinct from the classical critical capacity that measures the maximal number of achievable fixed points regardless of their stability. We further analyze the dependence of this critical load for stability on experimentally measurable quantities characterizing the statistics of memory patterns and the activation functions of neurons. Our analysis highlights the computational benefits of sparse-like patterns and threshold-linear activation functions and offers testable predictions for neural circuits supporting memory.

cond-mat.dis-nn↗