Inspired by the function-space theory of neural networks, we formulate and analyze a variation space for nonlinear operators between Hilbert spaces, defined through vector-valued Borel measures of bounded variation. We characterize its unit ball as the closed convex hull of a vector-valued single-neuron dictionary in Bochner spaces. For the ReLU activation, the bounded linear operators in this space are precisely the Schatten-$1$ operators, with equivalent norms. For operators in this space, we establish encoder--decoder approximation bounds in the Bochner $L^q$-norm, where the error decomposes into input and output encoding errors and a finite-width term of order $N^{-1/2}$. Under sub-Gaussian assumptions on the input and noise, we further derive high-probability generalization bounds for empirical least squares over path-norm-constrained encoder--decoder networks; the finite-sample contribution to the squared prediction error is of order $K^{-1/2}$ up to logarithmic factors. The finite-width and finite-sample constants are independent of the encoding dimensions and bases, with the latter also independent of the network width. When the encoding errors decay algebraically, these bounds yield algebraic approximation and learning rates, in contrast to the complexity barriers for Lipschitz and Fr\'echet differentiable operator classes.
Partially manipulated (half-truth) speech, where a short synthesised segment is spliced into an otherwise genuine utterance, is a harder and more realistic forensic threat than the fully synthesised deepfakes that dominate the literature. We present CAFNet, a lightweight (576K-parameter, 2.24 MB) cross-attentive architecture that fuses MFCC, LFCC, and Chroma-STFT features to jointly classify audio as real, fully fake, or half-truth, and regress the temporal boundaries of the synthesised region, at approximately 14 ms CPU latency. A component ablation shows cross-attention fusion is CAFNet's most load-bearing component; a deeply supervised auxiliary classification head from earlier iterations is not, and removing it improves every in-domain metric under 3-seed replication with substantially lower variance. On MLADDC T2+T3 the model reaches 97.55%$\pm$0.69% ternary accuracy and 0.037 s boundary mean absolute error (MAE), to our knowledge, the first reported continuous splice- boundary localisation result on this benchmark. Zero-shot evaluation on two independent benchmarks shows transfer is capability- and corpus-dependent rather than uniform: on Half-Truth Audio Detection dataset (HAD), detection recall reaches 84.9% and ternary classification resolves half-truth correctly on half of true half-truth clips (50.4%), while on PartialSpoof, binary detection stays near chance (AUC 0.5544). We treat this asymmetry, not a single generalization verdict, as the finding. HAD localisation improves in absolute terms but degrades in relative terms, since in-domain localisation improved faster. An architectural change validated purely in-domain thus shifted the cross-corpus transfer profile, evidence that cross-corpus evaluation should accompany, not follow, in-domain architecture decisions.
The F\"ollmer process is a Brownian motion conditioned to have a pre-specified distribution at time 1. This process can be interpreted as an ``augmented'' time-compressed version of the reverse stochastic differential equation (SDE) corresponding to the denoising diffusion probabilistic model (DDPM). While this fact has been indirectly used to analyze DDPM sampling errors via discretization of the reverse SDE, the connection between direct discretization of the F\"ollmer process and the DDPM sampler has not yet been fully explored. This paper clarifies this point while surveying relevant results from the literature. We show that discretized F\"ollmer processes give natural hyper-parameter settings of the DDPM sampler while accommodating a broader class of variance schedules than discretized reverse SDEs. Moreover, this allows us to systematically recover state-of-the-art results on DDPM sampling error bounds, along with slight improvements.
We study high-dimensional LASSO under differential privacy via objective perturbation with heterogeneous covariate scales. In practical scenarios, covariates often exhibit diverse scales; however, standard preprocessing is problematic under privacy constraints, as it consumes additional privacy budget. This heterogeneity induces effective anisotropy in the objective perturbation via the inverse Gram matrix of covariates, which can degrade the stability and accuracy of algorithms. To address this, we propose a Gram-based anisotropic objective perturbation, a ``pre-distortion" strategy that counteracts the distortion from the covariate structure to restore isotropy in the estimation process. Using an Approximate Message Passing (AMP) framework and state evolution analysis, we demonstrate that our proposed perturbation significantly stabilizes convergence and improves both statistical efficiency and privacy performance compared to standard uniform noise injection. Our results provide theoretical insights into designing stable and efficient private estimators without relying on data-dependent preprocessing.
Haruka Tanzawa, Ayaka Sakata· 0 citations
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Computed Tomography (CT) is a widely used imaging modality in medical and industrial applications. To limit radiation exposure and measurement time, there is a growing interest in sparse-view CT, where the number of projection views is significantly reduced. Deep neural networks have shown great promise in improving reconstruction quality in sparse-view CT, especially generative diffusion models. However, these methods struggle to scale to large 3D volumes due to several reasons: (i) the high memory and computational requirements of 3D models, (ii) the lack of large 3D training datasets, and (iii) the inconsistencies across slices when using 2D models independently on each slice. We overcome these limitations and scale diffusion-based sparse-view CT reconstruction to large 3D volumes by combining conditional diffusion with explicit data consistency. We propose Conditional Diffusion Posterior Alignment (CDPA) to enable scalable 3D sparse-view CT reconstruction. A 2D U-Net diffusion model is conditioned on an initial 3D reconstruction to improve inter-slice consistency, combined with data-consistency alignment to match measured projections. Experiments on synthetic and real Cone Beam CT (CBCT) data show state-of-the-art performance, with ablations that confirm the synergistic effects of the proposed pipeline. Finally, we show that the same principles also strengthen fast denoising U-Nets, yielding near-diffusion quality at a fraction of the computational cost.
Luis Barba, Johannes Kirschner, Benjamin Bejar· 0 citations
Large language models (LLMs) are increasingly deployed in applications with societal impact, raising concerns about the cultural biases they encode. We probe these representations by evaluating whether LLMs can perform author profiling from song lyrics in a zero-shot setting, inferring singers' gender and ethnicity without task-specific fine-tuning. Across several open-source models evaluated on more than 10,000 lyrics, we find that LLMs achieve non-trivial profiling performance but demonstrate systematic cultural alignment: most models default toward North American ethnicity, while DeepSeek-1.5B aligns more strongly with Asian ethnicity. This finding emerges from both the models' prediction distributions and an analysis of their generated rationales. To quantify these disparities, we introduce two fairness metrics, Modality Accuracy Divergence (MAD) and Recall Divergence (RD), and show that Ministral-8B displays the strongest ethnicity bias among the evaluated models, whereas Gemma-12B shows the most balanced behavior. Our code is available on [GitHub](https://github.com/ValentinLafargue/CulturalProbingLLM) and results on [HuggingFace](https://huggingface.co/datasets/ValentinLAFARGUE/AuthorProfilingResults).
Valentin Lafargue, Ariel Guerra-Adames, Emmanuelle Claeys et al.· 0 citations
Unlearning knowledge is a pressing and challenging task in Large Language Models (LLMs) because of their unprecedented capability to memorize and digest training data at scale, raising more significant issues regarding safety, privacy, and intellectual property. However, existing works, including parameter editing, fine-tuning, and distillation-based methods, are all focused on flat sentence-level data but overlook the relational, multi-hop, and reasoned knowledge in naturally structured data. In response to this gap, this paper introduces Graph Oblivion and Node Erasure (GONE), a benchmark for evaluating knowledge unlearning over structured knowledge graph (KG) facts in LLMs.This KG-based benchmark enables the disentanglement of three effects of unlearning: direct fact removal, reasoning-based leakage, and catastrophic forgetting. In addition, Neighborhood-Expanded Distribution Shaping (NEDS), a novel unlearning framework, is designed to leverage graph connectivity and identify anchor-correlated neighbors, thereby enforcing a precise semantic separation between the forgotten fact and its semantic neighborhood. Evaluations on LLaMA-3-8B and Mistral-7B across multiple knowledge editing and unlearning methods showcase NEDS's superior performance (1.000 on unlearning efficacy and 0.839 on locality) on GONE and other benchmarks. The dataset is available at https://huggingface.co/datasets/GONE-Anonymous/GONE.
Continual VideoQA with multimodal LLMs remains challenging because sequential adaptation induces task interference, while storing task-specific prompts becomes impractical as task sequences grow. We introduce DynaTokens, a transformer-based token generator that dynamically produces fine-tuning tokens on demand, enabling task-adaptive prompt updates through shared generation weights. To mitigate forgetting, we introduce meta-learning-inspired regularisers that look ahead to avoid task-specific sharp update directions while anchoring the evolving generator to prior-task behaviours. We theoretically connect this objective to sharpness-aware optimisation, showing how it favours flatter cross-task minima and improves retention. DynaTokens combines gradient-free routing based on robust pretrained token and visual embeddings with lightweight auxiliary multimodal supervision, reducing router drift during continual adaptation. Across standard continual VideoQA benchmarks, DynaTokens achieves higher average accuracy and substantially lower forgetting than strong baselines. It also improves zero-shot generalisation and remains effective in longer domain-incremental sequences with extended task shifts. Finally, we introduce a challenging ImageQA->VideoQA protocol and show that DynaTokens enables robust cross-modal continual transfer.
Toan Nguyen, Yang Liu, Celso De Melo et al.· 0 citations
Maximum likelihood prediction (MLP) is a core task at the heart of modern large language models. Here, we study a quantum version of this task for a simplified data model consisting of independent and identically distributed samples, as a first step. The quantum maximum likelihood predictor (QMLP) is obtained by embedding of empirical probability distributions into quantum states and performing a minimization of quantum relative entropy over a given class of states. We derive non-asymptotic performance guarantees for QMLP in terms of convergence rates and concentration inequalities, both in trace norm and quantum relative entropy. Our approach provides a unified framework to handle MLP within both classical and quantum LLMs. We also consider the related problem of quantum information projection and generalize the quantum Pythagorean theorem to mixture families specified by possibly non-self-adjoint linear constraints. We further show that the Pythagorean inequality continues to hold in the infinite-dimensional setting whenever the convex information-projection problem attains a finite minimum.
Adapting general-purpose LLMs into domain-specialized dense retrievers typically requires large-scale training on mixed-domain data. We show that merging independently trained domain-specialized experts consistently exceeds this approach across four decoder-only LLM families (0.6B-7B), four merging methods, and twelve medical and general retrieval tasks from MTEB, suggesting that parameter-space composition captures complementary domain strengths that large-scale mixed-domain training averages out. To further maximize expert quality, we introduce Synthesize-Train-Merge (STM), a modular framework that synthesizes hard negatives with a top-tier LLM and fine-tunes domain-specialized experts via LoRA before merging them, without continual pre-training. Synthesized hard negatives yield the largest gains for smaller models, and STM achieves strong performance on biomedical retrieval tasks while maintaining competitive general-domain results across all four backbone families.
Sameh Khattab, Jean-Philippe Corbeil, Osman Alperen \c{C}inar-Kora\c{s} et al.· 0 citations
The Gilbert-Pollak Conjecture \citep{gilbert1968steiner}, also known as the Steiner Ratio Conjecture, states that for any finite point set in the Euclidean plane, the Steiner minimum tree has length at least $\sqrt{3}/2 \approx 0.866$ times that of the Euclidean minimum spanning tree (the Steiner ratio). A sequence of improvements through the 1980s culminated in a lower bound of $0.824$, with no substantial progress reported over the past three decades. Recent advances in LLMs have demonstrated strong performance on contest-level mathematical problems, yet their potential for addressing open, research-level questions remains largely unexplored. In this work, we present a novel AI system for obtaining tighter lower bounds on the Steiner ratio. Rather than directly prompting LLMs to solve the conjecture, we task them with generating rule-constrained geometric lemmas implemented as executable code. These lemmas are then used to construct a collection of specialized functions, which we call verification functions, that yield theoretically certified lower bounds of the Steiner ratio. Through progressive lemma refinement driven by reflection, the system establishes a new certified lower bound of 0.8559 for the Steiner ratio. The entire research effort involves only thousands of LLM calls, demonstrating the strong potential of LLM-based systems for advanced mathematical research.
Yisi Ke, Tianyu Huang, Yankai Shu et al.· 0 citations
Machine Learning (ML) has deeply changed some fields recently, like Language and Vision and we may expect it to be relevant also to the analysis of of complex systems. Here we want to tackle the question of how and to which extent can one regress scale-free processes, i.e. processes displaying power law behavior, like earthquakes or avalanches? We are interested in predicting the large ones, i.e. rare events in the training set which therefore require extrapolation capabilities of the model. For this we consider two paradigmatic problems that are statistically self-similar. The first one is a 2-dimensional fractional Gaussian field obeying linear dynamics, self-similar by construction and amenable to exact analysis. The second one is the Abelian sandpile model, exhibiting self-organized criticality. The emerging paradigm of Geometric Deep Learning shows that including known symmetries into the model's architecture is key to success. Here one may hope to extrapolate only by leveraging scale invariance. This is however a peculiar symmetry, as it involves possibly non-trivial coarse-graining operations and anomalous scaling. We perform experiments on various existing architectures like U-net, Riesz network (scale invariant by construction), or our own proposals: a wavelet-decomposition based Graph Neural Network (with discrete scale symmetry), a Fourier embedding layer and a Fourier-Mellin Neural Operator. Based on these experiments and a complete characterization of the linear case, we identify the main issues relative to spectral biases and coarse-grained representations, and discuss how to alleviate them with the relevant inductive biases.
Anaclara Alvez-Canepa, Cyril Furtlehner, Fran\c{c}ois P. Landes· 0 citations
A weeklong summer workshop brought higher education faculty to campus to explore how AI and machine learning materials can be adapted for their classrooms.
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
MIT News · Artificial Intelligence· news.mit.eduAug 24, 2026
