The Geometries of Truth Are Orthogonal Across Tasks

Large Language Models (LLMs) have demonstrated impressive generalization capabilities across various tasks, but their claim to practical relevance is still mired by concerns on their reliability. Recent works have proposed examining the activations produced by an LLM at inference time to assess whether its answer to a question is correct. Some works claim that a "geometry of truth" can be learned from examples, in the sense that the activations that generate correct answers can be distinguished from those leading to mistakes with a linear classifier. In this work, we underline a limitation of these approaches: we observe that these "geometries of truth" are intrinsically task-dependent and fail to transfer across tasks. More precisely, we show that linear classifiers trained across distinct tasks share little similarity and, when trained with sparsity-enforcing regularizers, have almost disjoint supports. We show that more sophisticated approaches (e.g., using mixtures of probes and tasks) fail to overcome this limitation, likely because activation vectors commonly used to classify answers form clearly separated clusters when examined across tasks.

On Fitting Flow Models with Large Sinkhorn Couplings

Flow models transform data gradually from one modality (e.g. noise) onto another (e.g. images). Such models are parameterized by a time-dependent velocity field, trained to fit segments connecting pairs of source and target points. When the pairing between source and target points is given, training flow models boils down to a supervised regression problem. When no such pairing exists, as is the case when generating data from noise, training flows is much harder. A popular approach lies in picking source and target points independently. This can, however, lead to velocity fields that are slow to train, but also costly to integrate at inference time. In theory, one would greatly benefit from training flow models by sampling pairs from an optimal transport (OT) measure coupling source and target, since this would lead to a highly efficient flow solving the Benamou and Brenier dynamical OT problem. In practice, recent works have proposed to sample mini-batches of $n$ source and $n$ target points and reorder them using an OT solver to form better pairs. These works have advocated using batches of size $n\approx 256$, and considered OT solvers that return couplings that are either sharp (using e.g. the Hungarian algorithm) or blurred (using e.g. entropic regularization, a.k.a. Sinkhorn). We follow in the footsteps of these works by exploring the benefits of increasing $n$ by three to four orders of magnitude, and look more carefully on the effect of the entropic regularization $\varepsilon$ used in the Sinkhorn algorithm. Our analysis is facilitated by new scale invariant quantities to report the sharpness of a coupling, while our sharded computations across multiple GPU or GPU nodes allow scaling up $n$. We show that in both synthetic and image generation tasks, flow models greatly benefit when fitted with large Sinkhorn couplings, with a low entropic regularization $\varepsilon$.

Sample and Map from a Single Convex Potential: Generation using Conjugate Moment Measures

A common approach to generative modeling is to split model-fitting into two blocks: define first how to sample noise (e.g. Gaussian) and choose next what to do with it (e.g. using a single map or flows). We explore in this work an alternative route that ties sampling and mapping. We find inspiration in moment measures, a result that states that for any measure $\rho$ supported on a compact convex set of $\mathbb{R}^d$, there exists a unique convex potential $u$ such that $\rho=\nabla u\,\sharp\,e^{-u}$. While this does seem to tie effectively sampling (from log-concave distribution $e^{-u}$) and action (pushing particles through $\nabla u$), we observe on simple examples (e.g., Gaussians or 1D distributions) that this choice is ill-suited for practical tasks. We study an alternative factorization, where $\rho$ is factorized as $\nabla w^*\,\sharp\,e^{-w}$, where $w^*$ is the convex conjugate of $w$. We call this approach conjugate moment measures, and show far more intuitive results on these examples. Because $\nabla w^*$ is the Monge map between the log-concave distribution $e^{-w}$ and $\rho$, we rely on optimal transport solvers to propose an algorithm to recover $w$ from samples of $\rho$, and parameterize $w$ as an input-convex neural network.

Scaling Laws for Forgetting during Finetuning with Pretraining Data Injection

A widespread strategy to obtain a language model that performs well on a target domain is to finetune a pretrained model to perform unsupervised next-token prediction on data from that target domain. Finetuning presents two challenges: (i) if the amount of target data is limited, as in most practical applications, the model will quickly overfit, and (ii) the model will drift away from the original model, forgetting the pretraining data and the generic knowledge that comes with it. We aim to derive scaling laws that quantify these two phenomena for various target domains, amounts of available target data, and model scales. We measure the efficiency of injecting pretraining data into the finetuning data mixture to avoid forgetting and mitigate overfitting. A key practical takeaway from our study is that injecting as little as 1% of pretraining data in the finetuning data mixture prevents the model from forgetting the pretraining set.

Multivariate Conformal Prediction using Optimal Transport

Conformal prediction (CP) quantifies the uncertainty of machine learning models by constructing sets of plausible outputs. These sets are constructed by leveraging a so-called conformity score, a quantity computed using the input point of interest, a prediction model, and past observations. CP sets are then obtained by evaluating the conformity score of all possible outputs, and selecting them according to the rank of their scores. Due to this ranking step, most CP approaches rely on a score functions that are univariate. The challenge in extending these scores to multivariate spaces lies in the fact that no canonical order for vectors exists. To address this, we leverage a natural extension of multivariate score ranking based on optimal transport (OT). Our method, OTCP, offers a principled framework for constructing conformal prediction sets in multidimensional settings, preserving distribution-free coverage guarantees with finite data samples. We demonstrate tangible gains in a benchmark dataset of multivariate regression problems and address computational \& statistical trade-offs that arise when estimating conformity scores through OT maps.

Leveraging Cardiovascular Simulations for In-Vivo Prediction of Cardiac Biomarkers

Whole-body hemodynamics simulators, which model blood flow and pressure waveforms as functions of physiological parameters, are now essential tools for studying cardiovascular systems. However, solving the corresponding inverse problem of mapping observations (e.g., arterial pressure waveforms at specific locations in the arterial network) back to plausible physiological parameters remains challenging. Leveraging recent advances in simulation-based inference, we cast this problem as statistical inference by training an amortized neural posterior estimator on a newly built large dataset of cardiac simulations that we publicly release. To better align simulated data with real-world measurements, we incorporate stochastic elements modeling exogenous effects. The proposed framework can further integrate in-vivo data sources to refine its predictive capabilities on real-world data. In silico, we demonstrate that the proposed framework enables finely quantifying uncertainty associated with individual measurements, allowing trustworthy prediction of four biomarkers of clinical interest--namely Heart Rate, Cardiac Output, Systemic Vascular Resistance, and Left Ventricular Ejection Time--from arterial pressure waveforms and photoplethysmograms. Furthermore, we validate the framework in vivo, where our method accurately captures temporal trends in CO and SVR monitoring on the VitalDB dataset. Finally, the predictive error made by the model monotonically increases with the predicted uncertainty, thereby directly supporting the automatic rejection of unusable measurements.

Controlling Language and Diffusion Models by Transporting Activations

The increasing capabilities of large generative models and their ever more widespread deployment have raised concerns about their reliability, safety, and potential misuse. To address these issues, recent works have proposed to control model generation by steering model activations in order to effectively induce or prevent the emergence of concepts or behaviors in the generated output. In this paper we introduce Activation Transport (AcT), a general framework to steer activations guided by optimal transport theory that generalizes many previous activation-steering works. AcT is modality-agnostic and provides fine-grained control over the model behavior with negligible computational overhead, while minimally impacting model abilities. We experimentally show the effectiveness and versatility of our approach by addressing key challenges in large language models (LLMs) and text-to-image diffusion models (T2Is). For LLMs, we show that AcT can effectively mitigate toxicity, induce arbitrary concepts, and increase their truthfulness. In T2Is, we show how AcT enables fine-grained style control and concept negation.

Sparse Repellency for Shielded Generation in Text-to-image Diffusion Models

The increased adoption of diffusion models in text-to-image generation has triggered concerns on their reliability. Such models are now closely scrutinized under the lens of various metrics, notably calibration, fairness, or compute efficiency. We focus in this work on two issues that arise when deploying these models: a lack of diversity when prompting images, and a tendency to recreate images from the training set. To solve both problems, we propose a method that coaxes the sampled trajectories of pretrained diffusion models to land on images that fall outside of a reference set. We achieve this by adding repellency terms to the diffusion SDE throughout the generation trajectory, which are triggered whenever the path is expected to land too closely to an image in the shielded reference set. Our method is sparse in the sense that these repellency terms are zero and inactive most of the time, and even more so towards the end of the generation trajectory. Our method, named SPELL for sparse repellency, can be used either with a static reference set that contains protected images, or dynamically, by updating the set at each timestep with the expected images concurrently generated within a batch. We show that adding SPELL to popular diffusion models improves their diversity while impacting their FID only marginally, and performs comparatively better than other recent training-free diversity methods. We also demonstrate how SPELL can ensure a shielded generation away from a very large set of protected images by considering all 1.2M images from ImageNet as the protected set.

Simple ReFlow: Improved Techniques for Fast Flow Models

Diffusion and flow-matching models achieve remarkable generative performance but at the cost of many sampling steps, this slows inference and limits applicability to time-critical tasks. The ReFlow procedure can accelerate sampling by straightening generation trajectories. However, ReFlow is an iterative procedure, typically requiring training on simulated data, and results in reduced sample quality. To mitigate sample deterioration, we examine the design space of ReFlow and highlight potential pitfalls in prior heuristic practices. We then propose seven improvements for training dynamics, learning and inference, which are verified with thorough ablation studies on CIFAR10 $32 \times 32$, AFHQv2 $64 \times 64$, and FFHQ $64 \times 64$. Combining all our techniques, we achieve state-of-the-art FID scores (without / with guidance, resp.) for fast generation via neural ODEs: $2.23$ / $1.98$ on CIFAR10, $2.30$ / $1.91$ on AFHQv2, $2.84$ / $2.67$ on FFHQ, and $3.49$ / $1.74$ on ImageNet-64, all with merely $9$ neural function evaluations.

Disentangled Representation Learning through Geometry Preservation with the Gromov-Monge Gap

Learning disentangled representations in an unsupervised manner is a fundamental challenge in machine learning. Solving it may unlock other problems, such as generalization, interpretability, or fairness. While remarkably difficult to solve in general, recent works have shown that disentanglement is provably achievable under additional assumptions that can leverage geometrical constraints, such as local isometry. To use these insights, we propose a novel perspective on disentangled representation learning built on quadratic optimal transport. Specifically, we formulate the problem in the Gromov-Monge setting, which seeks isometric mappings between distributions supported on different spaces. We propose the Gromov-Monge-Gap (GMG), a regularizer that quantifies the geometry-preservation of an arbitrary push-forward map between two distributions supported on different spaces. We demonstrate the effectiveness of GMG regularization for disentanglement on four standard benchmarks. Moreover, we show that geometry preservation can even encourage unsupervised disentanglement without the standard reconstruction objective - making the underlying model decoder-free, and promising a more practically viable and scalable perspective on unsupervised disentanglement.