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Francesco Locatello

Publications and source records attributed to Francesco Locatello.

At least 19 recordsLinked to original sources
arXiv2026

Thinking at the Right Size: Amortized Distillation Across Post-Trained LLMs

Practical deployment of large language models (LLMs) requires families of post-trained variants---instruction-tuned, reasoning-tuned, and chat-style models---each at multiple sizes to meet diverse latency and memory budgets. Producing each (variant, size) pair independently is prohibitive, so model families typically span only a handful of coarse-grained sizes per post-trained variant. Boomerang distillation (Kangaslahti et al., 2026) reduces this cost along the size axis for base models. Through model size interpolation, it constructs models of intermediate sizes from a single teacher-student pair without additional training. However, it still treats each post-trained variant as a separate object of optimization. We introduce ADAPT---Amortized Distillation Across Post-Trained LLMs---a framework for amortizing distillation across both axes of a model family: size and post-training variant, producing $L \times K$ models for $L$ interpolated sizes across $K$ post-trained variants with a single distillation run. ADAPT combines two components. First, a two-phase distillation procedure constructs post-trained students through pre-training alignment and supervised fine-tuning distillation, enabling smooth size--performance interpolation on generation and reasoning tasks. Second, weight-delta initialization approximates this construction across post-trained variants by transferring the distillation-induced weight change from the base model to students initialized from different post-trained variants. The resulting continuum of interpolated models also enables adaptive model-size selection at inference time, improving the compute--accuracy trade-off for long-form reasoning tasks.

cs.LG↗
arXiv2026

Understanding Layer Patching in Model Size Interpolation

Zero-shot model size interpolation aims to create new models of intermediate target sizes by combining existing models without additional training. Recent work on boomerang distillation [Kangaslahti et al., 2026] shows that a student language model distilled from a larger teacher can be expanded by iteratively patching its layers, replacing student layers with contiguous blocks of teacher layers to obtain models whose size and performance interpolate between the student and the teacher. In this work, we provide the first systematic study of student-layer selection for model size interpolation. We cast finding the optimal layer subset for each model size as an optimization problem and prove it can be viewed as a shortest-path problem in a certain acyclic graph. In experiments, we show that patching strongly shapes interpolation behavior, with effects that vary substantially across model families. We find that simple sequential strategies--patching either from the first layer to the last or from the last to the first--often achieve surprisingly strong performance in practice. We further introduce KLPatch, a greedy patching algorithm based on KL divergence, which often improves over last-to-first patching and approximately solves the optimization problem. Together, our results provide a principled understanding of how layer patching affects model size interpolation and offer practical guidance for constructing near-optimal interpolated models.

cs.LG↗
arXiv2026

From Tokens to Policy: Causal and Interpretable Heterogeneous Treatment Effects Identification

Heterogeneous Treatment Effect (HTE) identification is crucial to explain the impact of an intervention and optimize our policies accordingly. Existing approaches trade expressivity for interpretability, but, if some active heterogeneity drivers are unmeasured, methods at both ends of this spectrum allow for spurious HTE characterization with no causal reading. In this work, we focus on controlled experiments and argue that an oracle HTE causal characterization via the latent interactors is now within reach, thanks to (i) more extensive pre-treatment measurements, i.e., multi-modal and multi-view, and (ii) scalable representations with minimal human supervision. We then re-frame HTE identification as a Markov-blanket discovery problem on a sufficient and aligned pre-treatment representation, and introduce Neural EXposure Interaction Search (NEXIS), an iterative procedure with provable and empirically validated consistent selection. We deploy NEXIS on two anti-poverty programs in Africa, augmenting each with satellite imagery capturing previously unmeasured environmental effect modifiers, leading to novel, interpretable and prescriptive guidelines to optimize the programs' next iterations.

cs.LG↗
arXiv2026

Assessing Sample Quality in Conditional Generation under Compositional Shift

Conditional generators provide a natural tool for controllable generation, including settings where the desired condition is a new composition of observed attributes or experimental factors. In many applications, especially in scientific domains, such models are attractive to explore conditions for which real samples are rare, expensive, or not yet observed. However, this creates a circularity for evaluation: standard conditional quality metrics require a reference target distribution, but in the extrapolative regime that distribution is unavailable by definition. We address this problem with a post-hoc, per-sample trust score for assessing conditional samples using only the training distribution. The score combines two estimable quantities: global realism, measuring compatibility with the real data manifold, and attribute-wise faithfulness, measuring whether a sample is closer to the requested attributes than to plausible alternatives. We show that the score can recover meaningful comparisons across extrapolated generations, under a mild coverage condition on the observed attributes. These comparisons enable effective filtering, ranking, and abstention of generations and can be used directly on off-the-shelf pretrained models. In biological imaging, selected samples preserve real morphological structure better and improve downstream predictive performance, while similar gains are observed on controlled vision benchmarks. Finally, we show how the score can be applied during generation, enabling abstention before full decoding. Code is available at https://github.com/berkerdemirel/faithful-cond-gen.

cs.LG↗
arXiv2026

Reconciling Causality and Non-Equilibrium Thermodynamics with Hamiltonian Causal Models

Causal modeling of physical temporal phenomena must handle interventions that act along trajectories, nonstationary induced laws, path-dependent effects, and feedback mediated by dynamics, all challenging in standard causal models. We introduce Hamiltonian Causal Models (HCMs), a trajectory-level framework in which observed variables interact with local environments and interventions act as controls of Hamiltonian mechanisms. HCMs separate immutable equations of motion from intervenable mechanisms and define causal effects as discrepancies between interventional path laws. A key motivation for HCMs is their natural interface with non-equilibrium thermodynamics. Entropy production quantifies the irreversibility of a process and is a central causal observable: it is estimable from data and witnesses causal effects along the system's evolution that are invisible to endpoint and cumulative versions of the standard average treatment effect. As in physics, cause and effect are not primitives of the relation between two random variables but arise from the non-invertibility of the thermodynamic arrow. With this, our paper reconciles the language of statistical causal models and non-stationary thermodynamics, offering new tools to describe causality in a wide range of physical systems.

cs.LG↗
arXiv2026

Toward Identifiable Sparse Autoencoders

Recently, sparse autoencoders (SAEs) have emerged as an attractive tool for interpreting and interacting with representations in practical neural networks. While it is common empirical folklore, we also show theoretically that SAEs are highly unstable: different training runs are likely to produce different concept dictionaries and sparse codes. We characterize the model properties that hinder the stability of real-world SAEs, and address each of these problems through minimal changes to the architecture and training procedure. Together, these changes yield two versions of an \textbf{i}dentifiable SAE (iSAE), a variant of the standard TopK SAE with lower reconstruction error and improved stability. We explain this improvement theoretically by connecting SAEs with traditional dictionary learning approaches, and show that the dictionaries learned in practice satisfy an approximate restricted isometry condition, rendering the corresponding sparse codes in those models near-identifiable.

cs.LG↗
arXiv2026

The Perception-Physics Paradox: Probing Scientific Alignment with TC-Bench

While Vision Foundation Models (VFMs) excel at predictive tasks on satellite imagery, their performance can arise from visual correlations rather than underlying structural invariants, making even perception-based out-of-distribution accuracy a poor proxy for scientific utility. As a result, models may look correct without reasoning correctly, a discrepancy we term the Perception-Physics Paradox. To address this gap, we introduce scientific alignment as an implicit objective for representation learning in scientific domains. We study a principled, testable aspect of scientific alignment through structural isomorphism, which requires latent representations to uniquely identify physical systems up to a linear reparameterization. This perspective induces a hierarchy of necessary conditions and yields a systematic probing protocol for physical and causal interpretability. To operationalize this framework, we release TC-Bench, a global, reproducible benchmark dataset with an automated construction pipeline for tropical cyclone research, and show that current VFMs rely on visual shortcuts that collapse in intense regimes, indicating that scientific alignment does not arise as a natural byproduct of scaling alone.

cs.LG↗
arXiv2026

The Rate-Distortion-Polysemanticity Tradeoff in SAEs

Sparse Autoencoders (SAEs) that can accurately reconstruct their input (minimizing distortion) by making efficient use of few features (minimizing the rate) often fail to learn monosemantic representations (highly interpretable), limiting their usefulness for mechanistic interpretability. In this paper, we characterise this tension in learning faithful, efficient, and interpretable explanations, introducing the Rate-Distortion-Polysemanticity tradeoff in SAEs. Under toy-modeling assumptions, we theoretically and empirically show that restricting the SAE to be monosemantic necessarily comes with an increase in rate and distortion. Assuming a generative model behind the input observations, we further demonstrate that the degree of polysemanticity of optimal SAEs is determined by the training data distribution, especially by the probability of features to co-occur. Finally, we extend the analysis to real-world settings by deriving necessary conditions that a polysemanticity measure should satisfy when the data-generating process is unknown, and we benchmark existing proxy metrics on SAEs trained on Large Language Models. Taken together, our findings show that polysemanticity is a data problem that should be accounted for when addressing it at the architectural and optimization level.

cs.LG↗
arXiv2026

Towards a holistic understanding of Selection Bias for Causal Effect Identification

Selection bias is pervasive in observational studies. For example, large scale biobanks data can exhibit ``healthy volunteer bias'' when respondents are healthier and of higher socio-economic status than the population they are meant to represent. Recovering causal effects from such sub-population is an important problem in causal inference, as estimating average treatment effects (ATE) from selected populations can result in a severely biased estimate of the ATE from the whole population. In this paper, we investigate the identifiability of the ATE under selection bias. We provide necessary and sufficient conditions for ATE identifiability, leveraging weak assumptions on probability classes to characterize propensity score and selection probability. Compared to previous works, our results extend existing graphical identifiability criteria and offer a more comprehensive understanding of causal effect identification with strictly weaker conditions in the presence of selection bias.

stat.ME↗
arXiv2026

Causal Learning with the Invariance Principle

Causal discovery, the problem of inferring the direction of causality, is generally ill-posed. We use the language of structural causal models (SCM) to show that assuming that the causal relations are acyclic and invariant across multiple environments (e.g., the way minimum wage affects employment rate is stable across different geographical regions), \textit{only} two auxiliary environments are sufficient to infer the causal graph for arbitrary nonlinear mechanisms. Moreover, we demonstrate that this implies identifiability of the SCM functional mechanisms: as a corollary, we show that \textit{two} auxiliary environments are sufficient to guarantee correct counterfactual inference. We empirically support our theoretical results on synthetic data.

stat.ML↗
arXiv2026

Controlling Transient Amplification Improves Long-horizon Rollouts

Autoregressive neural simulators now match classical solvers on short-horizon prediction of physical systems, yet their accuracy degrades rapidly when rolled out over long horizons. In this work, we identify transient amplification of perturbations around rollout trajectories as a structural mechanism driving rollout error. Using a linearization analysis we show that when the Jacobians along an autoregressive trajectory are non-normal and non-commuting, the model amplifies errors transiently, resulting in model rollout drift even when the overall system is asymptotically stable. Building on the analysis, we propose commutativity regularization: a combination of two penalties designed to reduce the normality defect of individual Jacobians and the commutator norm of Jacobians across steps. The penalties are estimated with Jacobian-vector products and have no inference-time cost. We show a propagator bound that quantifies rollout error under approximate commutativity and normality. We evaluate UNet and FNO variants with commutativity regularization on 1D and 2D spatio-temporal data in synthetic and real settings, showing successful long-horizon rollouts over thousands of steps. Further, we show that the method improves FourCastNet climate forecasts on ERA5 without using any new data. The gain is most pronounced out-of-distribution: trained on trajectories of a few hundred steps, regularized models remain in-distribution for thousands of rollout steps on initial conditions where baselines diverge.

cs.LG↗
arXiv2026

Learning Discrete Diffusion of Graphs via Free-Energy Gradient Flows

Diffusion-based models on continuous spaces have seen substantial recent progress through the mathematical framework of gradient flows, leveraging the Wasserstein-2 (${W}_2$) metric via the Jordan-Kinderlehrer-Otto (JKO) scheme. Despite the increasing popularity of diffusion models on discrete spaces using continuous-time Markov chains, a parallel theoretical framework based on gradient flows has remained elusive due to intrinsic challenges in translating the ${W}_2$ distance directly into these settings. In this work, we propose the first computational approach addressing these challenges, leveraging an appropriate metric $W_K$ on the simplex of probability distributions, which enables us to interpret widely used discrete diffusion paths, such as the discrete heat equation, as gradient flows of specific free-energy functionals. Through this theoretical insight, we introduce a novel methodology for learning diffusion dynamics over discrete spaces, which recovers the underlying functional directly by leveraging first-order optimality conditions for the JKO scheme. The resulting method optimizes a simple quadratic loss, trains extremely fast, does not require individual sample trajectories, and only needs a numerical preprocessing computing $W_K$-geodesics. We validate our method through extensive numerical experiments on synthetic data, showing that we can recover the underlying functional for a variety of graph classes.

cs.LG↗
arXiv2026

Statistical and structural identifiability in representation learning

Representation learning models exhibit a surprising stability in their internal representations. Whereas most prior work treats this stability as a single property, we formalize it as two distinct concepts: statistical identifiability (consistency of representations across runs) and structural identifiability (alignment of representations with some unobserved ground truth). Recognizing that perfect pointwise identifiability is generally unrealistic for modern representation learning models, we propose new model-agnostic definitions of statistical and structural near-identifiability of representations up to some error tolerance $\epsilon$. Leveraging these definitions, we prove a statistical $\epsilon$-near-identifiability result for the representations of models with nonlinear decoders, generalizing existing identifiability theory beyond last-layer representations in e.g. generative pre-trained transformers (GPTs) to near-identifiability of the intermediate representations of a broad class of models including (masked) autoencoders (MAEs) and supervised learners. Although these weaker assumptions confer weaker identifiability, we show that independent components analysis (ICA) can resolve much of the remaining linear ambiguity for this class of models, and validate and measure our near-identifiability claims empirically. With additional assumptions on the data-generating process, statistical identifiability extends to structural identifiability, yielding a simple and practical recipe for disentanglement: ICA post-processing of latent representations. On synthetic benchmarks, this approach achieves state-of-the-art disentanglement using a vanilla autoencoder. With a foundation model-scale MAE for cell microscopy, it disentangles biological variation from technical batch effects, substantially improving downstream generalization.

cs.LG↗
arXiv2026

Addressing Instrument-Outcome Confounding in Mendelian Randomization through Representation Learning

Mendelian Randomization (MR) is a prominent observational epidemiological research method designed to address unobserved confounding when estimating causal effects. However, core assumptions -- particularly the independence between instruments and unobserved confounders -- are often violated due to population stratification or assortative mating. Leveraging the increasing availability of multi-environment data, we propose a representation learning framework that exploits cross-environment invariance to recover latent exogenous components of genetic instruments. We provide theoretical guarantees for identifying these latent instruments under various mixing mechanisms and demonstrate the effectiveness of our approach through simulations and semi-synthetic experiments using data from the All of Us Research Hub.

cs.LG↗
arXiv2026

A Theory of How Pretraining Shapes Inductive Bias in Fine-Tuning

Pretraining and fine-tuning are central stages in modern machine learning systems. In practice, feature learning plays an important role across both stages: deep neural networks learn a broad range of useful features during pretraining and further refine those features during fine-tuning. However, an end-to-end theoretical understanding of how choices of initialization impact the ability to reuse and refine features during fine-tuning has remained elusive. Here we develop an analytical theory of the pretraining fine-tuning pipeline in diagonal linear networks, deriving exact expressions for the generalization error as a function of initialization parameters and task statistics. We find that different initialization choices place the network into four distinct fine-tuning regimes that are distinguished by their ability to support feature learning and reuse and therefore by the task statistics for which they are beneficial. In particular, a smaller initialization scale in earlier layers enables the network to both reuse and refine its features, leading to superior generalization on fine-tuning tasks that rely on a subset of pretraining features. We demonstrate empirically that the same initialization parameters impact generalization in ResNets trained on CIFAR-100 and SVHN as well as Transformers trained on modular arithmetic tasks. Overall, our results demonstrate an alytically how data and network initialization interact to shape fine-tuning generalization, highlighting an important role for the relative scale of initialization across different layers in enabling continued feature learning during fine-tuning.

cs.LG↗
arXiv2025

Head Pursuit: Probing Attention Specialization in Multimodal Transformers

Language and vision-language models have shown impressive performance across a wide range of tasks, but their internal mechanisms remain only partly understood. In this work, we study how individual attention heads in text-generative models specialize in specific semantic or visual attributes. Building on an established interpretability method, we reinterpret the practice of probing intermediate activations with the final decoding layer through the lens of signal processing. This lets us analyze multiple samples in a principled way and rank attention heads based on their relevance to target concepts. Our results show consistent patterns of specialization at the head level across both unimodal and multimodal transformers. Remarkably, we find that editing as few as 1% of the heads, selected using our method, can reliably suppress or enhance targeted concepts in the model output. We validate our approach on language tasks such as question answering and toxicity mitigation, as well as vision-language tasks including image classification and captioning. Our findings highlight an interpretable and controllable structure within attention layers, offering simple tools for understanding and editing large-scale generative models.

cs.CV↗
arXiv2025

Exploratory Causal Inference in SAEnce

Randomized Controlled Trials are one of the pillars of science; nevertheless, they rely on hand-crafted hypotheses and expensive analysis. Such constraints prevent causal effect estimation at scale, potentially anchoring on popular yet incomplete hypotheses. We propose to discover the unknown effects of a treatment directly from data. For this, we turn unstructured data from a trial into meaningful representations via pretrained foundation models and interpret them via a sparse autoencoder. However, discovering significant causal effects at the neural level is not trivial due to multiple-testing issues and effects entanglement. To address these challenges, we introduce Neural Effect Search, a novel recursive procedure solving both issues by progressive stratification. After assessing the robustness of our algorithm on semi-synthetic experiments, we showcase, in the context of experimental ecology, the first successful unsupervised causal effect identification on a real-world scientific trial.

cs.LG↗
arXiv2025

High-dimensional Analysis of Synthetic Data Selection

Despite the progress in the development of generative models, their usefulness in creating synthetic data that improve prediction performance of classifiers has been put into question. Besides heuristic principles such as "synthetic data should be close to the real data distribution", it is actually not clear which specific properties affect the generalization error. Our paper addresses this question through the lens of high-dimensional regression. Theoretically, we show that, for linear models, the covariance shift between the target distribution and the distribution of the synthetic data affects the generalization error but, surprisingly, the mean shift does not. Furthermore we prove that, in some settings, matching the covariance of the target distribution is optimal. Remarkably, the theoretical insights from linear models carry over to deep neural networks and generative models. We empirically demonstrate that the covariance matching procedure (matching the covariance of the synthetic data with that of the data coming from the target distribution) performs well against several recent approaches for synthetic data selection, across training paradigms, architectures, datasets and generative models used for augmentation.

stat.ML↗