arXiv subjects

Marco Cuturi

Publications and source records attributed to Marco Cuturi.

At least 19 recordsLinked to original sources

arXiv2026

DynaMiCS: Fine-tuning LLMs with Performance Constraints using Dynamic Mixtures

Multi-domain fine-tuning of large language models requires improving performance on target domains while preserving performance on constrained domains, such as general knowledge, instruction following, or safety evaluations. Existing data mixing strategies rely on fixed heuristics or adaptive rules that cannot explicitly enforce preservation of such capabilities. We propose DynaMiCS, a dynamic mixture optimizer that casts multi-domain fine-tuning as a constrained optimization problem. At each update, DynaMiCS performs short domain-specific probing runs to estimate a slope matrix of local cross-domain effects, capturing how training on each fine-tuning dataset affects each evaluation domain. These estimates are then used to compute mixture weights through optimization over the probability simplex, with the objective of improving target-domain performance while keeping constrained-domain losses below reference levels. Across multi-domain fine-tuning scenarios with varying numbers of target and constrained domains, DynaMiCS achieves stronger target-domain improvements and higher constraint satisfaction than fixed-mixture baselines, at lower computational cost and without reference models, per-example scoring, or manually tuned mixture weights.

cs.LG↗

arXiv2026

Locking Pretrained Weights via Deep Low-Rank Residual Distillation

The quality of open-weight language models has dramatically improved in recent years. Sharing weights greatly facilitates model adoption by enabling their use across diverse hardware and software platforms. They also allow for more open research and testing, to the extent that users can use them as checkpoints, fine-tune them according to their needs, and potentially redistribute them. In some cases, however, concerns on modifying these weights towards unauthorized uses may outweigh the pros of giving users such a freedom. Defending against such adaptation is non-trivial: since an adaptive attacker can observe all weights and architectures by definition, they can reverse simple structural defenses, and use optimization to defeat the simplest locking mechanisms. In this work, we exploit the inference-training asymmetry of automatic differentiation as a novel defense axis. We propose DLR-Lock, a method where the purveyor of the model purposely replaces each pretrained MLP in their model with a deep low-rank residual network (DLR-Net) of comparable parameter count, forcing activation memory that grows linearly with depth during backpropagation. DLR-Nets are efficiently trained via module-wise distillation. We show that, beyond this memory overhead, DLR-Lock results in architectural mismatches that complicate the optimization landscape of standard fine-tuning, and a backward pass that incurs disproportionately more overhead than the forward pass. Our defense succeeds in withstanding adaptive attackers with full knowledge of the defense strategy while preserving the original model's capabilities. Experiments on LLM validate these claims.

cs.LG↗

arXiv2026

Nectar: Neural Estimation of Cached-Token Attention via Regression

Evaluating softmax attention over a fixed long context requires reading every cached key-value pair for each new query token. For a given context (a book, a manual, a legal corpus) the attention output is a deterministic function of the query. We propose Nectar, which fits a compact neural network to this function for queries drawn from a task-relevant distribution. Nectar fits two networks per layer and KV-head: a target network that predicts the attention output and a score network that predicts the log-normalizer. The pair plugs into the standard masked self-attention at inference time, replacing the $O(n)$ attention over the cache with a forward pass whose cost does not depend on $n$. Each module carries on the order of $|\theta|$ parameters per layer and KV-head, typically much smaller than the $2nd$ KV-cache footprint at the same granularity. We report experiments on models from 1.7B to 8B parameters across five long-context datasets. The approximation error tracks the next-token accuracy gap to full attention, and allocating capacity non-uniformly across layers reduces that gap in our ablation. Beyond this analysis of metrics, we check that the text generations (following a question prompt) of a model equipped with a Nectar module match in semantic content those obtained by giving the same model access to the full cache.

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arXiv2026

Scaling Categorical Flow Maps

Continuous diffusion and flow matching models could represent a powerful alternative to autoregressive approaches for language modelling (LM), as they unlock a host of advantages currently reserved for continuous modalities, including accelerated sampling and tilting. Recently, several works have demonstrated the possibility of generating discrete data continuously by a simple flow matching process between a Gaussian and the one-hot encoded data distribution. They have further shown the feasibility of accelerated sampling via Categorical Flow Maps (CFMs), resulting in competitive sample quality in the few-step regime. However, this method had only been evaluated at relatively modest scales ($<1$B), leaving the question of its scalability completely open. In this article, we train a $1.7$B-parameter base flow model on $2.1$T tokens and self-distill it into a CFM that generates diverse, high-quality text in as few as $4$ inference steps while maintaining near-data-level token entropy. Furthermore, we introduce a likelihood bound for CFMs in the semi-discrete setting, and show that they can be used to score the model on standard LM benchmarks, achieving results in the same range as discrete diffusion methods. Finally, we uncover some of the challenges that arise from training these models at scale, and we provide prescriptive insights on loss weighting and time scheduling.

cs.LG↗

arXiv2026

HyperTransport: Amortized Conditioning of T2I Generative Models

As foundation models grow in capability, the ability to efficiently and reliably control their behavior becomes critical. Fine-tuning these models can be costly, and while prompting can be practical for controllability, it remains fragile due to models' high sensitivity to exact prompt wording and structure. This brittleness has driven interest in activation steering techniques that offer more stable and predictable control over model behavior. However, existing activation steering methods require per-concept optimization, which makes them ill-suited to deployment scenarios where the concept set is large, evolving, or only specified at request time: each new concept incurs at least minutes of optimization on the target model. We propose HyperTransport, a hypernetwork framework that amortizes this cost by mapping embeddings from a pretrained encoder (CLIP in our instantiation) directly to intervention parameters, trained end-to-end using an optimal transport loss. Once trained, HyperTransport produces each new intervention in a single hypernetwork forward pass, 3600-7000x faster than per-concept fitting. On concepts unseen during training, it matches the strongest per-concept baselines at inducing the target concept. By decoupling concept representation from intervention prediction, HyperTransport combines three capabilities that no existing approach offers as a set: amortized steering for open-ended concept sets, continuous interpretable strength control, and cross-modal conditioning where reference images can directly steer text-based generation. We validate HyperTransport on DMD2 and Nitro-1-PixArt across 167 held-out test concepts via CLIP-based metrics, a VLM-as-a-judge evaluation, and a user study. In pairwise comparisons, both human and VLM judges prefer HyperTransport over prompting ~2x as often.

cs.LG↗

arXiv2026

Stochastic KV Routing: Enabling Adaptive Depth-Wise Cache Sharing

Serving transformer language models with high throughput requires caching Key-Values (KVs) to avoid redundant computation during autoregressive generation. The memory footprint of KV caching is significant and heavily impacts serving costs. This work proposes to lessen these memory requirements. While recent work has largely addressed KV cache reduction via compression and eviction along the temporal axis, we argue that the \emph{depth} dimension offers an orthogonal and robust avenue for optimization. Although prior research suggests that a full cache for every layer is redundant, implementing cross-layer cache sharing remains a practical challenge; existing methods typically suffer from reduced throughput or increased time-to-first-token. In this paper, we demonstrate that dropping a layer's cache offers efficient optimization without information loss. We propose a simple training approach: random cross-layer attention. During training, layers randomly choose to attend either to their own KV states or those of a preceding layer. This stochastic process adapts the model to be robust to various depth-wise cache sharing strategies, ensuring flexibility for unknown hardware constraints at deployment time. Our evaluations show that applying this scheme during pre-training or fine-tuning enables depth-wise cache sharing for various model families. Furthermore, for larger models in data-constrained settings, this approach is suggestive of a regularization-like effect, frequently preserving or improving performance while significantly reducing the cache's memory footprint.

cs.LG↗

arXiv2026

Amortized Maximum Inner Product Search with Learned Support Functions

Maximum inner product search (MIPS) is a crucial subroutine in machine learning, requiring the identification of a vector taken within a database (the keys) that best aligns with a given query. We propose amortized MIPS: a regression-based approach that trains neural networks to directly predict MIPS solutions, amortizing the cost of repeatedly solving MIPS for queries drawn from a known distribution over a fixed key database. Our key insight is that the MIPS value function is the \emph{support} function of the set of keys, a well-studied convex function whose gradient yields the optimal key. This motivates two complementary amortized models: SupportNet, an input-convex neural network trained to regress the support function, and KeyNet, a vector-valued network that directly regresses the optimal key. SupportNet can serve as a cluster router, steering queries toward relevant database partitions, while KeyNet can be used as a drop-in replacement for the original query, fed directly to off-the-shelf indexing pipelines. Our experiments on the BEIR benchmark show that, for document embeddings, learned \SupportNet{}s and \KeyNet{}s significantly improve IVF match rates when accounting for compute effort, whether measured in FLOPs, number of probes, or wall-clock time. Our code is available at: https://github.com/apple/ml-amips.

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arXiv2026

The Coupling Within: Flow Matching via Distilled Normalizing Flows

Flow models have rapidly become the go-to method for training and deploying large-scale generators, owing their success to inference-time flexibility via adjustable integration steps. A crucial ingredient in flow training is the choice of coupling measure for sampling noise/data pairs that define the flow matching (FM) regression loss. While FM training defaults usually to independent coupling, recent works show that adaptive couplings informed by noise/data distributions (e.g., via optimal transport, OT) improve both model training and inference. We radicalize this insight by shifting the paradigm: rather than computing adaptive couplings directly, we use distilled couplings from a different, pretrained model capable of placing noise and data spaces in bijection -- a property intrinsic to normalizing flows (NF) through their maximum likelihood and invertibility requirements. Leveraging recent advances in NF image generation via auto-regressive (AR) blocks, we propose Normalized Flow Matching (NFM), a new method that distills the quasi-deterministic coupling of pretrained NF models to train student flow models. These students achieve the best of both worlds: significantly outperforming flow models trained with independent or even OT couplings, while also improving on the teacher AR-NF model.

cs.LG↗

arXiv2026

The Design Space of Tri-Modal Masked Diffusion Models

Discrete diffusion models have emerged as strong alternatives to autoregressive language models, with recent work initializing and fine-tuning a base unimodal model for bimodal generation. Diverging from previous approaches, we introduce the first tri-modal masked diffusion model pretrained from scratch on text, image-text, and audio-text data. We systematically analyze multimodal scaling laws, modality mixing ratios, noise schedules, and batch-size effects, and we provide optimized inference sampling defaults. Our batch-size analysis yields a novel stochastic differential equation (SDE)-based reparameterization that eliminates the need for tuning the optimal batch size as reported in recent work. This reparameterization decouples the physical batch size, often chosen based on compute constraints (GPU saturation, FLOP efficiency, wall-clock time), from the logical batch size, chosen to balance gradient variance during stochastic optimization. Finally, we pretrain a preliminary 3B-parameter tri-modal model on 6.4T tokens, demonstrating the capabilities of a unified design and achieving strong results in text generation, text-to-image tasks, and text-to-speech tasks. Our work represents the largest-scale systematic open study of multimodal discrete diffusion models conducted to date, providing insights into scaling behaviors across multiple modalities.

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arXiv2026

LaCy: What Small Language Models Can and Should Learn is Not Just a Question of Loss

Language models have consistently grown to compress more world knowledge into their parameters, but the knowledge that can be pretrained into them is upper-bounded by their parameter size. Especially the capacity of Small Language Models (SLMs) is limited, leading to factually incorrect generations. This problem is often mitigated by giving the SLM access to an outside source: the ability to query a larger model, documents, or a database. Under this setting, we study the fundamental question of \emph{which tokens an SLM can and should learn} during pretraining, versus \emph{which ones it should delegate} via a \texttt{ } token. We find that this is not simply a question of loss: although the loss is predictive of whether a predicted token mismatches the ground-truth, it is insufficient for identifying which predictions would actually lead to factual or semantically invalid continuations. Some high-loss tokens correspond to \emph{acceptable} alternative continuations of a pretraining document and therefore should not trigger a \texttt{ }. This suggests that learnability cannot be characterized from loss alone, but requires additional domain-specific signals about the role of a token in the sentence. In Wikipedia-like domains, we show that augmenting the loss signal with lightweight grammatical information from a spaCy parser substantially improves delegation decisions. Based on this insight, we propose LaCy, a novel pretraining method that combines loss with factuality signals to decide which tokens an SLM should learn. Our experiments demonstrate that LaCy models successfully learn which tokens to predict and when to call for help. This results in higher FactScores when generating in a cascade with a bigger model and outperforms Rho or LLM-judge trained SLMs, while being simpler and cheaper.

cs.CL↗

arXiv2025

Completed Hyperparameter Transfer across Modules, Width, Depth, Batch and Duration

Hyperparameter tuning can dramatically impact training stability and final performance of large-scale models. Recent works on neural network parameterisations, such as $\mu$P, have enabled transfer of optimal global hyperparameters across model sizes. These works propose an empirical practice of search for optimal global base hyperparameters at a small model size, and transfer to a large size. We extend these works in two key ways. To handle scaling along most important scaling axes, we propose the Complete$^{(d)}$ Parameterisation that unifies scaling in width and depth -- using an adaptation of CompleteP -- as well as in batch-size and training duration. Secondly, with our parameterisation, we investigate per-module hyperparameter optimisation and transfer. We characterise the empirical challenges of navigating the high-dimensional hyperparameter landscape, and propose practical guidelines for tackling this optimisation problem. We demonstrate that, with the right parameterisation, hyperparameter transfer holds even in the per-module hyperparameter regime. Our study covers an extensive range of optimisation hyperparameters of modern models: learning rates, AdamW parameters, weight decay, initialisation scales, and residual block multipliers. Our experiments demonstrate significant training speed improvements in Large Language Models with the transferred per-module hyperparameters.

cs.LG↗

arXiv2025

Learning Unmasking Policies for Diffusion Language Models

Diffusion (Large) Language Models (dLLMs) now match the downstream performance of their autoregressive counterparts on many tasks, while holding the promise of being more efficient during inference. One critical design aspect of dLLMs is the sampling procedure that selects which tokens to unmask at each diffusion step. Indeed, recent work has found that heuristic strategies such as confidence thresholding improve both sample quality and token throughput compared to random unmasking. However, such heuristics have downsides: they require manual tuning, and we observe that their performance degrades with larger block sizes. In this work, we instead propose to train sampling procedures using reinforcement learning. Specifically, we formalize masked diffusion sampling as a Markov decision process in which the dLLM serves as the environment, and propose a lightweight policy based on a single-layer transformer that maps dLLM token confidences to unmasking decisions. Our experiments show that these trained policies match the performance of state-of-the-art heuristics when combined with semi-autoregressive (block) generation, while outperforming them in the full-diffusion setting.

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arXiv2025

Removing Noise, not Finding Gold: Quality Filtering for Large-Scale Pretraining

Large-scale models are pretrained on massive web-crawled datasets containing documents of mixed quality, making data filtering essential. A popular method is Classifier-based Quality Filtering (CQF), which trains a binary classifier to distinguish between pretraining data and a small, high-quality set. It assigns each pretraining document a quality score defined as the classifier's score and retains only the top-scoring ones. We provide an in-depth analysis of CQF. We show that while CQF improves downstream task performance, it does not necessarily enhance language modeling on the high-quality set. Importantly, we find that training on CQF-selected data can outperform training directly on the high-quality set, even when the latter is sufficiently large. This finding alone is particularly striking, given the substantial effort and cost recently devoted to augmenting high-quality data. We explain this paradox by the fact that CQF implicitly filters the high-quality dataset as well as the low-quality one. Finally, we introduce an optimization-driven notion of data quality and demonstrate that it can be reliably estimated using small-scale proxy experiments. Altogether, our results both elucidate the mechanisms behind CQF and deepen our understanding of data selection methods widely used in practice.

cs.LG↗

arXiv2025

Flow Matching with Semidiscrete Couplings

Flow models parameterized as time-dependent velocity fields can generate data from noise by integrating an ODE. These models are often trained using flow matching, i.e. by sampling random pairs of noise and target points $(\mathbf{x}_0,\mathbf{x}_1)$ and ensuring that the velocity field is aligned, on average, with $\mathbf{x}_1-\mathbf{x}_0$ when evaluated along a segment linking $\mathbf{x}_0$ to $\mathbf{x}_1$. While these pairs are sampled independently by default, they can also be selected more carefully by matching batches of $n$ noise to $n$ target points using an optimal transport (OT) solver. Although promising in theory, the OT flow matching (OT-FM) approach is not widely used in practice. Zhang et al. (2025) pointed out recently that OT-FM truly starts paying off when the batch size $n$ grows significantly, which only a multi-GPU implementation of the Sinkhorn algorithm can handle. Unfortunately, the costs of running Sinkhorn can quickly balloon, requiring $O(n^2/\varepsilon^2)$ operations for every $n$ pairs used to fit the velocity field, where $\varepsilon$ is a regularization parameter that should be typically small to yield better results. To fulfill the theoretical promises of OT-FM, we propose to move away from batch-OT and rely instead on a semidiscrete formulation that leverages the fact that the target dataset distribution is usually of finite size $N$. The SD-OT problem is solved by estimating a dual potential vector using SGD; using that vector, freshly sampled noise vectors at train time can then be matched with data points at the cost of a maximum inner product search (MIPS). Semidiscrete FM (SD-FM) removes the quadratic dependency on $n/\varepsilon$ that bottlenecks OT-FM. SD-FM beats both FM and OT-FM on all training metrics and inference budget constraints, across multiple datasets, on unconditional/conditional generation, or when using mean-flow models.

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arXiv2025

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.

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arXiv2025

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 $\varepsilon$.

cs.LG↗

arXiv2025

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

The canonical approach in 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 $\rho$, 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 a convex potential $w$. 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. We also address the common sampling scenario in which the density of $\rho$ is known only up to a normalizing constant, and propose an algorithm to learn $w$ in this setting.

stat.ML↗

arXiv2025

LinEAS: End-to-end Learning of Activation Steering with a Distributional Loss

The growing use of generative models in daily life calls for efficient mechanisms to control their generation, to e.g., produce safe content or provide users with tools to explore style changes. Ideally, such mechanisms should require low volume of unpaired data (i.e., without explicit preference), and should be cheap, both at train and inference time, while preserving output quality. Recent research has shown that such mechanisms can be obtained by intervening exclusively on model activations, with the goal of correcting distributional differences between activations seen when using prompts from a source vs. a target set (e.g., toxic and non-toxic sentences). While cheap, these fast methods are inherently crude: their maps are tuned locally, not accounting for their impact on downstream layers, resulting in interventions that cause unintended shifts when used out-of-sample. We propose in this work linear end-to-end activation steering (LinEAS), an approach trained with a global loss that accounts simultaneously for all layer-wise distributional shifts. In addition to being more robust, the loss used to train LinEAS can be regularized with sparsifying norms, which can automatically carry out neuron selection. LinEAS only requires a handful of unpaired samples to be effective, and beats similar baselines on toxicity mitigation in language models, becoming competitive with oracle-dependent methods that have access to strong supervision. LinEAS is modality-agnostic and we empirically find that it outperforms existing activation steering methods at mitigating and including new concepts at the output of single-step text-to-image generation models.

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