arXiv subjects

Alberto Bernacchia

Publications and source records attributed to Alberto Bernacchia.

At least 19 recordsLinked to original sources

arXiv2026

Improved denoising diffusion probabilistic models with efficient non-diagonal covariance modeling

The sampling process of Denoising Diffusion Probabilistic Models (DDPMs) can be accelerated by leveraging second-order information in the form of approximations to the denoising posterior covariance -- allowing samples of acceptable quality to be produced in fewer but larger sampling steps. Previous attempts at using such information have used drastic (e.g.\ diagonal) simplifications of the covariance. These do not do justice to the peculiar statistical structure of natural images, which exhibit strong non-diagonal correlations between pixels and color channels, and a slow-decaying power-law frequency spectrum. Here, we develop a novel covariance model that captures these features. Our Kronecker-DCT (K-DCT) model uses a Kronecker-factored decomposition of inter-color covariances and spatial covariances modeled in the frequency domain using the Discrete Cosine Transform (DCT). The use of the DCT reduces the computational complexity from quadratic to log-linear, resulting in negligible computational and memory overhead in each denoising step. By learning K-DCT-structured amortizations of the denoising posterior covariance using pre-trained score models on CIFAR-10, Celeb-A, ImageNet and LSUN datasets, we show improved performance compared to previous SOTA denoising samplers, both in terms of FID and likelihoods, especially in the regime of few denoising steps.

cs.CV↗

arXiv2026

Exploiting weight-space symmetries for approximating curvature

Many machine learning techniques rely on approximating a loss function's curvature, but this is notoriously hard to do at the scale of modern deep networks. Surprisingly, no previous work has exploited the curvature constraints that arise from well known weight-space symmetries in loss landscapes. By analytically averaging over group actions that leave the loss invariant, we construct structured Hessian approximations from single gradients that can be tractably estimated, stored, and inverted. The choice of user-specified symmetry group directly governs the trade-off between approximation accuracy and computational cost. Moreover, our framework provides a unifying theoretical lens for viewing existing methods; in particular, a specific choice of symmetry group recovers Shampoo/Muon-like curvature estimates. We validate our method on a range of network architectures, and deploy it to second-order optimization benchmarks, including a small language model. Our curvature estimation framework might find applications in other machine learning problems such as uncertainty estimation, continual learning, compression/pruning, training data attribution, and more.

cs.LG↗

arXiv2026

Cross-Tokenizer LLM Distillation through a Byte-Level Interface

Cross-tokenizer distillation (CTD), the transfer of knowledge from a teacher to a student language model when the two use different tokenizers, remains a largely unsolved problem. Existing approaches rely on heuristic strategies to align mismatched vocabularies, introducing considerable complexity. In this paper, we propose a simple but effective baseline called Byte-Level Distillation (BLD) which enables CTD by operating at a common interface across tokenizers: the byte level. In more detail, we convert the teacher's output distribution to byte-level probabilities, attach a lightweight byte-level decoder head to the student, and distill through this shared byte-level interface. Despite its simplicity, BLD performs competitively with--and on several benchmarks surpasses--significantly more sophisticated CTD methods, across a range of distillation tasks with models from 1B to 8B parameters. Our results suggest that the byte level is a natural common ground for cross-tokenizer knowledge transfer, while also highlighting that consistent improvements across all tasks and benchmarks remain elusive, underscoring that CTD is still an open problem.

cs.CL↗

arXiv2025

Reinforcement Learning Using known Invariances

In many real-world reinforcement learning (RL) problems, the environment exhibits inherent symmetries that can be exploited to improve learning efficiency. This paper develops a theoretical and algorithmic framework for incorporating known group symmetries into kernel-based RL. We propose a symmetry-aware variant of optimistic least-squares value iteration (LSVI), which leverages invariant kernels to encode invariance in both rewards and transition dynamics. Our analysis establishes new bounds on the maximum information gain and covering numbers for invariant RKHSs, explicitly quantifying the sample efficiency gains from symmetry. Empirical results on a customized Frozen Lake environment and a 2D placement design problem confirm the theoretical improvements, demonstrating that symmetry-aware RL achieves significantly better performance than their standard kernel counterparts. These findings highlight the value of structural priors in designing more sample-efficient reinforcement learning algorithms.

cs.LG↗

arXiv2025

Bayesian Optimization from Human Feedback: Near-Optimal Regret Bounds

Bayesian optimization (BO) with preference-based feedback has recently garnered significant attention due to its emerging applications. We refer to this problem as Bayesian Optimization from Human Feedback (BOHF), which differs from conventional BO by learning the best actions from a reduced feedback model, where only the preference between two actions is revealed to the learner at each time step. The objective is to identify the best action using a limited number of preference queries, typically obtained through costly human feedback. Existing work, which adopts the Bradley-Terry-Luce (BTL) feedback model, provides regret bounds for the performance of several algorithms. In this work, within the same framework we develop tighter performance guarantees. Specifically, we derive regret bounds of $\tilde{\mathcal{O}}(\sqrt{\Gamma(T)T})$, where $\Gamma(T)$ represents the maximum information gain$\unicode{x2014}$a kernel-specific complexity term$\unicode{x2014}$and $T$ is the number of queries. Our results significantly improve upon existing bounds. Notably, for common kernels, we show that the order-optimal sample complexities of conventional BO$\unicode{x2014}$achieved with richer feedback models$\unicode{x2014}$are recovered. In other words, the same number of preferential samples as scalar-valued samples is sufficient to find a nearly optimal solution.

cs.LG↗

arXiv2025

Near-Optimal Sample Complexity in Reward-Free Kernel-Based Reinforcement Learning

Reinforcement Learning (RL) problems are being considered under increasingly more complex structures. While tabular and linear models have been thoroughly explored, the analytical study of RL under nonlinear function approximation, especially kernel-based models, has recently gained traction for their strong representational capacity and theoretical tractability. In this context, we examine the question of statistical efficiency in kernel-based RL within the reward-free RL framework, specifically asking: how many samples are required to design a near-optimal policy? Existing work addresses this question under restrictive assumptions about the class of kernel functions. We first explore this question by assuming a generative model, then relax this assumption at the cost of increasing the sample complexity by a factor of H, the length of the episode. We tackle this fundamental problem using a broad class of kernels and a simpler algorithm compared to prior work. Our approach derives new confidence intervals for kernel ridge regression, specific to our RL setting, which may be of broader applicability. We further validate our theoretical findings through simulations.

cs.LG↗

arXiv2024

Efficient Model Compression Techniques with FishLeg

In many domains, the most successful AI models tend to be the largest, indeed often too large to be handled by AI players with limited computational resources. To mitigate this, a number of compression methods have been developed, including methods that prune the network down to high sparsity whilst retaining performance. The best-performing pruning techniques are often those that use second-order curvature information (such as an estimate of the Fisher information matrix) to score the importance of each weight and to predict the optimal compensation for weight deletion. However, these methods are difficult to scale to high-dimensional parameter spaces without making heavy approximations. Here, we propose the FishLeg surgeon (FLS), a new second-order pruning method based on the Fisher-Legendre (FishLeg) optimizer. At the heart of FishLeg is a meta-learning approach to amortising the action of the inverse FIM, which brings a number of advantages. Firstly, the parameterisation enables the use of flexible tensor factorisation techniques to improve computational and memory efficiency without sacrificing much accuracy, alleviating challenges associated with scalability of most second-order pruning methods. Secondly, directly estimating the inverse FIM leads to less sensitivity to the amplification of stochasticity during inversion, thereby resulting in more precise estimates. Thirdly, our approach also allows for progressive assimilation of the curvature into the parameterisation. In the gradual pruning regime, this results in a more efficient estimate refinement as opposed to re-estimation. We find that FishLeg achieves higher or comparable performance against two common baselines in the area, most notably in the high sparsity regime when considering a ResNet18 model on CIFAR-10 (84% accuracy at 95% sparsity vs 60% for OBS) and TinyIM (53% accuracy at 80% sparsity vs 48% for OBS).

cs.LG↗

arXiv2024

Exact, Tractable Gauss-Newton Optimization in Deep Reversible Architectures Reveal Poor Generalization

Second-order optimization has been shown to accelerate the training of deep neural networks in many applications, often yielding faster progress per iteration on the training loss compared to first-order optimizers. However, the generalization properties of second-order methods are still being debated. Theoretical investigations have proved difficult to carry out outside the tractable settings of heavily simplified model classes -- thus, the relevance of existing theories to practical deep learning applications remains unclear. Similarly, empirical studies in large-scale models and real datasets are significantly confounded by the necessity to approximate second-order updates in practice. It is often unclear whether the observed generalization behaviour arises specifically from the second-order nature of the parameter updates, or instead reflects the specific structured (e.g.\ Kronecker) approximations used or any damping-based interpolation towards first-order updates. Here, we show for the first time that exact Gauss-Newton (GN) updates take on a tractable form in a class of deep reversible architectures that are sufficiently expressive to be meaningfully applied to common benchmark datasets. We exploit this novel setting to study the training and generalization properties of the GN optimizer. We find that exact GN generalizes poorly. In the mini-batch training setting, this manifests as rapidly saturating progress even on the \emph{training} loss, with parameter updates found to overfit each mini-batchatch without producing the features that would support generalization to other mini-batches. We show that our experiments run in the ``lazy'' regime, in which the neural tangent kernel (NTK) changes very little during the course of training. This behaviour is associated with having no significant changes in neural representations, explaining the lack of generalization.

cs.LG↗

arXiv2023

Score Normalization for a Faster Diffusion Exponential Integrator Sampler

Recently, Zhang et al. have proposed the Diffusion Exponential Integrator Sampler (DEIS) for fast generation of samples from Diffusion Models. It leverages the semi-linear nature of the probability flow ordinary differential equation (ODE) in order to greatly reduce integration error and improve generation quality at low numbers of function evaluations (NFEs). Key to this approach is the score function reparameterisation, which reduces the integration error incurred from using a fixed score function estimate over each integration step. The original authors use the default parameterisation used by models trained for noise prediction -- multiply the score by the standard deviation of the conditional forward noising distribution. We find that although the mean absolute value of this score parameterisation is close to constant for a large portion of the reverse sampling process, it changes rapidly at the end of sampling. As a simple fix, we propose to instead reparameterise the score (at inference) by dividing it by the average absolute value of previous score estimates at that time step collected from offline high NFE generations. We find that our score normalisation (DEIS-SN) consistently improves FID compared to vanilla DEIS, showing an improvement at 10 NFEs from 6.44 to 5.57 on CIFAR-10 and from 5.9 to 4.95 on LSUN-Church 64x64. Our code is available at https://github.com/mtkresearch/Diffusion-DEIS-SN

cs.LG↗

arXiv2023

Generative Diffusion Models for Radio Wireless Channel Modelling and Sampling

Channel modelling is essential to designing modern wireless communication systems. The increasing complexity of channel modelling and the cost of collecting high-quality wireless channel data have become major challenges. In this paper, we propose a diffusion model based channel sampling approach for rapidly synthesizing channel realizations from limited data. We use a diffusion model with a U Net based architecture operating in the frequency space domain. To evaluate how well the proposed model reproduces the true distribution of channels in the training dataset, two evaluation metrics are used: $i)$ the approximate $2$-Wasserstein distance between real and generated distributions of the normalized power spectrum in the antenna and frequency domains and $ii)$ precision and recall metric for distributions. We show that, compared to existing GAN based approaches which suffer from mode collapse and unstable training, our diffusion based approach trains stably and generates diverse and high-fidelity samples from the true channel distribution. We also show that we can pretrain the model on a simulated urban macro-cellular channel dataset and fine-tune it on a smaller, out-of-distribution urban micro-cellular dataset, therefore showing that it is feasible to model real world channels using limited data with this approach.

cs.AI↗

arXiv2023

Image generation with shortest path diffusion

The field of image generation has made significant progress thanks to the introduction of Diffusion Models, which learn to progressively reverse a given image corruption. Recently, a few studies introduced alternative ways of corrupting images in Diffusion Models, with an emphasis on blurring. However, these studies are purely empirical and it remains unclear what is the optimal procedure for corrupting an image. In this work, we hypothesize that the optimal procedure minimizes the length of the path taken when corrupting an image towards a given final state. We propose the Fisher metric for the path length, measured in the space of probability distributions. We compute the shortest path according to this metric, and we show that it corresponds to a combination of image sharpening, rather than blurring, and noise deblurring. While the corruption was chosen arbitrarily in previous work, our Shortest Path Diffusion (SPD) determines uniquely the entire spatiotemporal structure of the corruption. We show that SPD improves on strong baselines without any hyperparameter tuning, and outperforms all previous Diffusion Models based on image blurring. Furthermore, any small deviation from the shortest path leads to worse performance, suggesting that SPD provides the optimal procedure to corrupt images. Our work sheds new light on observations made in recent works and provides a new approach to improve diffusion models on images and other types of data.

cs.CV↗

arXiv2023

Delayed Feedback in Kernel Bandits

Black box optimisation of an unknown function from expensive and noisy evaluations is a ubiquitous problem in machine learning, academic research and industrial production. An abstraction of the problem can be formulated as a kernel based bandit problem (also known as Bayesian optimisation), where a learner aims at optimising a kernelized function through sequential noisy observations. The existing work predominantly assumes feedback is immediately available; an assumption which fails in many real world situations, including recommendation systems, clinical trials and hyperparameter tuning. We consider a kernel bandit problem under stochastically delayed feedback, and propose an algorithm with $\tilde{\mathcal{O}}(\sqrt{Γ_k(T)T}+\mathbb{E}[τ])$ regret, where $T$ is the number of time steps, $Γ_k(T)$ is the maximum information gain of the kernel with $T$ observations, and $τ$ is the delay random variable. This represents a significant improvement over the state of the art regret bound of $\tilde{\mathcal{O}}(Γ_k(T)\sqrt{T}+\mathbb{E}[τ]Γ_k(T))$ reported in Verma et al. (2022). In particular, for very non-smooth kernels, the information gain grows almost linearly in time, trivializing the existing results. We also validate our theoretical results with simulations.

stat.ML↗

arXiv2023

Sample Complexity of Kernel-Based Q-Learning

Modern reinforcement learning (RL) often faces an enormous state-action space. Existing analytical results are typically for settings with a small number of state-actions, or simple models such as linearly modeled Q-functions. To derive statistically efficient RL policies handling large state-action spaces, with more general Q-functions, some recent works have considered nonlinear function approximation using kernel ridge regression. In this work, we derive sample complexities for kernel based Q-learning when a generative model exists. We propose a nonparametric Q-learning algorithm which finds an $ε$-optimal policy in an arbitrarily large scale discounted MDP. The sample complexity of the proposed algorithm is order optimal with respect to $ε$ and the complexity of the kernel (in terms of its information gain). To the best of our knowledge, this is the first result showing a finite sample complexity under such a general model.

cs.LG↗

arXiv2022

Improved Convergence Rates for Sparse Approximation Methods in Kernel-Based Learning

Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high computational cost; given a dataset of $n$ samples, the cost grows as $\mathcal{O}(n^3)$. Existing sparse approximation methods can yield a significant reduction in the computational cost, effectively reducing the actual cost down to as low as $\mathcal{O}(n)$ in certain cases. Despite this remarkable empirical success, significant gaps remain in the existing results for the analytical bounds on the error due to approximation. In this work, we provide novel confidence intervals for the Nyström method and the sparse variational Gaussian process approximation method, which we establish using novel interpretations of the approximate (surrogate) posterior variance of the models. Our confidence intervals lead to improved performance bounds in both regression and optimization problems.

cs.LG↗

arXiv2022

How to distribute data across tasks for meta-learning?

Meta-learning models transfer the knowledge acquired from previous tasks to quickly learn new ones. They are trained on benchmarks with a fixed number of data points per task. This number is usually arbitrary and it is unknown how it affects performance at testing. Since labelling of data is expensive, finding the optimal allocation of labels across training tasks may reduce costs. Given a fixed budget of labels, should we use a small number of highly labelled tasks, or many tasks with few labels each? Should we allocate more labels to some tasks and less to others? We show that: 1) If tasks are homogeneous, there is a uniform optimal allocation, whereby all tasks get the same amount of data; 2) At fixed budget, there is a trade-off between number of tasks and number of data points per task, with a unique solution for the optimum; 3) When trained separately, harder task should get more data, at the cost of a smaller number of tasks; 4) When training on a mixture of easy and hard tasks, more data should be allocated to easy tasks. Interestingly, Neuroscience experiments have shown that human visual skills also transfer better from easy tasks. We prove these results mathematically on mixed linear regression, and we show empirically that the same results hold for few-shot image classification on CIFAR-FS and mini-ImageNet. Our results provide guidance for allocating labels across tasks when collecting data for meta-learning.

cs.LG↗

arXiv2021

Natural continual learning: success is a journey, not (just) a destination

Biological agents are known to learn many different tasks over the course of their lives, and to be able to revisit previous tasks and behaviors with little to no loss in performance. In contrast, artificial agents are prone to 'catastrophic forgetting' whereby performance on previous tasks deteriorates rapidly as new ones are acquired. This shortcoming has recently been addressed using methods that encourage parameters to stay close to those used for previous tasks. This can be done by (i) using specific parameter regularizers that map out suitable destinations in parameter space, or (ii) guiding the optimization journey by projecting gradients into subspaces that do not interfere with previous tasks. However, these methods often exhibit subpar performance in both feedforward and recurrent neural networks, with recurrent networks being of interest to the study of neural dynamics supporting biological continual learning. In this work, we propose Natural Continual Learning (NCL), a new method that unifies weight regularization and projected gradient descent. NCL uses Bayesian weight regularization to encourage good performance on all tasks at convergence and combines this with gradient projection using the prior precision, which prevents catastrophic forgetting during optimization. Our method outperforms both standard weight regularization techniques and projection based approaches when applied to continual learning problems in feedforward and recurrent networks. Finally, the trained networks evolve task-specific dynamics that are strongly preserved as new tasks are learned, similar to experimental findings in biological circuits.

cs.LG↗

arXiv2021

Uniform Generalization Bounds for Overparameterized Neural Networks

An interesting observation in artificial neural networks is their favorable generalization error despite typically being extremely overparameterized. It is well known that the classical statistical learning methods often result in vacuous generalization errors in the case of overparameterized neural networks. Adopting the recently developed Neural Tangent (NT) kernel theory, we prove uniform generalization bounds for overparameterized neural networks in kernel regimes, when the true data generating model belongs to the reproducing kernel Hilbert space (RKHS) corresponding to the NT kernel. Importantly, our bounds capture the exact error rates depending on the differentiability of the activation functions. In order to establish these bounds, we propose the information gain of the NT kernel as a measure of complexity of the learning problem. Our analysis uses a Mercer decomposition of the NT kernel in the basis of spherical harmonics and the decay rate of the corresponding eigenvalues. As a byproduct of our results, we show the equivalence between the RKHS corresponding to the NT kernel and its counterpart corresponding to the Matérn family of kernels, showing the NT kernels induce a very general class of models. We further discuss the implications of our analysis for some recent results on the regret bounds for reinforcement learning and bandit algorithms, which use overparameterized neural networks.

cs.LG↗

arXiv2021

Optimal Order Simple Regret for Gaussian Process Bandits

Consider the sequential optimization of a continuous, possibly non-convex, and expensive to evaluate objective function $f$. The problem can be cast as a Gaussian Process (GP) bandit where $f$ lives in a reproducing kernel Hilbert space (RKHS). The state of the art analysis of several learning algorithms shows a significant gap between the lower and upper bounds on the simple regret performance. When $N$ is the number of exploration trials and $γ_N$ is the maximal information gain, we prove an $\tilde{\mathcal{O}}(\sqrt{γ_N/N})$ bound on the simple regret performance of a pure exploration algorithm that is significantly tighter than the existing bounds. We show that this bound is order optimal up to logarithmic factors for the cases where a lower bound on regret is known. To establish these results, we prove novel and sharp confidence intervals for GP models applicable to RKHS elements which may be of broader interest.

stat.ML↗