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Luca Ambrogioni

Luca Ambrogioni contributes to research discovery and scholarly infrastructure.

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Machine Learning Artificial Intelligence Computation and Language Computer Vision Information Theory math.ST stat.OT

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preprint2026arXiv

Entropy Across the Bridge: Conditional-Marginal Discretization for Flow and Schrödinger Samplers

For a fixed flow-based generative model under a small inference budget, sample quality can depend strongly on where the sampler spends its few function evaluations. Flow matching and Schrödinger bridges define probability paths, yet their inference grids are usually heuristic or inherited from one-endpoint diffusion. We derive a conditional-marginal entropy-rate objective for bridge-aware discretization, separating endpoint-conditioned bridge geometry from marginal flow evolution, and use it to build a training-free entropic inference-time scheduler from first principles. For Gaussian Brownian bridges this rate is closed-form and U-shaped, motivating boundary-heavy nonuniform grids. On trained two-dimensional bridge/flow models, the estimated profile recovers the predicted shape and improves 10-step ODE-Heun MMD over linear by 18.1%, with a paired 22.7% SDE-Heun improvement in the same low-NFE sweep. On EDM/CIFAR-10, the entropic time-discretization gives the best tested five-step FID (186.3 \pm 4.0 versus 200.5 \pm 2.9 for linear and 238.0 \pm 5.3 for cosine). On AlphaFlow protein generation, entropic conditional-marginal (cond-marg) scheduling shows advantage in low-NFE regimes on both CAMEO22 and ATLAS benchmarks. These results support entropy-rate scheduling as a practical low-budget allocation signal for high-dimensional bridge and flow samplers.

preprint2026arXiv

Language Diffusion Models are Associative Memories Capable of Retrieving Unseen Data

When do language diffusion models memorize their training data, and how to quantitatively assess their true generative regime? We address these questions by showing that Uniform-based Discrete Diffusion Models (UDDMs) fundamentally behave as Associative Memories (AMs) $\textit{with emergent creative capabilities}$. The core idea of an AM is to reliably recover stored data points as $\textit{memories}$ by establishing distinct basins of attraction around them. Historically, models like Hopfield networks use an explicit energy function to guarantee these stable attractors. We broaden this perspective by leveraging the observation that energy is not strictly necessary, as basins of attraction can also be formed via conditional likelihood maximization. By evaluating token recovery of $\textit{training}$ and $\textit{test}$ examples, we identify in UDDMs a sharp memorization-to-generalization transition governed by the size of the training dataset: as it increases, basins around training examples shrink and basins around unseen test examples expand, until both later converge to the same level. Crucially, we can detect this transition using only the conditional entropy of predicted token sequences: memorization is characterized by vanishing conditional entropy, while in the generalization regime the conditional entropy of most tokens remains finite. Thus, conditional entropy offers a practical probe for the memorization-to-generalization transition in deployed models.

preprint2026arXiv

Towards Closing the Autoregressive Gap in Language Modeling via Entropy-Gated Continuous Bitstream Diffusion

Diffusion language models (DLMs) promise parallel, order-agnostic generation, but on standard benchmarks they have historically lagged behind autoregressive models in sample quality and diversity. Recent continuous flow and diffusion approaches over token embeddings have narrowed this gap, suggesting continuous state spaces are highly effective for language. In this work, we further close the autoregressive gap by modeling text as a continuous diffusion process over fixed-width binary bitstreams. Our approach represents semantic tokens as analog bit sequences and utilizes a matched-filter residual parameterization to isolate contextual learning from analytic independent-bit posteriors. Crucially, we adopt a stochastic sampler that applies Langevin-type corrections gated by the entropy-rate profile, automatically concentrating stochasticity in high-information regions while remaining nearly deterministic elsewhere. On the One Billion Word Benchmark (LM1B), our 130M-parameter bitstream model reaches a generative perplexity ($\GenPPL$) of $59.76$ at matched real-data entropy ($4.31$) using 256 neural function evaluations (NFEs), decisively outperforming prior DLM baselines and reaching the autoregressive reference. On OpenWebText (OWT), our stochastic sampler establishes a new continuous-DLM Pareto frontier, achieving $\GenPPL=27.06$ at an entropy of $5.26$ using $4\times$ fewer steps than previous 1024-NFE baselines. As an additional architectural benefit, bitstream diffusion removes the $\mathcal{O}(V)$ vocabulary scaling bottleneck shared by standard DLMs. By predicting $\mathcal{O}(\log V)$ bitwise logits via semantic bit-patching, our model yields a reduced memory footprint and higher throughput, demonstrating a scalable paradigm for language generation as vocabulary sizes grow.

preprint2022arXiv

Embedded-model flows: Combining the inductive biases of model-free deep learning and explicit probabilistic modeling

Normalizing flows have shown great success as general-purpose density estimators. However, many real world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose embedded-model flows (EMF), which alternate general-purpose transformations with structured layers that embed domain-specific inductive biases. These layers are automatically constructed by converting user-specified differentiable probabilistic models into equivalent bijective transformations. We also introduce gated structured layers, which allow bypassing the parts of the models that fail to capture the statistics of the data. We demonstrate that EMFs can be used to induce desirable properties such as multimodality, hierarchical coupling and continuity. Furthermore, we show that EMFs enable a high performance form of variational inference where the structure of the prior model is embedded in the variational architecture. In our experiments, we show that this approach outperforms state-of-the-art methods in common structured inference problems.

preprint2021arXiv

Automatic structured variational inference

Stochastic variational inference offers an attractive option as a default method for differentiable probabilistic programming. However, the performance of the variational approach depends on the choice of an appropriate variational family. Here, we introduce automatic structured variational inference (ASVI), a fully automated method for constructing structured variational families, inspired by the closed-form update in conjugate Bayesian models. These convex-update families incorporate the forward pass of the input probabilistic program and can therefore capture complex statistical dependencies. Convex-update families have the same space and time complexity as the input probabilistic program and are therefore tractable for a very large family of models including both continuous and discrete variables. We validate our automatic variational method on a wide range of low- and high-dimensional inference problems. We find that ASVI provides a clear improvement in performance when compared with other popular approaches such as the mean-field approach and inverse autoregressive flows. We provide an open source implementation of ASVI in TensorFlow Probability.

preprint2021arXiv

Automatic variational inference with cascading flows

The automation of probabilistic reasoning is one of the primary aims of machine learning. Recently, the confluence of variational inference and deep learning has led to powerful and flexible automatic inference methods that can be trained by stochastic gradient descent. In particular, normalizing flows are highly parameterized deep models that can fit arbitrarily complex posterior densities. However, normalizing flows struggle in highly structured probabilistic programs as they need to relearn the forward-pass of the program. Automatic structured variational inference (ASVI) remedies this problem by constructing variational programs that embed the forward-pass. Here, we combine the flexibility of normalizing flows and the prior-embedding property of ASVI in a new family of variational programs, which we named cascading flows. A cascading flows program interposes a newly designed highway flow architecture in between the conditional distributions of the prior program such as to steer it toward the observed data. These programs can be constructed automatically from an input probabilistic program and can also be amortized automatically. We evaluate the performance of the new variational programs in a series of structured inference problems. We find that cascading flows have much higher performance than both normalizing flows and ASVI in a large set of structured inference problems.

preprint2020arXiv

Explainable 3D Convolutional Neural Networks by Learning Temporal Transformations

In this paper we introduce the temporally factorized 3D convolution (3TConv) as an interpretable alternative to the regular 3D convolution (3DConv). In a 3TConv the 3D convolutional filter is obtained by learning a 2D filter and a set of temporal transformation parameters, resulting in a sparse filter where the 2D slices are sequentially dependent on each other in the temporal dimension. We demonstrate that 3TConv learns temporal transformations that afford a direct interpretation. The temporal parameters can be used in combination with various existing 2D visualization methods. We also show that insight about what the model learns can be achieved by analyzing the transformation parameter statistics on a layer and model level. Finally, we implicitly demonstrate that, in popular ConvNets, the 2DConv can be replaced with a 3TConv and that the weights can be transferred to yield pretrained 3TConvs. pretrained 3TConvnets leverage more than a decade of work on traditional 2DConvNets by being able to make use of features that have been proven to deliver excellent results on image classification benchmarks.

preprint2020arXiv

The Indian Chefs Process

This paper introduces the Indian Chefs Process (ICP), a Bayesian nonparametric prior on the joint space of infinite directed acyclic graphs (DAGs) and orders that generalizes Indian Buffet Processes. As our construction shows, the proposed distribution relies on a latent Beta Process controlling both the orders and outgoing connection probabilities of the nodes, and yields a probability distribution on sparse infinite graphs. The main advantage of the ICP over previously proposed Bayesian nonparametric priors for DAG structures is its greater flexibility. To the best of our knowledge, the ICP is the first Bayesian nonparametric model supporting every possible DAG. We demonstrate the usefulness of the ICP on learning the structure of deep generative sigmoid networks as well as convolutional neural networks.

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