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Authors

Konstantinos Kogkalidis, Jean-Philippe Bernardy, Vikas Garg

Abstract

We introduce a novel positional encoding strategy for Transformer-style models, addressing the shortcomings of existing, often ad hoc, approaches. Our framework provides a flexible mapping from the algebraic specification of a domain to an interpretation as orthogonal operators. This design preserves the algebraic characteristics of the source domain, ensuring that the model upholds the desired structural properties. Our scheme can accommodate various structures, including sequences, grids and trees, as well as their compositions. We conduct a series of experiments to demonstrate the practical applicability of our approach. Results suggest performance on par with or surpassing the current state-of-the-art, without hyperparameter optimizations or task search'' of any kind.

Authors

Daolang Huang, Yujia Guo, Luigi Acerbi, Samuel Kaski

Abstract

Many critical decisions, such as personalized medical diagnoses and product pricing, are made based on insights gained from designing, observing, and analyzing a series of experiments. This highlights the crucial role of experimental design, which goes beyond merely collecting information on system parameters as in traditional Bayesian experimental design (BED), but also plays a key part in facilitating downstream decision-making. Most recent BED methods use an amortized policy network to rapidly design experiments. However, the information gathered through these methods is suboptimal for down-the-line decision-making, as the experiments are not inherently designed with downstream objectives in mind. In this paper, we present an amortized decision-aware BED framework that prioritizes maximizing downstream decision utility. We introduce a novel architecture, the Transformer Neural Decision Process (TNDP), capable of instantly proposing the next experimental design, whilst inferring the downstream decision, thus effectively amortizing both tasks within a unified workflow. We demonstrate the performance of our method across several tasks, showing that it can deliver informative designs and facilitate accurate decision-making.

Authors

Tuomas Kynkäänniemi, Miika Aittala, Tero Karras, Samuli Laine, Timo Aila, Jaakko Lehtinen

Abstract:

Guidance is a crucial technique for extracting the best performance out of image-generating diffusion models. Traditionally, a constant guidance weight has been applied throughout the sampling chain of an image. We show that guidance is clearly harmful toward the beginning of the chain (high noise levels), largely unnecessary toward the end (low noise levels), and only beneficial in the middle. We thus restrict it to a specific range of noise levels, improving both the inference speed and result quality. This limited guidance interval improves the record FID in ImageNet-512 significantly, from 1.81 to 1.40. We show that it is quantitatively and qualitatively beneficial across different sampler parameters, network architectures, and datasets, including the large-scale setting of Stable Diffusion XL. We thus suggest exposing the guidance interval as a hyperparameter in all diffusion models that use guidance.

Authors

Kirill Brilliantov, Amauri Souza, Vikas Garg

Abstract

Heterogeneity, e.g., due to different types of layers or multiple sub-models, poses key challenges in analyzing the generalization behavior of several modern architectures. For instance, descriptors based on Persistent Homology (PH) are being increasingly integrated into Graph Neural Networks (GNNs) to augment them with rich topological features; however, the generalization of such PH schemes remains unexplored. We introduce a novel compositional PAC-Bayes framework that provides a general recipe to analyze a broad spectrum of models including those with heterogeneous layers. Specifically, we provide the first data-dependent generalization bounds for a widely adopted PH vectorization scheme (that subsumes persistence landscapes, images, and silhouettes) as well as PH-augmented GNNs. Using our framework, we also obtain bounds for GNNs and neural nets with ease. Our bounds also inform the design of novel regularizers. Empirical evaluations on several standard real-world datasets demonstrate that our theoretical bounds highly correlate with empirical generalization performance, leading to improved classifier design via our regularizers. Overall, this work bridges a crucial gap in the theoretical understanding of PH methods and general heterogeneous models, paving the way for the design of better models for (graph) representation learning.

Giangiacomo Mercatali, Yogesh Verma, Andre Freitas, Vikas Garg

We introduce a novel score-based diffusion framework named Twigs that incorporates multiple co-evolving flows for enriching conditional generation tasks. Specifically, a central or trunk diffusion process is associated with a primary variable (e.g., graph structure), and additional offshoot or stem processes are dedicated to dependent variables (e.g., graph properties or labels). A new strategy, which we call loop guidance, effectively orchestrates the flow of information between the trunk and the stem processes during sampling. This approach allows us to uncover intricate interactions and dependencies, and unlock new generative capabilities. We provide extensive experiments to demonstrate strong performance gains of the proposed method over contemporary baselines in the context of conditional graph generation, underscoring the potential of Twigs in challenging generative tasks such as inverse molecular design and molecular optimization.

Authors

Nicola Dainese*, Matteo Merler*, Minttu Alakuijala, Pekka Marttinen (equal contribution)

Abstract

In this work we consider Code World Models, world models generated by a Large Language Model (LLM) in the form of Python code for model-based Reinforcement Learning (RL). Calling code instead of LLMs for planning has potential to be more precise, reliable, interpretable, and extremely efficient. However, writing appropriate Code World Models requires the ability to understand complex instructions, to generate exact code with non-trivial logic and to self-debug a long program with feedback from unit tests and environment trajectories. To address these challenges, we propose Generate, Improve and Fix with Monte Carlo Tree Search (GIF-MCTS), a new code generation strategy for LLMs. To test our approach in an offline RL setting, we introduce the Code World Models Benchmark (CWMB), a suite of program synthesis and planning tasks comprised of 18 diverse RL environments paired with corresponding textual descriptions and curated trajectories. GIF-MCTS surpasses all baselines on the CWMB and two other benchmarks, and we show that the Code World Models synthesized with it can be successfully used for planning, resulting in model-based RL agents with greatly improved sample efficiency and inference speed.

Authors

Tero Karras, Miika Aittala, Tuomas Kynkäänniemi, Jaakko Lehtinen, Timo Aila, Samuli Laine

Abstract

The primary axes of interest in image-generating diffusion models are image quality, the amount of variation in the results, and how well the results align with a given condition, e.g., a class label or a text prompt. The popular classifier-free guidance approach uses an unconditional model to guide a conditional model, leading to simultaneously better prompt alignment and higher-quality images at the cost of reduced variation. These effects seem inherently entangled, and thus hard to control. We make the surprising observation that it is possible to obtain disentangled control over image quality without compromising the amount of variation by guiding generation using a smaller, less-trained version of the model itself rather than an unconditional model. This leads to significant improvements in ImageNet generation, setting record FIDs of 1.01 for 64x64 and 1.25 for 512x512, using publicly available networks. Furthermore, the method is also applicable to unconditional diffusion models, drastically improving their quality.

Authors

Quoc Trung Trinh, Markus Heinonen, Luigi Acerbi, Samuel Kaski

Abstract

Time series data are essential in a wide range of machine learning (ML) applications. However, temporal data are often scarce or highly sensitive, limiting data sharing and the use of data-intensive ML methods. A possible solution to this problem is the generation of synthetic datasets that resemble real data. In this work, we introduce Time Series Generative Modeling (TSGM), an open-source framework for the generative modeling and evaluation of snthetic time series datasets. TSGM includes a broad repertoire of machine learning methods: generative models, probabilistic, simulation-based approaches, and augmentation techniques. The framework enables users to evaluate the quality of the produced data from different angles: similarity, downstream effectiveness, predictive consistency, diversity, fairness, and privacy. TSGM is extensible and user-friendly, which allows researchers to rapidly implement their own methods and compare them in a shareable environment. The framework has been tested on open datasets and in production and proved to be beneficial in both cases.

Authors

Aleksander Nikitin, Jannik Kossen, Yarin Gal, Pekka Marttinen

Abstract

Uncertainty quantification in Large Language Models (LLMs) is crucial for applications where safety and reliability are important. In particular, uncertainty can be used to improve the trustworthiness of LLMs by detecting factually incorrect model responses, commonly called hallucinations. Critically, one should seek to capture the model’s semantic uncertainty, i.e., the uncertainty over the meanings of LLM outputs, rather than uncertainty over lexical or syntactic variations that do not affect answer correctness. To address this problem, we propose Kernel Language Entropy (KLE), a novel method for uncertainty estimation in white- and black-box LLMs. KLE defines positive semidefinite unit trace kernels to encode the semantic similarities of LLM outputs and quantifies uncertainty using the von Neumann entropy. It considers pairwise semantic dependencies between answers (or semantic clusters), providing more fine-grained uncertainty estimates than previous methods based on hard clustering of answers. We theoretically prove that KLE generalizes the previous state-of-the-art method called semantic entropy and empirically demonstrate that it improves uncertainty quantification performance across multiple natural language generation datasets and LLM architectures.

Authors

Konstantinos Kogkalidis, Orestis Melkonian, Jean-Philippe Bernardy

Abstract

Agda is a dependently-typed programming language and a proof assistant, pivotal in proof formalization and programming language theory.This paper extends the Agda ecosystem into machine learning territory, and, vice versa, makes Agda-related resources available to machine learning practitioners.We introduce and release a novel dataset of Agda program-proofs that is elaborate and extensive enough to support various machine learning applications -- the first of its kind.Leveraging the dataset's ultra-high resolution, which details proof states at the sub-type level, we propose a novel neural architecture targeted at faithfully representing dependently-typed programs on the basis of structural rather than nominal principles.We instantiate and evaluate our architecture in a premise selection setup, where it achieves promising initial results, surpassing strong baselines.

Authors

Nasib Ullah, Erik Schultheis, Mike Lasby, Yani Ioannou, Rohit Babbar

Abstract

In recent years, Dynamic Sparse Training (DST) has emerged as an alternative to post-training pruning for generating efficient models. In principle, DST allows for a much more memory efficient training process, as it maintains sparsity throughout the entire training run. However, current DST implementations fail to capitalize on this. Because sparse matrix multiplication is much less efficient than dense matrix multiplication on GPUs, most implementations simulate sparsity by masking weights. In this paper, we leverage recent advances in semi-structured sparse training to apply DST in the domain of classification with large output spaces, where memory-efficiency is paramount. With a label space of possibly millions of candidates, the classification layer alone will consume several gigabytes of memory. Switching from a dense to a fixed fan-in sparse layer updated with sparse evolutionary training (SET); however, severely hampers training convergence, especially at the largest label spaces. We find that the gradients fed back from the classifier into the text encoder make it much more difficult to learn good input representations, despite using a dense encoder. By employing an intermediate layer or adding an auxiliary training objective, we recover most of the generalisation performance of the dense model. Overall, we demonstrate the applicability of DST in a challenging domain, characterized by a highly skewed label distribution, that lies outside of DST’s typical benchmark datasets, and enable end-to-end training with millions of labels on commodity hardware.

Authors

Oliver Hamelijnck, Arno Solin, Theodoros Damoulas

Abstract

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models. Gaussian processes (GPs) are particularly suited to this task as they can model complex, non-linear phenomena whilst incorporating prior knowledge and quantifying uncertainty. Current approaches have found some success but are limited as they either achieve poor computational scalings or focus only on the temporal setting. This work addresses these issues by introducing a variational spatio-temporal state-space GP that handles linear and non-linear physical constraints while achieving efficient linear-in-time computation costs. We demonstrate our methods in a range of synthetic and real-world settings and outperform the current state-of-the-art in both predictive and computational performance.

Authors

Sebastiaan De Peuter, Shibei Zhu, Yujia Guo, Andrew Howes, Samuel Kaski

Abstract

Preference learning methods make use of models of human choice in order to infer the latent utilities that underlie human behaviour. However, accurate modeling of human choice behavior is challenging due to a range of context effects that arise from how humans contrast and evaluate options. Cognitive science has proposed several models that capture these intricacies but, due to their intractable nature, work on preference learning has, in practice, had to rely on tractable but simplified variants of the well-known Bradley-Terry model. In this paper, we take one state-of-the-art intractable cognitive model and propose a tractable surrogate that is suitable for deployment in preference learning. We then introduce a mechanism for fitting the surrogate to human data that cannot be explained by the original cognitive model. We demonstrate on large-scale human data that this model produces significantly better inferences on static and actively elicited data than existing Bradley-Terry variants. We further show in simulation that when using this model for preference learning, we can significantly improve a utility in a range of real-world tasks.

Authors

Alexander Nikitin, Letizia Iannucci, Samuel Kaski

Abstract

Time series data are essential in a wide range of machine learning (ML) applications. However, temporal data are often scarce or highly sensitive, limiting data sharing and the use of data-intensive ML methods. A possible solution to this problem is the generation of synthetic datasets that resemble real data. In this work, we introduce Time Series Generative Modeling (TSGM), an open-source framework for the generative modeling and evaluation of synthetic time series datasets. TSGM includes a broad repertoire of machine learning methods: generative models, probabilistic, simulation-based approaches, and augmentation techniques. The framework enables users to evaluate the quality of the produced data from different angles: similarity, downstream effectiveness, predictive consistency, diversity, fairness, and privacy. TSGM is extensible and user-friendly, which allows researchers to rapidly implement their own methods and compare them in a shareable environment. The framework has been tested on open datasets and in production and proved to be beneficial in both cases.

Authors

Tuan Anh Pham, Vikas Garg

Abstract

Graph neural networks (GNNs) have been analyzed from multiple perspectives, including the WL-hierarchy, which exposes limits on their expressivity to distinguish graphs. However, characterizing the class of functions that they learn has remained unresolved. We address this fundamental question for message passing GNNs under ReLU activations, i.e., the de-facto choice for most GNNs.We first show that such GNNs learn tropical rational signomial maps or continuous piecewise linear functions, establishing an equivalence with feedforward networks (FNNs). We then elucidate the role of the choice of aggregation and update functions, and derive the first general upper and lower bounds on the geometric complexity (i.e., the number of linear regions), establishing new results for popular architectures such as GraphSAGE and GIN. We also introduce and theoretically analyze several new architectures to illuminate the relative merits of the feedforward and the message passing layers, and the tradeoffs involving depth and number of trainable parameters. Finally, we also characterize the decision boundary for node and graph classification tasks.