The problem of learning single index and multi index models has gained significant interest as a fundamental task in high-dimensional statistics. Many recent works have analysed gradient-based methods, particularly in the setting of isotropic data distributions, often in the context of neural network training. Such studies have uncovered precise characterisations of algorithmic sample complexity in terms of certain analytic properties of the target function, such as the leap, information, and generative exponents. These properties establish a quantitative separation between low and high complexity learning tasks. In this work, we show that high complexity cases are rare. Specifically, we prove that introducing a small random perturbation to the data distribution--via a random shift in the first moment--renders any Gaussian single index model as easy to learn as a linear function. We further extend this result to a class of multi index models, namely sparse Boolean functions, also known as Juntas.

Novel materials drive progress across applications from energy storage to electronics. Automated characterization of material structures with machine learning methods offers a promising strategy for accelerating this key step in material design. In this work, we introduce an autoregressive language model that performs crystal structure prediction (CSP) from powder diffraction data. The presented model, deCIFer, generates crystal structures in the widely used Crystallographic Information File (CIF) format and can be conditioned on powder X-ray diffraction (PXRD) data. Unlike earlier works that primarily rely on high-level descriptors like composition, deCIFer performs CSP from diffraction data. We train deCIFer on nearly 2.3M unique crystal structures and validate on diverse sets of PXRD patterns for characterizing challenging inorganic crystal systems. Qualitative and quantitative assessments using the residual weighted profile and Wasserstein distance show that deCIFer produces structures that more accurately match the target diffraction data when conditioned, compared to the unconditioned case. Notably, deCIFer can achieve a 94% match rate on unseen data. deCIFer bridges experimental diffraction data with computational CSP, lending itself as a powerful tool for crystal structure characterization and accelerating materials discovery.

In this paper, we experiment with novelty-based variants of OpenAI-ES, the NS-ES and NSR-ES algorithms, and evaluate their effectiveness in training complex, transformer-based architectures designed for the problem of reinforcement learning such as Decision Transformers. We also test if we can accelerate the novelty-based training of these larger models by seeding the training by a pretrained models. By this, we build on our previous work, where we tested the ability of evolution strategies - specifically the aforementioned OpenAI-ES - to train the Decision Transformer architecture. The results were mixed. NS-ES showed progress, but it would clearly need many more iterations for it to yield interesting results. NSR-ES, on the other hand, proved quite capable of being straightforwardly used on larger models, since its performance appears as similar between the feed-forward model and Decision Transformer, as it was for the OpenAI-ES in our previous work.

While encoder-only models such as BERT and ModernBERT are ubiquitous in real-world NLP applications, their conventional reliance on task-specific classification heads can limit their applicability compared to decoder-based large language models (LLMs). In this work, we introduce ModernBERT-Large-Instruct, a 0.4B-parameter encoder model that leverages its masked language modelling (MLM) head for generative classification. Our approach employs an intentionally simple training loop and inference mechanism that requires no heavy pre-processing, heavily engineered prompting, or architectural modifications. ModernBERT-Large-Instruct exhibits strong zero-shot performance on both classification and knowledge-based tasks, outperforming similarly sized LLMs on MMLU and achieving 93% of Llama3-1B's MMLU performance with 60% less parameters. We also demonstrate that, when fine-tuned, the generative approach using the MLM head matches or even surpasses traditional classification-head methods across diverse NLU tasks.This capability emerges specifically in models trained on contemporary, diverse data mixes, with models trained on lower volume, less-diverse data yielding considerably weaker performance. Although preliminary, these results demonstrate the potential of using the original generative masked language modelling head over traditional task-specific heads for downstream tasks. Our work suggests that further exploration into this area is warranted, highlighting many avenues for future improvements.

Negation, a linguistic construct conveying absence, denial, or contradiction, poses significant challenges for multilingual multimodal foundation models. These models excel in tasks like machine translation, text-guided generation, image captioning, audio interactions, and video processing but often struggle to accurately interpret negation across diverse languages and cultural contexts. In this perspective paper, we propose a comprehensive taxonomy of negation constructs, illustrating how structural, semantic, and cultural factors influence multimodal foundation models. We present open research questions and highlight key challenges, emphasizing the importance of addressing these issues to achieve robust negation handling. Finally, we advocate for specialized benchmarks, language-specific tokenization, fine-grained attention mechanisms, and advanced multimodal architectures. These strategies can foster more adaptable and semantically precise multimodal foundation models, better equipped to navigate and accurately interpret the complexities of negation in multilingual, multimodal environments.

O'Boyle 1, Sida Wang 2, Gabriel Synnaeve 2, Hugh Leather 2 1 University of Edinburgh 2 Meta AI A BSTRACT Code generation and understanding are critical capabilities for large language models (LLMs). Thus, most LLMs are pretrained and fine-tuned on code data. However, these datasets typically treat code as static strings and rarely exploit the dynamic information about their execution. Building upon previous work on trace modeling, we study Execution Tuning (E.T.), a training procedure in which we explicitly model real-world program execution traces without requiring manual test annotations. We train and evaluate models on different execution trace granularities (line and instruction-level) and strategies on the task of output prediction, obtaining 80% accuracy on CruxEval and MBPP, and showing the advantages of dynamic scratchpads (i.e., self-contained intermediate computations updated by the model rather than accumulated as a history of past computations) on long executions (up to 14k steps). Finally, we discuss E.T.'s practical applications. Current state-of-the-art general-purpose LLMs are thought to contain considerable proportions of code in their pretraining data (OpenAI et al., 2024), which is known to improve reasoning capabilities even in tasks seemingly unrelated to code (Aryabumi et al., 2024). However, datasets used to train code LLMs (such as Lozhkov et al. (2024)) typically treat code as static strings and rarely exploit the dynamic information about their execution. Executability is one of the key differences between code and natural language, and most code datasets neglect dimensions of the code domain such as reasoning over code execution, which in turn could lead to better code understanding. This fundamental limitation has sparked a renewed interest in modeling program executions, connecting with the pre-LLM neural program evaluation literature (Zaremba & Sutskever, 2014; Graves et al., 2014), which studied whether neural networks could learn to execute programs.

In sparse principal component analysis we are given noisy observations of a lowrank matrix of dimension n p and seek to reconstruct it under additional sparsity assumptions.

This paper presents a representation theory for permutation-valued functions, which in their general form can also be called listwise ranking functions. Pointwise ranking functions assign a score to each object independently, without taking into account the other objects under consideration; whereas listwise loss functions evaluate the set of scores assigned to all objects as a whole. In many supervised learning to rank tasks, it might be of interest to use listwise ranking functions instead; in particular, the Bayes Optimal ranking functions might themselves be listwise, especially if the loss function is listwise. A key caveat to using listwise ranking functions has been the lack of an appropriate representation theory for such functions. We show that a natural symmetricity assumption that we call exchangeability allows us to explicitly characterize the set of such exchangeable listwise ranking functions. Our analysis draws from the theories of tensor analysis, functional analysis and De Finetti theorems. We also present experiments using a novel reranking method motivated by our representation theory.

We present a technique for significantly speeding up Alternating Least Squares (ALS) and Gradient Descent (GD), two widely used algorithms for tensor factorization. By exploiting properties of the Khatri-Rao product, we show how to efficiently address a computationally challenging sub-step of both algorithms. Our algorithm, DFacTo, only requires two sparse matrix-vector products and is easy to parallelize. DFacTo is not only scalable but also on average 4 to 10 times faster than competing algorithms on a variety of datasets. For instance, DFacTo only takes 480 seconds on 4 machines to perform one iteration of the ALS algorithm and 1,143 seconds to perform one iteration of the GD algorithm on a 6.5 million 2.5 million 1.5 million dimensional tensor with 1.2 billion non-zero entries.

We consider the Principal Component Analysis problem for large tensors of arbitrary order k under a single-spike (or rank-one plus noise) model. On the one hand, we use information theory, and recent results in probability theory, to establish necessary and sufficient conditions under which the principal component can be estimated using unbounded computational resources. It turns out that this is possible as soon as the signal-to-noise ratio β becomes larger than C k log k (and in particular β can remain bounded as the problem dimensions increase). On the other hand, we analyze several polynomial-time estimation algorithms, based on tensor unfolding, power iteration and message passing ideas from graphical models. We show that, unless the signal-to-noise ratio diverges in the system dimensions, none of these approaches succeeds. This is possibly related to a fundamental limitation of computationally tractable estimators for this problem. We discuss various initializations for tensor power iteration, and show that a tractable initialization based on the spectrum of the unfolded tensor outperforms significantly baseline methods, statistically and computationally. Finally, we consider the case in which additional side information is available about the unknown signal. We characterize the amount of side information that allows the iterative algorithms to converge to a good estimate.