Analyzing volumetric data with rotational invariance or equivariance is an active topic in current research. Existing deep-learning approaches utilize either group convolutional networks limited to discrete rotations or steerable convolutional networks with constrained filter structures. This work proposes a novel equivariant neural network architecture that achieves analytical Equivariance to Local Pattern Orientation on the continuous SO(3) group while allowing unconstrained trainable filters - EquiLoPO Network. Our key innovations are a group convolutional operation leveraging irreducible representations as the Fourier basis and a local activation function in the SO(3) space that provides a well-defined mapping from input to output functions, preserving equivariance. By integrating these operations into a ResNet-style architecture, we propose a model that overcomes the limitations of prior methods. A comprehensive evaluation on diverse 3D medical imaging datasets from MedMNIST3D demonstrates the effectiveness of our approach, which consistently outperforms state of the art. This work suggests the benefits of true rotational equivariance on SO(3) and flexible unconstrained filters enabled by the local activation function, providing a flexible framework for equivariant deep learning on volumetric data with potential applications across domains. Our code is publicly available at \url{https://gricad-gitlab.univ-grenoble-alpes.fr/GruLab/ILPO/-/tree/main/EquiLoPO}.

Effective recognition of spatial patterns and learning their hierarchy is crucial in modern spatial data analysis. Volumetric data applications seek techniques ensuring invariance not only to shifts but also to pattern rotations. While traditional methods can readily achieve translational invariance, rotational invariance possesses multiple challenges and remains an active area of research. Here, we present ILPO-Net (Invariant to Local Patterns Orientation Network), a novel approach that handles arbitrarily shaped patterns with the convolutional operation inherently invariant to local spatial pattern orientations using the Wigner matrix expansions. Our architecture seamlessly integrates the new convolution operator and, when benchmarked on diverse volumetric datasets such as MedMNIST and CATH, demonstrates superior performance over the baselines with significantly reduced parameter counts - up to 1000 times fewer in the case of MedMNIST. Beyond these demonstrations, ILPO-Net's rotational invariance paves the way for other applications across multiple disciplines. Our code is publicly available at https://gricad-gitlab.univ-grenoble-alpes.fr/GruLab/ILPO/-/tree/main/ILPONet.

Modular deep learning is the state-of-the-art solution for lifting the curse of multilinguality, preventing the impact of negative interference and enabling cross-lingual performance in Multilingual Pre-trained Language Models. However, a trade-off of this approach is the reduction in positive transfer learning from closely related languages. In response, we introduce a novel method called language arithmetic, which enables training-free post-processing to address this limitation. Inspired by the task arithmetic framework, we apply learning via addition to the language adapters, transitioning the framework from a multi-task to a multilingual setup. The effectiveness of the proposed solution is demonstrated on three downstream tasks in a MAD-X-based set of cross-lingual schemes, acting as a post-processing procedure. Language arithmetic consistently improves the baselines with significant gains in the most challenging cases of zero-shot and low-resource applications. Our code and models are available at https://github.com/mklimasz/language-arithmetic .

The pretraining of state-of-the-art large language models now requires trillions of words of text, which is orders of magnitude more than available for the vast majority of languages. While including text in more than one language is an obvious way to acquire more pretraining data, multilinguality is often seen as a curse, and most model training efforts continue to focus near-exclusively on individual large languages. We believe that multilinguality can be a blessing and that it should be possible to substantially improve over the capabilities of monolingual models for small languages through multilingual training. In this study, we introduce Poro 34B, a 34 billion parameter model trained for 1 trillion tokens of Finnish, English, and programming languages, and demonstrate that a multilingual training approach can produce a model that not only substantially advances over the capabilities of existing models for Finnish, but also excels in translation and is competitive in its class in generating English and programming languages. We release the model parameters, scripts, and data under open licenses at https://huggingface.co/LumiOpen/Poro-34B.

Federated learning is an emerging machine learning approach that allows the construction of a model between several participants who hold their own private data. This method is secure and privacy-preserving, suitable for training a machine learning model using sensitive data from different sources, such as hospitals. In this paper, the authors propose two innovative methodologies for Particle Swarm Optimisation-based federated learning of Fuzzy Cognitive Maps in a privacy-preserving way. In addition, one relevant contribution this research includes is the lack of an initial model in the federated learning process, making it effectively blind. This proposal is tested with several open datasets, improving both accuracy and precision.

This study explores the use of Large Language Models (LLMs) for automatic evaluation of knowledge graph (KG) completion models. Historically, validating information in KGs has been a challenging task, requiring large-scale human annotation at prohibitive cost. With the emergence of general-purpose generative AI and LLMs, it is now plausible that human-in-the-loop validation could be replaced by a generative agent. We introduce a framework for consistency and validation when using generative models to validate knowledge graphs. Our framework is based upon recent open-source developments for structural and semantic validation of LLM outputs, and upon flexible approaches to fact checking and verification, supported by the capacity to reference external knowledge sources of any kind. The design is easy to adapt and extend, and can be used to verify any kind of graph-structured data through a combination of model-intrinsic knowledge, user-supplied context, and agents capable of external knowledge retrieval.

Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinear Dynamical Systems (\sindy) framework, which uses sparse regression to identify governing equations from data. This study introduces an enhanced method, Nested SINDy, that aims to increase the expressivity of the SINDy approach thanks to a nested structure. Indeed, traditional symbolic regression and system identification methods often fail with complex systems that cannot be easily described analytically. Nested SINDy builds on the SINDy framework by introducing additional layers before and after the core SINDy layer. This allows the method to identify symbolic representations for a wider range of systems, including those with compositions and products of functions. We demonstrate the ability of the Nested SINDy approach to accurately find symbolic expressions for simple systems, such as basic trigonometric functions, and sparse (false but accurate) analytical representations for more complex systems. Our results highlight Nested SINDy's potential as a tool for symbolic regression, surpassing the traditional SINDy approach in terms of expressivity. However, we also note the challenges in the optimization process for Nested SINDy and suggest future research directions, including the designing of a more robust methodology for the optimization process. This study proves that Nested SINDy can effectively discover symbolic representations of dynamical systems from data, offering new opportunities for understanding complex systems through data-driven methods.

With the advent of large language models(LLMs) enhanced by the chain-of-thought(CoT) methodology, visual reasoning problem is usually decomposed into manageable sub-tasks and tackled sequentially with various external tools. However, such a paradigm faces the challenge of the potential "determining hallucinations" in decision-making due to insufficient visual information and the limitation of low-level perception tools that fail to provide abstract summaries necessary for comprehensive reasoning. We argue that converging visual context acquisition and logical reasoning is pivotal for tackling visual reasoning tasks. This paper delves into the realm of multimodal CoT to solve intricate visual reasoning tasks with multimodal large language models(MLLMs) and their cognitive capability. To this end, we propose an innovative multimodal CoT framework, termed Cantor, characterized by a perception-decision architecture. Cantor first acts as a decision generator and integrates visual inputs to analyze the image and problem, ensuring a closer alignment with the actual context. Furthermore, Cantor leverages the advanced cognitive functions of MLLMs to perform as multifaceted experts for deriving higher-level information, enhancing the CoT generation process. Our extensive experiments demonstrate the efficacy of the proposed framework, showing significant improvements in multimodal CoT performance across two complex visual reasoning datasets, without necessitating fine-tuning or ground-truth rationales. Project Page: https://ggg0919.github.io/cantor/ .

Sequence modeling is a crucial area across various domains, including Natural Language Processing (NLP), speech recognition, time series forecasting, music generation, and bioinformatics. Recurrent Neural Networks (RNNs) and Long Short Term Memory Networks (LSTMs) have historically dominated sequence modeling tasks like Machine Translation, Named Entity Recognition (NER), etc. However, the advancement of transformers has led to a shift in this paradigm, given their superior performance. Yet, transformers suffer from $O(N^2)$ attention complexity and challenges in handling inductive bias. Several variations have been proposed to address these issues which use spectral networks or convolutions and have performed well on a range of tasks. However, they still have difficulty in dealing with long sequences. State Space Models(SSMs) have emerged as promising alternatives for sequence modeling paradigms in this context, especially with the advent of S4 and its variants, such as S4nd, Hippo, Hyena, Diagnol State Spaces (DSS), Gated State Spaces (GSS), Linear Recurrent Unit (LRU), Liquid-S4, Mamba, etc. In this survey, we categorize the foundational SSMs based on three paradigms namely, Gating architectures, Structural architectures, and Recurrent architectures. This survey also highlights diverse applications of SSMs across domains such as vision, video, audio, speech, language (especially long sequence modeling), medical (including genomics), chemical (like drug design), recommendation systems, and time series analysis, including tabular data. Moreover, we consolidate the performance of SSMs on benchmark datasets like Long Range Arena (LRA), WikiText, Glue, Pile, ImageNet, Kinetics-400, sstv2, as well as video datasets such as Breakfast, COIN, LVU, and various time series datasets. The project page for Mamba-360 work is available on this webpage.\url{https://github.com/badripatro/mamba360}.

Structured data sources, such as tables, graphs, and databases, are ubiquitous knowledge sources. Despite the demonstrated capabilities of large language models (LLMs) on plain text, their proficiency in interpreting and utilizing structured data remains limited. Our investigation reveals a notable deficiency in LLMs' ability to process structured data, e.g., ChatGPT lags behind state-of-the-art (SoTA) model by an average of 35%. To augment the Structured Knowledge Grounding (SKG) capabilities in LLMs, we have developed a comprehensive instruction tuning dataset comprising 1.1 million examples. Utilizing this dataset, we train a series of models, referred to as StructLM, based on the Mistral and the CodeLlama model family, ranging from 7B to 34B parameters. Our StructLM series surpasses task-specific models on 16 out of 18 evaluated datasets and establishes new SoTA performance on 8 SKG tasks. Furthermore, StructLM demonstrates strong generalization across 6 novel held-out SKG tasks, outperforming TableLlama by an average of 35\% and Flan-UL2 20B by an average of 10\%. Contrary to expectations, we observe that scaling model size offers marginal benefits, with StructLM-34B showing only slight improvements over StructLM-7B. This suggests that structured knowledge grounding is still a challenging task and requires more innovative design to push to a new level.