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This work compares large language models (LLMs) and neuro-symbolic approaches in solving Raven's progressive matrices (RPM), a visual abstract reasoning test that involves the understanding of mathematical rules such as progression or arithmetic addition. Providing the visual attributes directly as textual prompts, which assumes an oracle visual perception module, allows us to measure the model's abstract reasoning capability in isolation. Despite providing such compositionally structured representations from the oracle visual perception and advanced prompting techniques, both GPT-4 and Llama-3 70B cannot achieve perfect accuracy on the center constellation of the I-RAVEN dataset. Our analysis reveals that the root cause lies in the LLM's weakness in understanding and executing arithmetic rules. As a potential remedy, we analyze the Abductive Rule Learner with Context-awareness (ARLC), a neuro-symbolic approach that learns to reason with vector-symbolic architectures (VSAs). Here, concepts are represented with distributed vectors s.t. dot products between encoded vectors define a similarity kernel, and simple element-wise operations on the vectors perform addition/subtraction on the encoded values. We find that ARLC achieves almost perfect accuracy on the center constellation of I-RAVEN, demonstrating a high fidelity in arithmetic rules. To stress the length generalization capabilities of the models, we extend the RPM tests to larger matrices (3x10 instead of typical 3x3) and larger dynamic ranges of the attribute values (from 10 up to 1000). We find that the LLM's accuracy of solving arithmetic rules drops to sub-10%, especially as the dynamic range expands, while ARLC can maintain a high accuracy due to emulating symbolic computations on top of properly distributed representations. Our code is available at https://github.com/IBM/raven-large-language-models.

Kernel functions are vital ingredients of several machine learning algorithms, but often incur significant memory and computational costs. We introduce an approach to kernel approximation in machine learning algorithms suitable for mixed-signal Analog In-Memory Computing (AIMC) architectures. Analog In-Memory Kernel Approximation addresses the performance bottlenecks of conventional kernel-based methods by executing most operations in approximate kernel methods directly in memory. The IBM HERMES Project Chip, a state-of-the-art phase-change memory based AIMC chip, is utilized for the hardware demonstration of kernel approximation. Experimental results show that our method maintains high accuracy, with less than a 1% drop in kernel-based ridge classification benchmarks and within 1% accuracy on the Long Range Arena benchmark for kernelized attention in Transformer neural networks. Compared to traditional digital accelerators, our approach is estimated to deliver superior energy efficiency and lower power consumption. These findings highlight the potential of heterogeneous AIMC architectures to enhance the efficiency and scalability of machine learning applications.

We advance the recently proposed neuro-symbolic Differentiable Tree Machine, which learns tree operations using a combination of transformers and Tensor Product Representations. We investigate the architecture and propose two key components. We first remove a series of different transformer layers that are used in every step by introducing a mixture of experts. This results in a Differentiable Tree Experts model with a constant number of parameters for any arbitrary number of steps in the computation, compared to the previous method in the Differentiable Tree Machine with a linear growth. Given this flexibility in the number of steps, we additionally propose a new termination algorithm to provide the model the power to choose how many steps to make automatically. The resulting Terminating Differentiable Tree Experts model sluggishly learns to predict the number of steps without an oracle. It can do so while maintaining the learning capabilities of the model, converging to the optimal amount of steps., Comment: Accepted at the 18th International Conference on Neural-Symbolic Learning and Reasoning (NeSy) 2024

We introduce the Abductive Rule Learner with Context-awareness (ARLC), a model that solves abstract reasoning tasks based on Learn-VRF. ARLC features a novel and more broadly applicable training objective for abductive reasoning, resulting in better interpretability and higher accuracy when solving Raven's progressive matrices (RPM). ARLC allows both programming domain knowledge and learning the rules underlying a data distribution. We evaluate ARLC on the I-RAVEN dataset, showcasing state-of-the-art accuracy across both in-distribution and out-of-distribution (unseen attribute-rule pairs) tests. ARLC surpasses neuro-symbolic and connectionist baselines, including large language models, despite having orders of magnitude fewer parameters. We show ARLC's robustness to post-programming training by incrementally learning from examples on top of programmed knowledge, which only improves its performance and does not result in catastrophic forgetting of the programmed solution. We validate ARLC's seamless transfer learning from a 2x2 RPM constellation to unseen constellations. Our code is available at https://github.com/IBM/abductive-rule-learner-with-context-awareness., Comment: Accepted at the 18th International Conference on Neural-Symbolic Learning and Reasoning (NeSy) 2024 [Spotlight]

We analyze the capabilities of Transformer language models in learning compositional discrete tasks. To this end, we evaluate training LLaMA models and prompting GPT-4 and Gemini on four tasks demanding to learn a composition of several discrete sub-tasks. In particular, we measure how well these models can reuse primitives observable in the sub-tasks to learn the composition task. Our results indicate that compositional learning in state-of-the-art Transformer language models is highly sample inefficient: LLaMA requires more data samples than relearning all sub-tasks from scratch to learn the compositional task; in-context prompting with few samples is unreliable and fails at executing the sub-tasks or correcting the errors in multi-round code generation. Further, by leveraging complexity theory, we support these findings with a theoretical analysis focused on the sample inefficiency of gradient descent in memorizing feedforward models. We open source our code at https://github.com/IBM/limitations-lm-algorithmic-compositional-learning., Comment: NeurIPS 2024

Analog-Based In-Memory Computing (AIMC) inference accelerators can be used to efficiently execute Deep Neural Network (DNN) inference workloads. However, to mitigate accuracy losses, due to circuit and device non-idealities, Hardware-Aware (HWA) training methodologies must be employed. These typically require significant information about the underlying hardware. In this paper, we propose two Post-Training (PT) optimization methods to improve accuracy after training is performed. For each crossbar, the first optimizes the conductance range of each column, and the second optimizes the input, i.e, Digital-to-Analog Converter (DAC), range. It is demonstrated that, when these methods are employed, the complexity during training, and the amount of information about the underlying hardware can be reduced, with no notable change in accuracy ($\leq$0.1%) when finetuning the pretrained RoBERTa transformer model for all General Language Understanding Evaluation (GLUE) benchmark tasks. Additionally, it is demonstrated that further optimizing learned parameters PT improves accuracy., Comment: Accepted at 2024 IEEE International Symposium on Circuits and Systems (ISCAS)

While artificial intelligence (AI) models have achieved human or even superhuman performance in many well-defined applications, they still struggle to show signs of broad and flexible intelligence. The Abstraction and Reasoning Corpus (ARC), a visual intelligence benchmark introduced by Fran\c{c}ois Chollet, aims to assess how close AI systems are to human-like cognitive abilities. Most current approaches rely on carefully handcrafted domain-specific program searches to brute-force solutions for the tasks present in ARC. In this work, we propose a general learning-based framework for solving ARC. It is centered on transforming tasks from the vision to the language domain. This composition of language and vision allows for pre-trained models to be leveraged at each stage, enabling a shift from handcrafted priors towards the learned priors of the models. While not yet beating state-of-the-art models on ARC, we demonstrate the potential of our approach, for instance, by solving some ARC tasks that have not been solved previously., Comment: The first two authors have contributed equally to this work. Accepted as regular paper at CVPR 2023 Workshop and Challenges for New Frontiers in Visual Language Reasoning: Compositionality, Prompts and Causality (NFVLR)

Collaborative Filtering (CF) is a widely used technique which allows to leverage past users' preferences data to identify behavioural patterns and exploit them to predict custom recommendations. In this work, we illustrate our review of different CF techniques in the context of the Computational Intelligence Lab (CIL) CF project at ETH Z\"urich. After evaluating the performances of the individual models, we show that blending factorization-based and similarity-based approaches can lead to a significant error decrease (-9.4%) on the best-performing stand-alone model. Moreover, we propose a novel stochastic extension of a similarity model, SCSR, which consistently reduce the asymptotic complexity of the original algorithm.