Deep neural networks (DNNs) struggle at systematic generalization (SG). Several studies have evaluated the possibility of promoting SG through the proposal of novel architectures, loss functions, or training methodologies. Few studies, however, have focused on the role of training data properties in promoting SG. In this work, we investigate the impact of certain data distributional properties, as inductive biases for the SG ability of a multi-modal language model. To this end, we study three different properties. First, data diversity, instantiated as an increase in the possible values a latent property in the training distribution may take. Second, burstiness, where we probabilistically restrict the number of possible values of latent factors on particular inputs during training. Third, latent intervention, where a particular latent factor is altered randomly during training. We find that all three factors significantly enhance SG, with diversity contributing an 89% absolute increase in accuracy in the most affected property. Through a series of experiments, we test various hypotheses to understand why these properties promote SG. Finally, we find that Normalized Mutual Information (NMI) between latent attributes in the training distribution is strongly predictive of out-of-distribution generalization. We find that a mechanism by which lower NMI induces SG is in the geometry of representations. In particular, we find that NMI induces more parallelism in neural representations (i.e., input features coded in parallel neural vectors) of the model, a property related to the capacity of reasoning by analogy. Our code is available at: https://github.com/fdelrio89/data-systematic

We propose the first method to show theoretical limitations for one-layer softmax transformers with arbitrarily many precision bits (even infinite). We establish those limitations for three tasks that require advanced reasoning. The first task, Match 3 (Sanford et al., 2023), requires looking at all possible token triplets in an input sequence. The second and third tasks address compositionality-based reasoning: function composition (Peng et al., 2024) and binary relations composition, respectively. We formally prove the inability of one-layer softmax Transformers to solve any of these tasks. To overcome these limitations, we introduce Strassen attention and prove that, equipped with this mechanism, a one-layer transformer can in principle solve all these tasks. Importantly, we show that it enjoys sub-cubic running-time complexity, making it more scalable than similar previously proposed mechanisms, such as higher-order attention (Sanford et al., 2023). To complement our theoretical findings, we experimentally studied Strassen attention and compared it against standard (Vaswani et al, 2017), higher-order attention (Sanford et al., 2023), and triangular attention (Bergen et al. 2021). Our results help to disentangle all these attention mechanisms, highlighting their strengths and limitations. In particular, Strassen attention outperforms standard attention significantly on all the tasks. Altogether, understanding the theoretical limitations can guide research towards scalable attention mechanisms that improve the reasoning abilities of Transformers.

Understanding how Transformers work and how they process information is key to the theoretical and empirical advancement of these machines. In this work, we demonstrate the existence of two phenomena in Transformers, namely _isolation_ and _continuity_. Both of these phenomena hinder Transformers to learn even simple pattern sequences. Isolation expresses that any learnable sequence must be isolated from another learnable sequence, and hence some sequences cannot be learned by a single Transformer at the same time. Continuity entails that an attractor basin forms around a learned sequence, such that any sequence falling in that basin will collapse towards the learned sequence. Here, we mathematically prove these phenomena emerge in all Transformers that use compact positional encoding, and design rigorous experiments, demonstrating that the theoretical limitations we shed light on occur on the practical scale.

Recent advancements in natural language processing by large language models (LLMs), such as GPT-4, have been suggested to approach Artificial General Intelligence.And yet, it is still under dispute whether LLMs possess similar reasoning abilities to humans.This study evaluates GPT-4 and various other LLMs in judging the profoundness of mundane, motivational, and pseudo-profound statements.We found a significant statement-to-statement correlation between the LLMs and humans, irrespective of the type of statements and the prompting technique used.However, LLMs systematically overestimate the profoundness of nonsensical statements, with the exception of Tk-instruct, which uniquely underestimates the profoundness of statements.Only fewshot learning prompts, as opposed to chain-ofthought prompting, draw LLMs ratings closer to humans.Furthermore, this work provides insights into the potential biases induced by Reinforcement Learning from Human Feedback (RLHF), inducing an increase in the bias to overestimate the profoundness of statements.

We propose a general method to break down a main complex task into a set of intermediary easier sub-tasks, which are formulated in natural language as binary questions related to the final target task.Our method allows for representing each example by a vector consisting of the answers to these questions.We call this representation Natural Language Learned Features (NLLF).NLLF is generated by a small transformer language model (e.g., BERT) that has been trained in a Natural Language Inference (NLI) fashion, using weak labels automatically obtained from a Large Language Model (LLM).We show that the LLM normally struggles for the main task using in-context learning, but can handle these easiest subtasks and produce useful weak labels to train a BERT.The NLI-like training of the BERT allows for tackling zeroshot inference with any binary question, and not necessarily the ones seen during the training.We show that this NLLF vector not only helps to reach better performances by enhancing any classifier, but that it can be used as input of an easy-to-interpret machine learning model like a decision tree.This decision tree is interpretable but also reaches high performances, surpassing those of a pre-trained transformer in some cases.We have successfully applied this method to two completely different tasks: detecting incoherence in students' answers to open-ended mathematics exam questions, and screening abstracts for a systematic literature review of scientific papers on climate change and agroecology.

Adaptive sequential behavior is a hallmark of human cognition. In particular, humans can learn to produce precise spatiotemporal sequences given a certain context. For instance, musicians can not only reproduce learned action sequences in a context-dependent manner, they can also quickly and flexibly reapply them in any desired tempo or rhythm without overwriting previous learning. Existing neural network models fail to account for these properties. We argue that this limitation emerges from the fact that sequence information (i.e., the position of the action) and timing (i.e., the moment of response execution) are typically stored in the same neural network weights. Here, we augment a biologically plausible recurrent neural network of cortical dynamics to include a basal ganglia-thalamic module which uses reinforcement learning to dynamically modulate action. This "associative cluster-dependent chain" (ACDC) model modularly stores sequence and timing information in distinct loci of the network. This feature increases computational power and allows ACDC to display a wide range of temporal properties (e.g., multiple sequences, temporal shifting, rescaling, and compositionality), while still accounting for several behavioral and neurophysiological empirical observations. Finally, we apply this ACDC network to show how it can learn the famous "Thunderstruck" song intro and then flexibly play it in a "bossa nova" rhythm without further training.