Takuya Ito

Takuya Ito, Murray Campbell, Lior Horesh et al.

The rapid development of artificial intelligence (AI) systems has created an urgent need for their scientific quantification. While their fluency across a variety of domains is impressive, AI systems fall short on tests requiring algorithmic reasoning -- a glaring limitation given the necessity for interpretable and reliable technology. Despite a surge of reasoning benchmarks emerging from the academic community, no theoretical framework exists to quantify algorithmic reasoning in AI systems. Here, we adopt a framework from computational complexity theory to quantify algorithmic generalization using algebraic expressions: algebraic circuit complexity. Algebraic circuit complexity theory -- the study of algebraic expressions as circuit models -- is a natural framework to study the complexity of algorithmic computation. Algebraic circuit complexity enables the study of generalization by defining benchmarks in terms of the computational requirements to solve a problem. Moreover, algebraic circuits are generic mathematical objects; an arbitrarily large number of samples can be generated for a specified circuit, making it an ideal experimental sandbox for the data-hungry models that are used today. In this Perspective, we adopt tools from algebraic circuit complexity, apply them to formalize a science of algorithmic generalization, and address key challenges for its successful application to AI science.

Xiaoxuan Lei, Takuya Ito, Pouya Bashivan

Working memory is a central cognitive ability crucial for intelligent decision-making. Recent experimental and computational work studying working memory has primarily used categorical (i.e., one-hot) inputs, rather than ecologically relevant, multidimensional naturalistic ones. Moreover, studies have primarily investigated working memory during single or few cognitive tasks. As a result, an understanding of how naturalistic object information is maintained in working memory in neural networks is still lacking. To bridge this gap, we developed sensory-cognitive models, comprising a convolutional neural network (CNN) coupled with a recurrent neural network (RNN), and trained them on nine distinct N-back tasks using naturalistic stimuli. By examining the RNN's latent space, we found that: (1) Multi-task RNNs represent both task-relevant and irrelevant information simultaneously while performing tasks; (2) The latent subspaces used to maintain specific object properties in vanilla RNNs are largely shared across tasks, but highly task-specific in gated RNNs such as GRU and LSTM; (3) Surprisingly, RNNs embed objects in new representational spaces in which individual object features are less orthogonalized relative to the perceptual space; (4) The transformation of working memory encodings (i.e., embedding of visual inputs in the RNN latent space) into memory was shared across stimuli, yet the transformations governing the retention of a memory in the face of incoming distractor stimuli were distinct across time. Our findings indicate that goal-driven RNNs employ chronological memory subspaces to track information over short time spans, enabling testable predictions with neural data.

Takuya Ito, Luca Cocchi, Tim Klinger et al.

In transformers, the positional encoding (PE) provides essential information that distinguishes the position and order amongst tokens in a sequence. Most prior investigations of PE effects on generalization were tailored to 1D input sequences, such as those presented in natural language, where adjacent tokens (e.g., words) are highly related. In contrast, many real world tasks involve datasets with highly non-trivial positional arrangements, such as datasets organized in multiple spatial dimensions, or datasets for which ground truth positions are not known. Here we find that the choice of initialization of a learnable PE greatly influences its ability to learn interpretable PEs that lead to enhanced generalization. We empirically demonstrate our findings in three experiments: 1) A 2D relational reasoning task; 2) A nonlinear stochastic network simulation; 3) A real world 3D neuroscience dataset, applying interpretability analyses to verify the learning of accurate PEs. Overall, we find that a learned PE initialized from a small-norm distribution can 1) uncover interpretable PEs that mirror ground truth positions in multiple dimensions, and 2) lead to improved generalization. These results illustrate the feasibility of learning identifiable and interpretable PEs for enhanced generalization.

Takuya Ito, Soham Dan, Mattia Rigotti et al.

The advent of the Transformer has led to the development of large language models (LLM), which appear to demonstrate human-like capabilities. To assess the generality of this class of models and a variety of other base neural network architectures to multimodal domains, we evaluated and compared their capacity for multimodal generalization. We introduce a multimodal question-answer benchmark to evaluate three specific types of out-of-distribution (OOD) generalization performance: distractor generalization (generalization in the presence of distractors), systematic compositional generalization (generalization to new task permutations), and productive compositional generalization (generalization to more complex tasks structures). We found that across model architectures (e.g., RNNs, Transformers, Perceivers, etc.), models with multiple attention layers, or models that leveraged cross-attention mechanisms between input domains, fared better. Our positive results demonstrate that for multimodal distractor and systematic generalization, either cross-modal attention or models with deeper attention layers are key architectural features required to integrate multimodal inputs. On the other hand, neither of these architectural features led to productive generalization, suggesting fundamental limitations of existing architectures for specific types of multimodal generalization. These results demonstrate the strengths and limitations of specific architectural components underlying modern neural models for multimodal reasoning. Finally, we provide Generic COG (gCOG), a configurable benchmark with several multimodal generalization splits, for future studies to explore.