Tankut Can

Antonios Georgiou, Tankut Can, Mikhail Katkov et al.

The statistical study of human memory requires large-scale experiments, involving many stimuli conditions and test subjects. While this approach has proven to be quite fruitful for meaningless material such as random lists of words, naturalistic stimuli, like narratives, have until now resisted such a large-scale study, due to the quantity of manual labor required to design and analyze such experiments. In this work, we develop a pipeline that uses large language models (LLMs) both to design naturalistic narrative stimuli for large-scale recall and recognition memory experiments, as well as to analyze the results. We performed online memory experiments with a large number of participants and collected recognition and recall data for narratives of different sizes. We found that both recall and recognition performance scale linearly with narrative length; however, for longer narratives people tend to summarize the content rather than recalling precise details. To investigate the role of narrative comprehension in memory, we repeated these experiments using scrambled versions of the narratives. Although recall performance declined significantly, recognition remained largely unaffected. Recalls in this condition seem to follow the original narrative order rather than the actual scrambled presentation, pointing to a contextual reconstruction of the story in memory. Finally, using LLM text embeddings, we construct a simple measure for each clause based on semantic similarity to the whole narrative, that shows a strong correlation with recall probability. Overall, our work demonstrates the power of LLMs in accessing new regimes in the study of human memory, as well as suggesting novel psychologically informed benchmarks for LLM performance.

Weishun Zhong, Doron Sivan, Tankut Can et al.

The entropy rate of printed English is famously estimated to be about one bit per character, a benchmark that modern large language models (LLMs) have only recently approached. This entropy rate implies that English contains nearly 80 percent redundancy relative to the five bits per character expected for random text. We introduce a statistical model that attempts to capture the intricate multi-scale structure of natural language, providing a first-principles account of this redundancy level. Our model describes a procedure of self-similarly segmenting text into semantically coherent chunks down to the single-word level. The semantic structure of the text can then be hierarchically decomposed, allowing for analytical treatment. Numerical experiments with modern LLMs and open datasets suggest that our model quantitatively captures the structure of real texts at different levels of the semantic hierarchy. The entropy rate predicted by our model agrees with the estimated entropy rate of printed English. Moreover, our theory further reveals that the entropy rate of natural language is not fixed but should increase systematically with the semantic complexity of corpora, which are captured by the only free parameter in our model.

Timothy Doyeon Kim, Tankut Can, Kamesh Krishnamurthy

Understanding how the dynamics in biological and artificial neural networks implement the computations required for a task is a salient open question in machine learning and neuroscience. In particular, computations requiring complex memory storage and retrieval pose a significant challenge for these networks to implement or learn. Recently, a family of models described by neural ordinary differential equations (nODEs) has emerged as powerful dynamical neural network models capable of capturing complex dynamics. Here, we extend nODEs by endowing them with adaptive timescales using gating interactions. We refer to these as gated neural ODEs (gnODEs). Using a task that requires memory of continuous quantities, we demonstrate the inductive bias of the gnODEs to learn (approximate) continuous attractors. We further show how reduced-dimensional gnODEs retain their modeling power while greatly improving interpretability, even allowing explicit visualization of the structure of learned attractors. We introduce a novel measure of expressivity which probes the capacity of a neural network to generate complex trajectories. Using this measure, we explore how the phase-space dimension of the nODEs and the complexity of the function modeling the flow field contribute to expressivity. We see that a more complex function for modeling the flow field allows a lower-dimensional nODE to capture a given target dynamics. Finally, we demonstrate the benefit of gating in nODEs on several real-world tasks.

Aditya Cowsik, Tankut Can, Paolo Glorioso

Commonly used optimization algorithms often show a trade-off between good generalization and fast training times. For instance, stochastic gradient descent (SGD) tends to have good generalization; however, adaptive gradient methods have superior training times. Momentum can help accelerate training with SGD, but so far there has been no principled way to select the momentum hyperparameter. Here we study training dynamics arising from the interplay between SGD with label noise and momentum in the training of overparametrized neural networks. We find that scaling the momentum hyperparameter $1-β$ with the learning rate to the power of $2/3$ maximally accelerates training, without sacrificing generalization. To analytically derive this result we develop an architecture-independent framework, where the main assumption is the existence of a degenerate manifold of global minimizers, as is natural in overparametrized models. Training dynamics display the emergence of two characteristic timescales that are well-separated for generic values of the hyperparameters. The maximum acceleration of training is reached when these two timescales meet, which in turn determines the scaling limit we propose. We confirm our scaling rule for synthetic regression problems (matrix sensing and teacher-student paradigm) and classification for realistic datasets (ResNet-18 on CIFAR10, 6-layer MLP on FashionMNIST), suggesting the robustness of our scaling rule to variations in architectures and datasets.

Weishun Zhong, Tankut Can, Antonis Georgiou et al.

Traditional studies of memory for meaningful narratives focus on specific stories and their semantic structures but do not address common quantitative features of recall across different narratives. We introduce a statistical ensemble of random trees to represent narratives as hierarchies of key points, where each node is a compressed representation of its descendant leaves, which are the original narrative segments. Recall is modeled as constrained by working memory capacity from this hierarchical structure. Our analytical solution aligns with observations from large-scale narrative recall experiments. Specifically, our model explains that (1) average recall length increases sublinearly with narrative length, and (2) individuals summarize increasingly longer narrative segments in each recall sentence. Additionally, the theory predicts that for sufficiently long narratives, a universal, scale-invariant limit emerges, where the fraction of a narrative summarized by a single recall sentence follows a distribution independent of narrative length.

Tankut Can

The basic problem of semantic compression is to minimize the length of a message while preserving its meaning. This differs from classical notions of compression in that the distortion is not measured directly at the level of bits, but rather in an abstract semantic space. In order to make this precise, we take inspiration from cognitive neuroscience and machine learning and model semantic space as a continuous Euclidean vector space. In such a space, stimuli like speech, images, or even ideas, are mapped to high-dimensional real vectors, and the location of these embeddings determines their meaning relative to other embeddings. This suggests that a natural metric for semantic similarity is just the Euclidean distance, which is what we use in this work. We map the optimization problem of determining the minimal-length, meaning-preserving message to a spin glass Hamiltonian and solve the resulting statistical mechanics problem using replica theory. We map out the replica symmetric phase diagram, identifying distinct phases of semantic compression: a first-order transition occurs between lossy and lossless compression, whereas a continuous crossover is seen from extractive to abstractive compression. We conclude by showing numerical simulations of compressions obtained by simulated annealing and greedy algorithms, and argue that while the problem of finding a meaning-preserving compression is computationally hard in the worst case, there exist efficient algorithms which achieve near optimal performance in the typical case.

Kamesh Krishnamurthy, Tankut Can, David J. Schwab

Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) and neuroscience. Prior theoretical work has focused on RNNs with additive interactions. However, gating - i.e. multiplicative - interactions are ubiquitous in real neurons and also the central feature of the best-performing RNNs in ML. Here, we show that gating offers flexible control of two salient features of the collective dynamics: i) timescales and ii) dimensionality. The gate controlling timescales leads to a novel, marginally stable state, where the network functions as a flexible integrator. Unlike previous approaches, gating permits this important function without parameter fine-tuning or special symmetries. Gates also provide a flexible, context-dependent mechanism to reset the memory trace, thus complementing the memory function. The gate modulating the dimensionality can induce a novel, discontinuous chaotic transition, where inputs push a stable system to strong chaotic activity, in contrast to the typically stabilizing effect of inputs. At this transition, unlike additive RNNs, the proliferation of critical points (topological complexity) is decoupled from the appearance of chaotic dynamics (dynamical complexity). The rich dynamics are summarized in phase diagrams, thus providing a map for principled parameter initialization choices to ML practitioners.

Tankut Can, Kamesh Krishnamurthy, David J. Schwab

Recurrent neural networks (RNNs) are powerful dynamical models for data with complex temporal structure. However, training RNNs has traditionally proved challenging due to exploding or vanishing of gradients. RNN models such as LSTMs and GRUs (and their variants) significantly mitigate these issues associated with training by introducing various types of gating units into the architecture. While these gates empirically improve performance, how the addition of gates influences the dynamics and trainability of GRUs and LSTMs is not well understood. Here, we take the perspective of studying randomly initialized LSTMs and GRUs as dynamical systems, and ask how the salient dynamical properties are shaped by the gates. We leverage tools from random matrix theory and mean-field theory to study the state-to-state Jacobians of GRUs and LSTMs. We show that the update gate in the GRU and the forget gate in the LSTM can lead to an accumulation of slow modes in the dynamics. Moreover, the GRU update gate can poise the system at a marginally stable point. The reset gate in the GRU and the output and input gates in the LSTM control the spectral radius of the Jacobian, and the GRU reset gate also modulates the complexity of the landscape of fixed-points. Furthermore, for the GRU we obtain a phase diagram describing the statistical properties of fixed-points. We also provide a preliminary comparison of training performance to the various dynamical regimes realized by varying hyperparameters. Looking to the future, we have introduced a powerful set of techniques which can be adapted to a broad class of RNNs, to study the influence of various architectural choices on dynamics, and potentially motivate the principled discovery of novel architectures.