arXiv subjects

Leon Lufkin

Publications and source records attributed to Leon Lufkin.

5 recordsLinked to original sources

arXiv2026

Hybrid Associative Memories

Recurrent neural networks (RNNs) and self-attention are both widely used sequence-mixing layers that maintain an internal memory. However, this memory is constructed using two orthogonal mechanisms: RNNs compress the entire past into a fixed-size state, whereas self-attention's state stores every past time step growing its state (the KV cache) linearly with the sequence length. This results in orthogonal strengths and weaknesses. Self-attention layers excel at retrieving information in the context but have large memory and computational costs, while RNNs are more efficient but degrade over longer contexts and underperform for precise recall tasks. Prior work combining these mechanisms has focused primarily on naively interleaving them to reduce computational cost without regard to their complementary mechanisms. We propose the Hybrid Associative Memory (HAM) layer, which combines self-attention and RNNs while leveraging their individual strengths: the RNN compresses the entire sequence, while attention supplements it *only* with information that is difficult for the RNN to predict, which is hence the most valuable information to explicitly store. HAM layers enable data-dependent growth of the KV cache, which can be precisely controlled by the user with a single, continuous threshold. We find that this fine-grained control of the KV cache growth rate has a smooth trade-off with loss and performance. Empirically, we show that our hybrid architecture offers strong, competitive performance relative to RNNs and Transformers even at substantially lower KV-cache usage.

cs.LG↗

arXiv2025

Nonlinear dynamics of localization in neural receptive fields

Localized receptive fields -- neurons that are selective for certain contiguous spatiotemporal features of their input -- populate early sensory regions of the mammalian brain. Unsupervised learning algorithms that optimize explicit sparsity or independence criteria replicate features of these localized receptive fields, but fail to explain directly how localization arises through learning without efficient coding, as occurs in early layers of deep neural networks and might occur in early sensory regions of biological systems. We consider an alternative model in which localized receptive fields emerge without explicit top-down efficiency constraints -- a feedforward neural network trained on a data model inspired by the structure of natural images. Previous work identified the importance of non-Gaussian statistics to localization in this setting but left open questions about the mechanisms driving dynamical emergence. We address these questions by deriving the effective learning dynamics for a single nonlinear neuron, making precise how higher-order statistical properties of the input data drive emergent localization, and we demonstrate that the predictions of these effective dynamics extend to the many-neuron setting. Our analysis provides an alternative explanation for the ubiquity of localization as resulting from the nonlinear dynamics of learning in neural circuits.

cs.LG↗

arXiv2024

Sharp Information-Theoretic Thresholds for Shuffled Linear Regression

This paper studies the problem of shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we consider the model $y = Π_* X β_* + w$, where $X$ is an $n \times d$ standard Gaussian design matrix, $w$ is Gaussian noise with entrywise variance $σ^2$, $Π_*$ is an unknown $n \times n$ permutation matrix, and $β_*$ is the regression coefficient, also unknown. Previous work has shown that, in the large $n$-limit, the minimal signal-to-noise ratio ($\mathsf{SNR}$), $\lVert β_* \rVert^2/σ^2$, for recovering the unknown permutation exactly with high probability is between $n^2$ and $n^C$ for some absolute constant $C$ and the sharp threshold is unknown even for $d=1$. We show that this threshold is precisely $\mathsf{SNR} = n^4$ for exact recovery throughout the sublinear regime $d=o(n)$. As a by-product of our analysis, we also determine the sharp threshold of almost exact recovery to be $\mathsf{SNR} = n^2$, where all but a vanishing fraction of the permutation is reconstructed.

math.ST↗

arXiv2023

The QUATRO Application Suite: Quantum Computing for Models of Human Cognition

Research progress in quantum computing has, thus far, focused on a narrow set of application domains. Expanding the suite of quantum application domains is vital for the discovery of new software toolchains and architectural abstractions. In this work, we unlock a new class of applications ripe for quantum computing research -- computational cognitive modeling. Cognitive models are critical to understanding and replicating human intelligence. Our work connects computational cognitive models to quantum computer architectures for the first time. We release QUATRO, a collection of quantum computing applications from cognitive models. The development and execution of QUATRO shed light on gaps in the quantum computing stack that need to be closed to ease programming and drive performance. Among several contributions, we propose and study ideas pertaining to quantum cloud scheduling (using data from gate- and annealing-based quantum computers), parallelization, and more. In the long run, we expect our research to lay the groundwork for more versatile quantum computer systems in the future.

cs.CE↗

arXiv2022

Emergent organization of receptive fields in networks of excitatory and inhibitory neurons

Local patterns of excitation and inhibition that can generate neural waves are studied as a computational mechanism underlying the organization of neuronal tunings. Sparse coding algorithms based on networks of excitatory and inhibitory neurons are proposed that exhibit topographic maps as the receptive fields are adapted to input stimuli. Motivated by a leaky integrate-and-fire model of neural waves, we propose an activation model that is more typical of artificial neural networks. Computational experiments with the activation model using both natural images and natural language text are presented. In the case of images, familiar "pinwheel" patterns of oriented edge detectors emerge; in the case of text, the resulting topographic maps exhibit a 2-dimensional representation of granular word semantics. Experiments with a synthetic model of somatosensory input are used to investigate how the network dynamics may affect plasticity of neuronal maps under changes to the inputs.

q-bio.NC↗