12 accepted papers
As large language models scale to longer contexts, attention layers suffer from a fundamental pathology: attention scores collapse toward uniformity as context length $n$ increases, causing tokens to cluster excessively, a phenomenon known as rank-collapse. While $\text{\emph{attention scaling}}$ ef…
This paper considers the problem of converting a given dense linear layer into a low-precision version. The tradeoff between minimizing description length and discrepancy introduced at the output of the layer is analyzed information theoretically (IT). It is shown that the popular GPTQ algorithm may…
The meta-task of obtaining and aligning representations through contrastive pretraining is steadily gaining importance since its introduction in CLIP and ALIGN. In this paper we theoretically explain the advantages of synchronizing with trainable inverse temperature and bias under the sigmoid loss,…
Post-training quantization (PTQ) has emerged as a critical technique for efficient deployment of large language models (LLMs). This work proposes NestQuant, a novel PTQ scheme for weights and activations that is based on self-similar nested lattices. Recent works have mathematically shown such quan…
We study the effect of normalization schemes on token representations in deep transformers. Modeling their evolution as interacting particles on the sphere, we show that normalization acts as a form of speed regulation. This perspective enables a unified analysis of several schemes---including **Pos…
This work presents a modification of the self-attention dynamics proposed in Geshkovski et al to better reflect the practically relevant, causally masked attention used in transformer architectures for generative AI. This modification translates into an interacting particle system that cannot be int…
Given $n$ observations from two balanced classes, consider the task of labeling an additional $m$ inputs that are known to all belong to \emph{one} of the two classes. Special cases of this problem are well-known: with complete knowledge of class distributions ($n=\infty$) the problem is solved opt…
We study the single-channel source separation problem involving orthogonal frequency-division multiplexing (OFDM) signals, which are ubiquitous in many modern-day digital communication systems. Related efforts have been pursued in monaural source separation, where state-of-the-art neural architectur…
We propose a new method for separating superimposed sources using diffusion-based generative models. Our method relies only on separately trained statistical priors of independent sources to establish a new objective function guided by $\textit{maximum a posteriori}$ estimation with an $\textit{$\a…
Viewing Transformers as interacting particle systems, we describe the geometry of learned representations when the weights are not time-dependent. We show that particles, representing tokens, tend to cluster toward particular limiting objects as time tends to infinity. Using techniques from dynamica…
The deployment of massive MIMO systems has revived much of the interest in the study of the large-system performance of multiuser detection systems. In this paper, we prove a non-trivial upper bound on the bit-error rate (BER) of the MAP detector for BPSK signal transmission and equal-power conditio…
We study the estimation of the mutual information I(X;T_$\ell$) between the input X to a deep neural network (DNN) and the output vector T_$\ell$ of its $\ell$-th hidden layer (an “internal representation”). Focusing on feedforward networks with fixed weights and noisy internal representations, we d…