28 accepted papers
We show that Chain-of-Thought (CoT) enables a fixed single-layer transformer to efficiently approximate the training process of an $N$-layer feed-forward network in-context. Since FFNs are universal approximators, this result provides strong theoretical evidence for the expressive power of CoT. Spec…
We introduce Genome-Factory, the first integrated Python library for tuning, deploying, and interpreting genomic foundation models. Our core contribution is to simplify and unify the workflow for genomic model development: data collection, model tuning, inference, benchmarking, and interpretability.…
We prove that a minimal Transformer with frozen weights emulates a broad class of algorithms by in-context prompting. We formalize two modes of in-context algorithm emulation. In the *task-specific mode*, for any continuous function $f: \mathbb{R} \to \mathbb{R}$, we show the existence of a single-h…
We study flow-matching transformers when data lie on a low-dimensional manifold. Our key insight is a flow decomposition that splits motion along the manifold from motion off the manifold. The scheme works for first- and higher-order flow matching and ties model complexity to the intrinsic manifold …
Structured \underline{S}tate-\underline{S}pace \underline{D}uality (SSD) [Dao \& Gu, ICML 2024] is an equivalence between a simple Structured \underline{S}tate-\underline{S}pace \underline{M}odel (SSM) and a masked attention mechanism. In particular, a state-space model with a scalar-times-identity …
We prove that with linear transformations, both (i) two-layer self-attention and (ii) one-layer self-attention followed by a softmax function are universal approximators for continuous sequence-to-sequence functions on compact domains. Our main technique is a new interpolation-based method for analy…
We study the in-context universal approximation and compositional generalization of softmax Transformers. We prove an in-context universality result: a fixed-weight softmax Transformer approximates a broad class of continuous sequence-to-sequence functions. Building on this universality, we establis…
We establish the universal approximation capability of single-layer, single-head self- and cross-attention mechanisms with minimal attached structures. Our key insight is to interpret single-head attention as an input domain-partition mechanism that assigns distinct values to subregions. This allo…
We study the computational limits of Low-Rank Adaptation (LoRA) for finetuning transformer-based models using fine-grained complexity theory. Our key observation is that the existence of low-rank decompositions within the gradient computation of LoRA adaptation leads to possible algorithmic speedup.…
To address the challenge of scarce computational resources in genomic modeling, we introduce GERM, a genomic foundation model optimized for accessibility and adaptability. GERM improves upon models like DNABERT-2 by eliminating outliers that hinder low-rank adaptation and post-training quantization,…
We investigate the statistical and computational limits of prompt tuning for transformer-based foundation models. Our key contributions are that prompt tuning on *single-head* transformers with only a *single* self-attention layer: (i) is universal, and (ii) supports efficient (even almost-linear…
Flow matching is an emerging generative modeling framework that learns continuous-time dynamics to map noise into data. To enhance expressiveness and sampling efficiency, recent works have explored incorporating high-order trajectory information. Despite the empirical success, a holistic theoretica…
We investigate the transformer's capability for in-context learning (ICL) to simulate the training process of deep models. Our key contribution is providing a positive example of using a transformer to train a deep neural network by gradient descent in an implicit fashion via ICL. Specifically, we…
We provide an exactly solvable example for interpreting In-Context Learning (ICL) with one-layer attention models as conditional retrieval of dense associative memory models. Our main contribution is to interpret ICL as memory reshaping in the modern Hopfield model from a conditional memory set (in-…
We revisit the Bayesian Black–Litterman (BL) portfolio model and remove its reliance on subjective investor views. Classical BL requires an investor “view”: a forecast vector $q$ and its uncertainty matrix $\Omega$ that describe how much a chosen portfolio should outperform the market. Our key idea…
We present a nonparametric interpretation for deep learning compatible modern Hopfield models and utilize this new perspective to debut efficient variants. Our key contribution stems from interpreting the memory storage and retrieval processes in modern Hopfield models as a nonparametric regression…
We investigate the approximation and estimation rates of conditional diffusion transformers (DiTs) with classifier-free guidance. We present a comprehensive analysis for “in-context” conditional DiTs under various common assumptions: generic and strong Hölder, linear latent (subspace), and Lipschitz…
We present a three-stage framework for training deep learning models specializing in antibody sequence-structure co-design. We first pre-train a language model using millions of antibody sequence data. Then, we employ the learned representations to guide the training of a diffusion model for joint o…
We introduce the **Bi**-Directional **S**parse **Hop**field Network (**BiSHop**), a novel end-to-end framework for tabular learning. BiSHop handles the two major challenges of deep tabular learning: non-rotationally invariant data structure and feature sparsity in tabular data. Our key motivation co…
We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of all possible modern Hopfield models based on the norm of patt…
We investigate the statistical and computational limits of latent **Di**ffusion **T**ransformers (**DiTs**) under the low-dimensional linear latent space assumption. Statistically, we study the universal approximation and sample complexity of the DiTs score function, as well as the distribution reco…
We introduce an Outlier-Efficient Modern Hopfield Model (termed `OutEffHop`) and use it to address the outlier inefficiency problem of training gigantic transformer-based models. Our main contribution is a novel associative memory model facilitating _outlier-efficient_ associative memory retrievals.…
We study the optimal memorization capacity of modern Hopfield models and Kernelized Hopfield Models (KHMs), a transformer-compatible class of Dense Associative Memories. We present a tight analysis by establishing a connection between the memory configuration of KHMs and spherical codes from informa…
We present **STanHop-Net** (**S**parse **Tan**dem **Hop**field **Net**work) for multivariate time series prediction with memory-enhanced capabilities. At the heart of our approach is **STanHop**, a novel Hopfield-based neural network block, which sparsely learns and stores both temporal and cross-se…
We propose a two-stage optimization formulation for the memory retrieval dynamics of modern Hopfield models, termed $\mathtt{U\text{-}Hop}$. Our key contribution is a learnable feature map $\Phi$ which transforms the Hopfield energy function into a kernel space. This transformation ensures convergen…
We introduce the concept of programmable feature engineering for time series modeling and propose a feature programming framework. This framework generates large amounts of predictive features for noisy multivariate time series while allowing users to incorporate their inductive bias with minimal ef…
This paper addresses the challenges in accurate and real-time traffic congestion prediction under uncertainty by proposing Ising-Traffic, a dual-model Ising-based traffic prediction framework that delivers higher accuracy and lower latency than SOTA solutions. While traditional solutions face the di…
We introduce the sparse modern Hopfield model as a sparse extension of the modern Hopfield model. Like its dense counterpart, the sparse modern Hopfield model equips a memory-retrieval dynamics whose one-step approximation corresponds to the sparse attention mechanism. Theoretically, our key contri…