Minimalist Softmax Attention Provably Learns Constrained Boolean Functions

We study the computational limits of learning $k$-bit Boolean functions (specifically, $\mathrm{AND}$, $\mathrm{OR}$, and their noisy variants), using a minimalist single-head softmax-attention mechanism, where $k=\Theta(d)$ relevant bits are selected from $d$ inputs. We show that these simple $\mathrm{AND}$ and $\mathrm{OR}$ functions are unsolvable with a single-head softmax-attention mechanism alone. However, with teacher forcing, the same minimalist attention is capable of solving them. These findings offer two key insights: Architecturally, solving these Boolean tasks requires only minimalist attention, without deep Transformer blocks or FFNs. Methodologically, one gradient descent update with supervision suffices and replaces the multi-step Chain-of-Thought (CoT) reasoning scheme of [Kim and Suzuki, ICLR 2025] for solving Boolean problems. Together, the bounds expose a fundamental gap between what this minimal architecture achieves under ideal supervision and what is provably impossible under standard training.

Fast and Low-Cost Genomic Foundation Models via Outlier Removal

We propose the first unified adversarial attack benchmark for Genomic Foundation Models (GFMs), named GERM. Unlike existing GFM benchmarks, GERM offers the first comprehensive evaluation framework to systematically assess the vulnerability of GFMs to adversarial attacks. Methodologically, we evaluate the adversarial robustness of five state-of-the-art GFMs using four widely adopted attack algorithms and three defense strategies. Importantly, our benchmark provides an accessible and comprehensive framework to analyze GFM vulnerabilities with respect to model architecture, quantization schemes, and training datasets. Empirically, transformer-based models exhibit greater robustness to adversarial perturbations compared to HyenaDNA, highlighting the impact of architectural design on vulnerability. Moreover, adversarial attacks frequently target biologically significant genomic regions, suggesting that these models effectively capture meaningful sequence features.

Transformers are Deep Optimizers: Provable In-Context Learning for Deep Model Training

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 provide an explicit construction of a $(2N+4)L$-layer transformer capable of simulating $L$ gradient descent steps of an $N$-layer ReLU network through ICL. We also give the theoretical guarantees for the approximation within any given error and the convergence of the ICL gradient descent. Additionally, we extend our analysis to the more practical setting using Softmax-based transformers. We validate our findings on synthetic datasets for 3-layer, 4-layer, and 6-layer neural networks. The results show that ICL performance matches that of direct training.

Computational Limits of Low-Rank Adaptation (LoRA) for Transformer-Based Models

We study the computational limits of Low-Rank Adaptation (LoRA) update 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. This allows us to (i) identify a phase transition behavior and (ii) prove the existence of nearly linear algorithms by controlling the LoRA update computation term by term, assuming the Strong Exponential Time Hypothesis (SETH). For the former, we identify a sharp transition in the efficiency of all possible rank-$r$ LoRA update algorithms for transformers, based on specific norms resulting from the multiplications of the input sequence $\mathbf{X}$, pretrained weights $\mathbf{W^\star}$, and adapter matrices $\alpha \mathbf{B} \mathbf{A} / r$. Specifically, we derive a shared upper bound threshold for such norms and show that efficient (sub-quadratic) approximation algorithms of LoRA exist only below this threshold. For the latter, we prove the existence of nearly linear approximation algorithms for LoRA adaptation by utilizing the hierarchical low-rank structures of LoRA gradients and approximating the gradients with a series of chained low-rank approximations. To showcase our theory, we consider two practical scenarios: partial (e.g., only $\mathbf{W}_V$ and $\mathbf{W}_Q$) and full adaptations (e.g., $\mathbf{W}_Q$, $\mathbf{W}_V$, and $\mathbf{W}_K$) of weights in attention heads.