Laura Gomezjurado Gonzalez

Tatsuhiro Nakamori, Laura Gomezjurado Gonzalez, Ganesh Talluri et al.

Low-rank gradient compression reduces communication in distributed training by representing updates with rank-$r$ factors. Dion is a recent method that approximates Muon, a spectral optimizer that orthogonalizes momentum, using one step of power iteration followed by column normalization (rescaling each column of the right factor to unit length). This makes it compatible with fully sharded data parallel training, but it converges more slowly than full-rank spectral methods. We show that this gap is geometric: column normalization does not yield the rank-$r$ polar factor that Muon implicitly targets, so the resulting direction violates the dual-norm constraint of the low-rank spectral geometry, and the rate picks up an extra factor of $\sqrt{r}$ even though the low-rank approximation of the gradient itself is accurate. The same mismatch enters the smoothness term and the error-feedback recursion in the analysis, which has a knock-on effect on empirical performance. We propose Orth-Dion, which replaces column normalization with QR orthogonalization of the right factor. Under non-Euclidean smoothness, with $L_r$ the curvature constant along rank-$r$ directions, Orth-Dion attains rate $O(\sqrt{L_r/T})$, matching exact spectral methods at the same per-step communication cost as Dion. The proof removes the bounded-drift assumption common in prior error-feedback analyses via a self-consistent fixed-point argument, and uses a time-averaged contraction that only requires the error sequence to contract on average rather than at every step. Experiments on large-scale language model pre-training validate the predicted $\sqrt{r}$ scaling and show that Orth-Dion closes the convergence gap to Muon at Dion's communication cost.

Hiroki Naganuma, Kotaro Yoshida, Laura Gomezjurado Gonzalez et al.

Model editing techniques, particularly task arithmetic using task vectors, have shown promise in efficiently modifying pre-trained models through arithmetic operations like task addition and negation. Despite computational advantages, these methods may inadvertently affect model fairness, creating risks in sensitive applications like hate speech detection. However, the fairness implications of task arithmetic remain largely unexplored, presenting a critical gap in the existing literature. We systematically examine how manipulating task vectors affects fairness metrics, including Demographic Parity and Equalized Odds. To rigorously assess these effects, we benchmark task arithmetic against full fine-tuning, a costly but widely used baseline, and Low-Rank Adaptation (LoRA), a prevalent parameter-efficient fine-tuning method. Additionally, we explore merging task vectors from models fine-tuned on demographic subgroups vulnerable to hate speech, investigating whether fairness outcomes can be controlled by adjusting task vector coefficients, potentially enabling tailored model behavior. Our results offer novel insights into the fairness implications of model editing and establish a foundation for fairness-aware and responsible model editing practices.

Laura Gomezjurado Gonzalez

Grokking in transformers trained on algorithmic tasks is characterized by a long delay between training-set fit and abrupt generalization, but the source of that delay remains poorly understood. In encoder-decoder arithmetic models, we argue that this delay reflects limited access to already learned structure rather than failure to acquire that structure in the first place. We study one-step Collatz prediction and find that the encoder organizes parity and residue structure within the first few thousand training steps, while output accuracy remains near chance for tens of thousands more. Causal interventions support the decoder bottleneck hypothesis. Transplanting a trained encoder into a fresh model accelerates grokking by 2.75 times, while transplanting a trained decoder actively hurts. Freezing a converged encoder and retraining only the decoder eliminates the plateau entirely and yields 97.6% accuracy, compared to 86.1% for joint training. What makes the decoder's job harder or easier depends on numeral representation. Across 15 bases, those whose factorization aligns with the Collatz map's arithmetic (e.g., base 24) reach 99.8% accuracy, while binary fails completely because its representations collapse and never recover. The choice of base acts as an inductive bias that controls how much local digit structure the decoder can exploit, producing large differences in learnability from the same underlying task.