Luca Zhou

Daniele Solombrino, Antonio Andrea Gargiulo, Adrian Robert Minut et al.

We show that robustness to post-training quantization (PTQ) is a transferable direction in weight space. We call this direction the quantization vector: extracted from a donor task by simple weight-space arithmetic, it can be used to patch a receiver model and improve robustness to PTQ-induced noise by as much as 60%, without receiver-side quantization-aware training (QAT). Because the method requires no receiver training data, it provides a zero-shot, low-cost alternative to QAT for extremely low-bit deployment. We demonstrate this on Vision Transformer (ViT) models. More broadly, our results suggest that quantization robustness is not merely a byproduct of task-specific training, but a reusable feature of weight-space geometry that can be transferred rather than retrained.

Luca Zhou, Bo Zhao, Rose Yu et al.

Model merging combines knowledge from separately fine-tuned models, yet success factors remain poorly understood. While recent work treats mergeability as an intrinsic property, we show with an architecture-agnostic framework that it fundamentally depends on both the merging method and the partner tasks. Using linear optimization over a set of interpretable pairwise metrics (e.g., gradient L2 distance), we uncover properties correlating with post-merge performance across four merging methods. We find substantial variation in success drivers (46.7% metric overlap; 55.3% sign agreement), revealing method-specific "fingerprints". Crucially, however, subspace overlap and gradient alignment metrics consistently emerge as foundational, method-agnostic prerequisites for compatibility. These findings provide a diagnostic foundation for understanding mergeability and motivate future fine-tuning strategies that explicitly encourage these properties.

Luca Zhou, Sajel Shah, Emanuele Rodolà et al.

Math and science reasoning benchmarks rely on pass@k, the fraction of sampled chains that reach gold, as the canonical per-example difficulty signal. The same signal drives RL with verifiable rewards, math data curation, synthetic curricula, and verifier training. We show this proxy has a persistent blind spot on its hardest stratum: on the eight free-form math cells we test (GSM8K and MATH across four open-weight models), 10.3-22.9% of the examples that no sampling seed solves in six tries are instead solved at matched compute by a six-chain deterministic regime. These are greedy decoding plus five cheap residual-stream perturbations applied via activation grafting, while greedy alone solves at most 6% on these math cells. Recovery scales with the additional budget, across perturbations whose mechanistic distinctness we verify across all twelve cells (cross-kind fix-set Jaccard <= 0.47 in every setup). Activation grafting is used as an intervention on internal representations, not a decoding method; we use it purely as a diagnostic and diversification tool, and our recovered items show that the pass@k= 0 % stratum is structurally identifiable in the residual stream rather than that the unmodified model reaches them under ordinary inference.

Luca Zhou, Daniele Solombrino, Donato Crisostomi et al.

Model merging has emerged as a cost-efficient approximation to multitask learning. Among merging strategies, task arithmetic is notable for its simplicity and effectiveness. In this work, we provide a theoretical motivation for task vectors by highlighting that, under single-epoch full-batch gradient descent, they are equivalent to multitask gradients. This insight leads us to reinterpret model merging as a single step in an iterative procedure that Alternates between Tuning and Merging (ATM). We propose two applications of ATM: (1) as an alternative to multitask learning in scenarios where data sharing is restricted (e.g., federated settings), and (2) as a lightweight refinement step to improve existing model merging methods using a small validation set. Experiments across diverse vision tasks demonstrate the effectiveness of ATM.

Luca Zhou

Recent work motivates moving large language model (LLM) evaluation from mean-based to tail-aware metrics, including conditional value-at-risk and tail-index estimates of reward-model error. We ask whether the canonical extreme-value-theory tail-index parameter, which isolates how heavy a tail is from how large the tail mass is, adds discriminative information beyond the mean and a standard tail-magnitude statistic in LLM evaluation. We pre-register a protocol covering admissibility, goodness-of-fit, threshold-stability, and effect-size requirements for any positive tail-shape claim. The protocol is the contribution of this paper; the empirical study below is a demonstration of what its gates catch. Applied to a standard LLM toxicity-evaluation setup under two structurally different scorer families, the protocol catches three distinct modes of false positives that a naive analysis would have published, and rejects the headline tail-shape claim on both scorers. We conclude that tail-shape estimation in the LLM toxicity-evaluation setups we examined is more fragile than the recent literature suggests, and recommend the protocol as a starting point for tail-index claims in similar setups.

Luca Zhou, Daniele Solombrino, Donato Crisostomi et al.

Task arithmetic has emerged as a simple yet powerful technique for model merging, enabling the combination of multiple finetuned models into one. Despite its empirical success, a clear theoretical explanation of why and when it works is lacking. This paper provides a rigorous theoretical foundation for task arithmetic by establishing a connection between task vectors and gradients of the task losses. We show that under standard gradient descent, a task vector generated from one epoch of finetuning is exactly equivalent to the negative gradient of the loss, scaled by the learning rate. For the practical multi-epoch setting, we prove that this equivalence holds approximately, with a second-order error term that we explicitly bound for feed-forward networks. Our empirical analysis across seven vision benchmarks corroborates our theory, demonstrating that the first-epoch gradient dominates the finetuning trajectory in both norm and direction. A key implication is that merging models finetuned for only a single epoch often yields performance comparable to merging fully converged models. These findings reframe task arithmetic as a form of approximate multitask learning, providing a clear rationale for its effectiveness and highlighting the critical role of early training dynamics in model merging.