In transfer learning, the learner leverages auxiliary data to improve generalization on a main task. However, the precise theoretical understanding of when and how auxiliary data help remains incomplete. We provide new insights on this issue in two canonical linear settings: ordinary least squares regression and under-parameterized linear neural networks. For linear regression, we derive exact closed-form expressions for the expected generalization error with bias-variance decomposition, yielding necessary and sufficient conditions for auxiliary tasks to improve generalization on the main task. We also derive globally optimal task weights as outputs of solvable optimization programs, with consistency guarantees for empirical estimates. For linear neural networks with shared representations of width $q \leq K$, where $K$ is the number of auxiliary tasks, we derive a non-asymptotic expectation bound on the generalization error, yielding the first non-vacuous sufficient condition for beneficial auxiliary learning in this setting, as well as principled directions for task weight curation. We achieve this by proving a new column-wise low-rank perturbation bound for random matrices, which improves upon existing bounds by preserving fine-grained column structures. Our results are verified on synthetic data simulated with controlled parameters.

We would like to thank all the reviewers for writing the insightful comments, especially during this difficult time. However, lowering training loss may cause overfitting, especially when training data is scarce. The superiority of ARML is verified in the experiments. The error rates decreases when each new task is added. In'Baseline + ARML ', for fair comparison, we stick to the same training process, We will add more elaboration on this in the final version. We will try other tasks, e.g., reinforcement learning.

We thank the reviewers for valuable and timely comments. We'd like to first emphasize the challenges and contributions: Section 3.2 explains how to calculate this hyper-gradient of Framework for BackPropagation, LeCun, 1988), and widely adopted in the literature [14, 15, 35]. We would like to further polish the notation to be more consistent. 'Pretrain (Top)' is much better than'Pretrain (Down)'.

When aligning large language models (LLMs), their performance on various tasks (such as being helpful, harmless, and honest) depends heavily on the composition of their training data. However, selecting a data mixture that achieves strong performance across all tasks is challenging. Existing approaches rely on large ablation studies, heuristics, or human intuition, but these can be prohibitively expensive and suboptimal. We study this problem in the setting of preference optimization via DPO and introduce AutoMixAlign (AMA), a theoretically-grounded algorithm that adaptively mixes datasets during training to balance performance across tasks. AMA first trains \textit{specialist models} for each task to determine losses that correspond to strong task performance. Then, it trains a generalist model using a novel minimax optimization that prioritizes tasks for which generalist model losses deviate most from specialist model losses. To optimize this problem, we propose two algorithms: (1) AMA-R, which adaptively reweights the objective to prioritize tasks, and (2) AMA-S, which adaptively adjusts how much data is sampled from each task to prioritize tasks. Both algorithms achieve a convergence rate of $O(1/\sqrt{T})$ in the convex case. AMA-R's convergence result follows from Sagawa et al. (2019), and we provide a convergence proof for AMA-S using online learning techniques such as EXP3. We evaluate AMA on several multitask alignment setups and find that AMA outperforms the standard alignment approach -- which simply optimizes the total loss across all tasks -- and also outperforms model merging methods.

The performance of large language models (LLMs) across diverse downstream applications is fundamentally governed by the quality and composition of their pretraining corpora. Existing domain reweighting algorithms primarily optimize data mixtures for a single target task, thereby resulting in models that overfit to specialized objectives while exhibiting substantial performance degradation on other benchmarks. This paper introduces Group Robust Multi-target Adaptive PrEtraining (GRAPE), a novel multi-source-multi-target domain reweighting framework designed to calibrate pretraining data mixtures for robust performance across multiple target tasks simultaneously. GRAPE dynamically adjusts sampling weights across source domains (domain weights) while concurrently modulating task weights that quantify the relative importance of each individual target task. This adaptive process prioritizes tasks based on their learning difficulty throughout training. We formulate this interleaved reweighting mechanism as a minimax optimization problem: The inner maximization adjusts task weights leveraging group distributed-robust-optimization (DRO), where those tasks demonstrating the least improvement under the current data mixture are prioritized with higher weights; The outer minimization then optimizes domain weights to maximize loss reduction on the prioritized tasks. Experiments on ClimbLab and SlimPajama datasets demonstrate that GRAPE consistently outperforms baseline methods in terms of reasoning performance across 6 benchmarks. Furthermore, when applied to multilingual targets, GRAPE effectively identifies optimal training mixtures from mainstream languages, achieving superior language modeling capabilities across 8 low-resource target languages.

Implicit sentiment analysis (ISA) presents significant challenges due to the absence of salient cue words. Previous methods have struggled with insufficient data and limited reasoning capabilities to infer underlying opinions. Integrating multi-task learning (MTL) with large language models (LLMs) offers the potential to enable models of varying sizes to reliably perceive and recognize genuine opinions in ISA. However, existing MTL approaches are constrained by two sources of uncertainty: data-level uncertainty, arising from hallucination problems in LLM-generated contextual information, and task-level uncertainty, stemming from the varying capacities of models to process contextual information. To handle these uncertainties, we introduce MT-ISA, a novel MTL framework that enhances ISA by leveraging the generation and reasoning capabilities of LLMs through automatic MTL. Specifically, MT-ISA constructs auxiliary tasks using generative LLMs to supplement sentiment elements and incorporates automatic MTL to fully exploit auxiliary data. We introduce data-level and task-level automatic weight learning (AWL), which dynamically identifies relationships and prioritizes more reliable data and critical tasks, enabling models of varying sizes to adaptively learn fine-grained weights based on their reasoning capabilities. We investigate three strategies for data-level AWL, while also introducing homoscedastic uncertainty for task-level AWL. Extensive experiments reveal that models of varying sizes achieve an optimal balance between primary prediction and auxiliary tasks in MT-ISA. This underscores the effectiveness and adaptability of our approach.

In industrial recommendation systems, multi-task learning (learning multiple tasks simultaneously on a single model) is a predominant approach to save training/serving resources and improve recommendation performance via knowledge transfer between the joint learning tasks. However, multi-task learning often suffers from negative transfer: one or several tasks are less optimized than training them separately. To carefully balance the optimization, we propose a gradient balancing approach called MultiBalance, which is suitable for industrial-scale multi-task recommendation systems. It balances the per-task gradients to alleviate the negative transfer, while saving the huge cost for grid search or manual explorations for appropriate task weights. Moreover, compared with prior work that normally balance the per-task gradients of shared parameters, MultiBalance is more efficient since only requiring to access per-task gradients with respect to the shared feature representations. We conduct experiments on Meta's large-scale ads and feeds multi-task recommendation system, and observe that MultiBalance achieves significant gains (e.g., 0.738% improvement for normalized entropy (NE)) with neutral training cost in Queries Per Second (QPS), which is significantly more efficient than prior methods that balance per-task gradients of shared parameters with 70~80% QPS degradation.