UBER: Uncertainty-Based Evolution with Large Language Models for Automatic Heuristic Design

NP-hard problem-solving traditionally relies on heuristics, but manually crafting effective heuristics for complex problems remains challenging. While recent work like FunSearch has demonstrated that large language models (LLMs) can be leveraged for heuristic design in evolutionary algorithm (EA) frameworks, their potential is not fully realized due to its deficiency in exploitation and exploration. We present UBER (Uncertainty-Based Evolution for Refinement), a method that enhances LLM+EA methods for automatic heuristic design by integrating uncertainty on top of the FunSearch framework. UBER introduces two key innovations: an Uncertainty-Inclusive Evolution Process (UIEP) for adaptive exploration-exploitation balance, and a principled Uncertainty-Inclusive Island Reset (UIIS) strategy for maintaining population diversity. Through extensive experiments on challenging NP-complete problems, UBER demonstrates significant improvements over FunSearch. Our work provides a new direction for the synergy of LLMs and EA, advancing the field of automatic heuristic design.

Value Residual Learning For Alleviating Attention Concentration In Transformers

Transformers can capture long-range dependencies using self-attention, allowing tokens to attend to all others directly. However, stacking multiple attention layers leads to attention concentration. One natural way to address this issue is to use cross-layer attention, allowing information from earlier layers to be directly accessible to later layers. However, this approach is computationally expensive. To address this problem, we propose Transformer with residual value (ResFormer) which approximates cross-layer attention through adding a residual connection from the values of the the first layer to all subsequent layers. Based on this method, one variant is the Transformer with single layer value (SVFormer), where all layers share the same value embedding from first layer, reducing the KV cache by nearly 50%. Comprehensive empirical evidence demonstrates that ResFormer mitigates attention concentration problem in deeper layers and enhances representation across most layers, outperforming the vanilla Transformer, DenseFormer, and NeuTRENO in training error as well as downstream tasks. SVFormer trains significantly faster than the vanilla Transformer and performs better than other methods like GQA and CLA, with performance influenced by sequence length and cumulative learning rate.

Dynamics of Instruction Tuning: Each Ability of Large Language Models Has Its Own Growth Pace

Instruction tuning is a burgeoning method to elicit the general intelligence of Large Language Models (LLMs). However, the creation of instruction data is still largely heuristic, leading to significant variation in quality and distribution across existing datasets. Experimental conclusions drawn from these datasets are also inconsistent, with some studies emphasizing the importance of scaling instruction numbers, while others argue that a limited number of samples suffice. To better understand data construction guidelines, we deepen our focus from the overall model performance to the growth of each underlying ability, such as creative writing, code generation, and logical reasoning. We systematically investigate the effects of data volume, parameter size, and data construction methods on the development of various abilities, using hundreds of model checkpoints (7b to 33b) fully instruction-tuned on a new collection of over 40k human-curated instruction data. This proposed dataset is stringently quality-controlled and categorized into ten distinct LLM abilities. Our study reveals three primary findings: (i) Despite data volume and parameter scale directly impacting models' overall performance, some abilities are more responsive to their increases and can be effectively trained using limited data, while some are highly resistant to these changes. (ii) Human-curated data strongly outperforms synthetic data from GPT-4 in efficiency and can constantly enhance model performance with volume increases, but is unachievable with synthetic data. (iii) Instruction data brings powerful cross-ability generalization, with evaluation results on out-of-domain data mirroring the first two observations. Furthermore, we demonstrate how these findings can guide more efficient data constructions, leading to practical performance improvements on public benchmarks.