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Chain-of-Thought (CoT) reasoning in smaller language models is a challenging natural language process problem yet highly desirable in many real-life applications. Existing CoT knowledge distillation methods often suffer from overly conservative memorization in smaller LLMs, leading to low generalization confidence. As fully preserving the CoT ability of teacher model is impossible, we hypothesize that adversarial CoT fine-tuning is crucial for developing smaller LLM with robust CoT generalization. To this end, we propose \textit{PRompt-Assisted Domain-Adversarial fine-tuning} (PRADA), a principled fine-tuning framework that integrates diverse CoT domains. Specifically, PRADA pioneers two CoT improvements in smaller LLM: (1) Recovering the domain-invariant feature insight which typically lost during distillation with domain adversarial fine-tuning; (2) Enhancing the domain adaptability of CoT prompt engineering by employing domain-adversarial approaches. We theoretically demonstrate the effectiveness of our approach and empirically show that it significantly outperforms the state of the arts in a wide range of tasks. Moreover, our empirical findings reveal that the smaller LLM, when

Large language models (LLMs)-based query expansion for information retrieval augments queries with generated hypothetical documents with LLMs. However, its performance relies heavily on the scale of the language models (LMs), necessitating larger, more advanced LLMs. This approach is costly, computationally intensive, and often has limited accessibility. To address these limitations, we introduce GOLFer - Smaller LMs-Generated Documents Hallucination Filter & Combiner - a novel method leveraging smaller open-source LMs for query expansion. GOLFer comprises two modules: a hallucination filter and a documents combiner. The former detects and removes non-factual and inconsistent sentences in generated documents, a common issue with smaller LMs, while the latter combines the filtered content with the query using a weight vector to balance their influence. We evaluate GOLFer alongside dominant LLM-based query expansion methods on three web search and ten low-resource datasets. Experimental results demonstrate that GOLFer consistently outperforms other methods using smaller LMs, and maintains competitive performance against methods using large-size LLMs, demonstrating its effectivene

Large language models (LLMs) have become ubiquitous, thus it is important to understand their risks and limitations. Smaller LLMs can be deployed where compute resources are constrained, such as edge devices, but with different propensity to generate harmful output. Mitigation of LLM harm typically depends on annotating the harmfulness of LLM output, which is expensive to collect from humans. This work studies two questions: How do smaller LLMs rank regarding generation of harmful content? How well can larger LLMs annotate harmfulness? We prompt three small LLMs to elicit harmful content of various types, such as discriminatory language, offensive content, privacy invasion, or negative influence, and collect human rankings of their outputs. Then, we evaluate three state-of-the-art large LLMs on their ability to annotate the harmfulness of these responses. We find that the smaller models differ with respect to harmfulness. We also find that large LLMs show low to moderate agreement with humans. These findings underline the need for further work on harm mitigation in LLMs.

Large language models (LLMs) have demonstrated strong effectiveness and robustness while fine-tuned as dense retrievers. However, their large parameter size brings significant inference time computational challenges, including high encoding costs for large-scale corpora and increased query latency, limiting their practical deployment. While smaller retrievers offer better efficiency, they often fail to generalize effectively with limited supervised fine-tuning data. In this work, we introduce DRAMA, a training framework that leverages LLMs to train smaller generalizable dense retrievers. In particular, we adopt pruned LLMs as the backbone and train on diverse LLM-augmented data in a single-stage contrastive learning setup. Experiments show that DRAMA offers better multilingual and long-context capabilities than traditional encoder-based retrievers, and achieves strong performance across multiple tasks and languages. These highlight the potential of connecting the training of smaller retrievers with the growing advancements in LLMs, bridging the gap between efficiency and generalization.

While large models pre-trained on high-quality data exhibit excellent performance on mathematical reasoning (e.g., GSM8k, MultiArith), it remains challenging to specialize smaller models for these tasks. Common approaches to address this challenge include knowledge distillation from large teacher models and data augmentation (e.g., rephrasing questions and generating synthetic solutions). Despite these efforts, smaller models struggle with arithmetic computations, leading to errors in mathematical reasoning. In this work, we leverage a synthetic arithmetic dataset generated programmatically to enhance the reasoning capabilities of smaller models. We investigate two key approaches to incorporate this dataset: (1) intermediate fine-tuning, in which a model is fine-tuned on the arithmetic dataset before training it on a reasoning dataset, and (2) integrating the arithmetic dataset into an instruction-tuning mixture, allowing the model to learn arithmetic skills alongside general instruction-following abilities. Our experiments on multiple reasoning benchmarks demonstrate that incorporating an arithmetic dataset, whether through targeted fine-tuning or within an instruction-tuning mixt

Large Language Models (LLMs) have recently made significant advances in code generation through the 'Chain-of-Thought' prompting technique. This technique empowers the model to autonomously devise "solution plans" to tackle intricate programming challenges, thereby improving its performance in code generation. Nevertheless, smaller models have been struggling to keep up with LLMs in deducing these plans, adversely affecting their code generation capabilities. Given the considerable size and associated deployment costs, along with concerns about data security, many teams opt for deploying smaller models for code generation. Consequently, there arises a compelling need for transferring LLMs' code generation reasoning abilities to the smaller models. In this paper, we propose the CodePLAN framework, which aims to transfer LLMs' reasoning capabilities to smaller models through distillation. We adopt a multi-task learning approach, jointly undertaking code generation and solution plan generation tasks, to enhance the code generation capabilities of the smaller model. To ensure the superior quality of the solution plans, we advocate for the utilization of backward reasoning and plan samp

This study explores the effectiveness of layer pruning for developing more efficient BERT models tailored to specific downstream tasks in low-resource languages. Our primary objective is to evaluate whether pruned BERT models can maintain high performance while reducing model size and complexity. We experiment with several BERT variants, including MahaBERT-v2 and Google-Muril, applying different pruning strategies and comparing their performance to smaller, scratch-trained models like MahaBERT-Small and MahaBERT-Smaller. We fine-tune these models on Marathi datasets, specifically Short Headlines Classification (SHC), Long Paragraph Classification (LPC) and Long Document Classification (LDC), to assess their classification accuracy. Our findings demonstrate that pruned models, despite having fewer layers, achieve comparable performance to their fully-layered counterparts while consistently outperforming scratch-trained models of similar size. Notably, pruning layers from the middle of the model proves to be the most effective strategy, offering performance competitive with pruning from the top and bottom. However, there is no clear winner, as different pruning strategies perform bet

We investigated Agentic RL with large language models on the \textsc{TravelPlanner} benchmark. Our approach, \textsc{Planner-R1}, achieved a \textbf{56.9\%} final-pass rate with only 180 training queries, a $2.7\times$ improvement over GPT-5's $21.2\%$ baseline and the strongest agentic result on the public leaderboard. A central finding was that smaller models (8B) were highly responsive to reward shaping: with dense process-level signals, they reached competitive performance while being $3.5\times$ more compute-efficient and $1.5\times$ more memory-efficient than 32B models. Larger models were more robust under sparse rewards but exhibited smaller relative gains from shaping and higher variance across runs. While curriculum learning offered no significant benefit, shaped rewards consistently amplified learning dynamics, making 8B models the most efficient setting for agentic RL. Crucially, these gains did not come at the cost of overfitting: fine-tuned models mostly maintained or exceeded baseline performance on out-of-domain tasks, including \textsc{Multi-IF}, \textsc{NaturalPlan}, and $τ$-\textsc{Bench}. These results establish reward shaping as a decisive lever for scaling age

Recent research has shown that smaller language models can acquire substantial reasoning abilities when fine-tuned with reasoning exemplars crafted by a significantly larger teacher model. We explore this paradigm for the financial domain, focusing on the challenge of answering questions that require multi-hop numerical reasoning over financial texts. We assess the performance of several smaller models that have been fine-tuned to generate programs that encode the required financial reasoning and calculations. Our findings demonstrate that these fine-tuned smaller models approach the performance of the teacher model. To provide a granular analysis of model performance, we propose an approach to investigate the specific student model capabilities that are enhanced by fine-tuning. Our empirical analysis indicates that fine-tuning refines the student models ability to express and apply the required financial concepts along with adapting the entity extraction for the specific data format. In addition, we hypothesize and demonstrate that comparable financial reasoning capability can be induced using relatively smaller datasets.

Although both Google Gemini (1.5 Flash) and ChatGPT (4o and 4o-mini) give research quality evaluation scores that correlate positively with expert scores in nearly all fields, and more strongly that citations in most, it is not known whether this is true for smaller Large Language Models (LLMs). In response, this article assesses Google's Gemma-3-27b-it, a downloadable LLM (60Gb). The results for 104,187 articles show that Gemma-3-27b-it scores correlate positively with an expert research quality score proxy for all 34 Units of Assessment (broad fields) from the UK Research Excellence Framework 2021. The Gemma-3-27b-it correlations have 83.8% of the strength of ChatGPT 4o and 94.7% of the strength of ChatGPT 4o-mini correlations. Differently from the two larger LLMs, the Gemma-3-27b-it correlations do not increase substantially when the scores are averaged across five repetitions, its scores tend to be lower, and its reports are relatively uniform in style. Overall, the results show that research quality score estimation can be conducted by offline LLMs, so this capability is not an emergent property of the largest LLMs. Moreover, score improvement through repetition is not a unive

We construct a randomized vector quantizer which has a smaller maximum error compared to all known lattice quantizers with the same entropy for dimensions 5, 6, ..., 48, and also has a smaller mean squared error compared to known lattice quantizers with the same entropy for dimensions 35, ..., 47, in the high resolution limit. Moreover, our randomized quantizer has a desirable property that the quantization error is always uniform over the ball and independent of the input. Our construction is based on applying rejection sampling on universal quantization, which allows us to shape the error distribution to be any continuous distribution, not only uniform distributions over basic cells of a lattice as in conventional dithered quantization. We also characterize the high SNR limit of one-shot channel simulation for any additive noise channel under a mild assumption (e.g., the AWGN channel), up to an additive constant of 1.45 bits.

While Large Language Models show remarkable performance in natural language understanding, their resource-intensive nature makes them less accessible. In contrast, smaller language models such as MiniCPM offer more sustainable scalability, but often underperform without specialized optimization. In this paper, we explore the enhancement of smaller language models through the improvement of their text embeddings. We select three language models, MiniCPM, Phi-2, and Gemma, to conduct contrastive fine-tuning on the NLI dataset. Our results demonstrate that this fine-tuning method enhances the quality of text embeddings for all three models across various benchmarks, with MiniCPM showing the most significant improvements of an average 56.33% performance gain. The contrastive fine-tuning code is publicly available at https://github.com/trapoom555/Language-Model-STS-CFT.

Instruction tuning has been widely used to unleash the complete potential of large language models. Notably, complex and diverse instructions are of significant importance as they can effectively align models with various downstream tasks. However, current approaches to constructing large-scale instructions predominantly favour powerful models such as GPT-4 or those with over 70 billion parameters, under the empirical presumption that such larger language models (LLMs) inherently possess enhanced capabilities. In this study, we question this prevalent assumption and conduct an in-depth exploration into the potential of smaller language models (SLMs) in the context of instruction evolution. Extensive experiments across three scenarios of instruction evolution reveal that smaller language models (SLMs) can synthesize more effective instructions than LLMs. Further analysis demonstrates that SLMs possess a broader output space during instruction evolution, resulting in more complex and diverse variants. We also observe that the existing metrics fail to focus on the impact of the instructions. Thus, we propose Instruction Complex-Aware IFD (IC-IFD), which introduces instruction complexi

While large language models (LLMs) have demonstrated exceptional performance in recent natural language processing (NLP) tasks, their deployment poses substantial challenges due to high computational and memory demands in real-world applications. Recent studies have focused on enhancing smaller models through knowledge distillation from LLMs, yielding promising results. However, these models often struggle to match the performance of LLMs, especially in tasks that require reasoning. In this work, we introduce Mixed Distillation (MD) framework, which capitalizes on the strengths of Program of Thought (PoT) and Chain of Thought (CoT) capabilities within LLMs, combining multiple prompting techniques and distilling these capabilities into smaller models. Our experimental results show that MD significantly enhances the single-path and multi-path reasoning ability of smaller models in various tasks. In terms of accuracy and generality of reasoning tasks, the model generated by it exceeds the comprehensive performance of two individually distilled models. Notably, LLaMA2-7B and CodeLlama-7B using MD achieved remarkable improvements of (84.5%) and (85.5%), respectively, outperforming GPT-3

We equip a smaller Language Model to generalise to answering challenging compositional questions that have not been seen in training. To do so we propose a combination of multitask supervised pretraining on up to 93 tasks designed to instill diverse reasoning abilities, and a dense retrieval system that aims to retrieve a set of evidential paragraph fragments. Recent progress in question-answering has been achieved either through prompting methods against very large pretrained Language Models in zero or few-shot fashion, or by fine-tuning smaller models, sometimes in conjunction with information retrieval. We focus on the less explored question of the extent to which zero-shot generalisation can be enabled in smaller models with retrieval against a corpus within which sufficient information to answer a particular question may not exist. We establish strong baselines in this setting for diverse evaluation datasets (StrategyQA, CommonsenseQA, IIRC, DROP, Musique and ARC-DA), and show that performance can be significantly improved by adding retrieval-augmented training datasets which are designed to expose our models to a variety of heuristic reasoning strategies such as weighing part

We state an algorithm that, given an automata network and a block-sequential update schedule, produces an automata network of the same size or smaller with the same limit dynamics under the parallel update schedule. Then, we focus on the family of automata cycles which share a unique path of automata, called tangential cycles, and show that a restriction of our algorithm allows to reduce any instance of these networks under a block-sequential update schedule into a smaller parallel network of the family and to characterize the number of reductions operated while conserving their limit dynamics. We also show that any tangential cycles reduced by our main algorithm are transformed into a network whose size is that of the largest cycle of the initial network. We end by showing that the restricted algorithm allows the direct characterization of block-sequential double cycles as parallel ones.

The surprising ability of Large Language Models (LLMs) to perform well on complex reasoning with only few-shot chain-of-thought prompts is believed to emerge only in very large-scale models (100+ billion parameters). We show that such abilities can, in fact, be distilled down from GPT-3.5 ($\ge$ 175B) to T5 variants ($\le$ 11B). We propose model specialization, to specialize the model's ability towards a target task. The hypothesis is that large models (commonly viewed as larger than 100B) have strong modeling power, but are spread on a large spectrum of tasks. Small models (commonly viewed as smaller than 10B) have limited model capacity, but if we concentrate their capacity on a specific target task, the model can achieve a decent improved performance. We use multi-step math reasoning as our testbed because it is a very typical emergent ability. We show two important aspects of model abilities: (1). there exists a very complex balance/ tradeoff between language models' multi-dimensional abilities; (2). by paying the price of decreased generic ability, we can clearly lift up the scaling curve of models smaller than 10B towards a specialized multi-step math reasoning ability. We fu

The Hubble constant problem is that the values of Hubble constant from the observation of cosmic microwave background assuming the LambdaCDM model disagrees with the values from direct measurements. This problem suggests some new physics beyond the LambdaCDM model. Typically there are two ways of reconciliation: one is the realization of smaller value of sound horizon at recombination, and the other is the modification of the way of expansion of the universe after recombination. In this letter we examine the latter possibility by comparing two typical phenomenological dark energy models with the distance-redshift relation provided by Pantheon catalogue of supernova observations and galaxy surveys by BOSS and eBOSS collaborations. Though these phenomenological dark energy models globally fit observations better than the LambdaCDM model, they are strongly disfavored by the distance-redshift relation as almost the same level as the LambdaCDM model defined by cosmic microwave background observations. The distance-redshift relation strongly suggests some new physics which realize smaller value of sound horizon at recombination.

Large Language Models (LLMs) have gained considerable notoriety in the field of natural language to SQL tasks (NL2SQL). In this study, we show how task decomposition can greatly benefit LLMs in database understanding and query generation in order to answer human questions with an SQL query. We fined-tuned open source models, specifically Llama-2 and Code Llama, by combining 2 different models each designated to focus on one of two tasks in order to leverage each model's core competency to further increase the accuracy of the final SQL query. We propose a new framework to divide the schema into chunks in order to fit more information into a limited context. Our results are comparable with those obtained by GPT-4 at the same time being 135 times smaller, 90 times faster and more than 100 times cheaper than GPT-4.