MathFusion: Enhancing Mathematic Problem-solving of LLM through Instruction Fusion

Large Language Models (LLMs) have shown impressive progress in mathematical reasoning. While data augmentation is promising to enhance mathematical problem-solving ability, current approaches are predominantly limited to instance-level modifications-such as rephrasing or generating syntactic variations-which fail to capture and leverage the intrinsic relational structures inherent in mathematical knowledge. Inspired by human learning processes, where mathematical proficiency develops through systematic exposure to interconnected concepts, we introduce MathFusion, a novel framework that enhances mathematical reasoning through cross-problem instruction synthesis. MathFusion implements this through three fusion strategies: (1) sequential fusion, which chains related problems to model solution dependencies; (2) parallel fusion, which combines analogous problems to reinforce conceptual understanding; and (3) conditional fusion, which creates context-aware selective problems to enhance reasoning flexibility. By applying these strategies, we generate a new dataset, \textbf{MathFusionQA}, followed by fine-tuning models (DeepSeekMath-7B, Mistral-7B, Llama3-8B) on it. Experimental results demonstrate that MathFusion achieves substantial improvements in mathematical reasoning while maintaining high data efficiency, boosting performance by 18.0 points in accuracy across diverse benchmarks while requiring only 45K additional synthetic instructions, representing a substantial improvement over traditional single-instruction approaches. Our datasets, models, and code are publicly available at https://github.com/QizhiPei/mathfusion.

MetaLadder: Ascending Mathematical Solution Quality via Analogical-Problem Reasoning Transfer

Large Language Models (LLMs) have demonstrated promising capabilities in solving mathematical reasoning tasks, leveraging Chain-of-Thought (CoT) data as a vital component in guiding answer generation. Current paradigms typically generate CoT and answers directly for a given problem, diverging from human problem-solving strategies to some extent. Humans often solve problems by recalling analogous cases and leveraging their solutions to reason about the current task. Inspired by this cognitive process, we propose \textbf{MetaLadder}, a novel framework that explicitly prompts LLMs to recall and reflect on meta-problems, those structurally or semantically analogous problems, alongside their CoT solutions before addressing the target problem. Additionally, we introduce a problem-restating mechanism to enhance the model's comprehension of the target problem by regenerating the original question, which further improves reasoning accuracy. Therefore, the model can achieve reasoning transfer from analogical problems, mimicking human-like "learning from examples" and generalization abilities. Extensive experiments on mathematical benchmarks demonstrate that our MetaLadder significantly boosts LLMs' problem-solving accuracy, largely outperforming standard CoT-based methods (\textbf{10.3\%} accuracy gain) and other methods. Our code and data has been released at https://github.com/LHL3341/MetaLadder.

On Memory Construction and Retrieval for Personalized Conversational Agents

To deliver coherent and personalized experiences in long-term conversations, existing approaches typically perform retrieval augmented response generation by constructing memory banks from conversation history at either the turn-level, session-level, or through summarization techniques. In this paper, we present two key findings: (1) The granularity of memory unit matters: Turn-level, session-level, and summarization-based methods each exhibit limitations in both memory retrieval accuracy and the semantic quality of the retrieved content. (2) Prompt compression methods, such as \textit{LLMLingua-2}, can effectively serve as a denoising mechanism, enhancing memory retrieval accuracy across different granularities. Building on these insights, we propose SeCom, a method that constructs a memory bank with topical segments by introducing a conversation Segmentation model, while performing memory retrieval based on Compressed memory units. Experimental results show that SeCom outperforms turn-level, session-level, and several summarization-based methods on long-term conversation benchmarks such as LOCOMO and Long-MT-Bench+. Additionally, the proposed conversation segmentation method demonstrates superior performance on dialogue segmentation datasets such as DialSeg711, TIAGE, and SuperDialSeg.

TokenSelect: Efficient Long-Context Inference and Length Extrapolation for LLMs via Dynamic Token-Level KV Cache Selection

With the development of large language models (LLMs), the ability to handle longer contexts has become a key capability for Web applications such as cross-document understanding and LLM-powered search systems. However, this progress faces two major challenges: performance degradation due to sequence lengths out-of-distribution, and excessively long inference times caused by the quadratic computational complexity of attention. These issues hinder the application of LLMs in long-context scenarios. In this paper, we propose Dynamic Token-Level KV Cache Selection (TokenSelect), a model-agnostic, training-free method for efficient and accurate long-context inference. TokenSelect builds upon the observation of non-contiguous attention sparsity, using Query-Key dot products to measure per-head KV Cache criticality at token-level. By per-head soft voting mechanism, TokenSelect selectively involves a small number of critical KV cache tokens in the attention calculation without sacrificing accuracy. To further accelerate TokenSelect, we designed the Selection Cache based on observations of consecutive Query similarity and implemented efficient dot product kernel, significantly reducing the overhead of token selection. A comprehensive evaluation of TokenSelect demonstrates up to 23.84x speedup in attention computation and up to 2.28x acceleration in end-to-end latency, while providing superior performance compared to state-of-the-art long-context inference methods.

LLMLingua-2: Data Distillation for Efficient and Faithful Task-Agnostic Prompt Compression

This paper focuses on task-agnostic prompt compression for better generalizability and efficiency. Considering the redundancy in natural language, existing approaches compress prompts by removing tokens or lexical units according to their information entropy obtained from a causal language model such as LLaMa-7B. The challenge is that information entropy may be a suboptimal compression metric: (i) it only leverages unidirectional context and may fail to capture all essential information needed for prompt compression; (ii) it is not aligned with the prompt compression objective. To address these issues, we propose a data distillation procedure to derive knowledge from an LLM to compress prompts without losing crucial information, and meantime, introduce an extractive text compression dataset. We formulate prompt compression as a token classification problem to guarantee the faithfulness of the compressed prompt to the original one, and use a Transformer encoder as the base architecture to capture all essential information for prompt compression from the full bidirectional context. Our approach leads to lower latency by explicitly learning the compression objective with smaller models such as XLM-RoBERTa-large and mBERT. We evaluate our method on both in-domain and out-of-domain datasets, including MeetingBank, LongBench, ZeroScrolls, GSM8K, and BBH. Despite its small size, our model shows significant performance gains over strong baselines and demonstrates robust generalization ability across different LLMs. Additionally, our model is 3x-6x faster than existing prompt compression methods, while accelerating the end-to-end latency by 1.6x-2.9x with compression ratios of 2x-5x.

From Trojan Horses to Castle Walls: Unveiling Bilateral Backdoor Effects in Diffusion Models

While state-of-the-art diffusion models (DMs) excel in image generation, concerns regarding their security persist. Earlier research highlighted DMs' vulnerability to backdoor attacks, but these studies placed stricter requirements than conventional methods like 'BadNets' in image classification. This is because the former necessitates modifications to the diffusion sampling and training procedures. Unlike the prior work, we investigate whether generating backdoor attacks in DMs can be as simple as BadNets, i.e., by only contaminating the training dataset without tampering the original diffusion process. In this more realistic backdoor setting, we uncover bilateral backdoor effects that not only serve an adversarial purpose (compromising the functionality of DMs) but also offer a defensive advantage (which can be leveraged for backdoor defense). Specifically, we find that a BadNets-like backdoor attack remains effective in DMs for producing incorrect images (misaligned with the intended text conditions), and thereby yielding incorrect predictions when DMs are used as classifiers. Meanwhile, backdoored DMs exhibit an increased ratio of backdoor triggers, a phenomenon we refer to as `trigger amplification', among the generated images. We show that this latter insight can be used to enhance the detection of backdoor-poisoned training data. Even under a low backdoor poisoning ratio, studying the backdoor effects of DMs is also valuable for designing anti-backdoor image classifiers. Last but not least, we establish a meaningful linkage between backdoor attacks and the phenomenon of data replications by exploring DMs' inherent data memorization tendencies. The codes of our work are available at https://github.com/OPTML-Group/BiBadDiff.