"Socrates is human. All humans are mortal. Therefore, Socrates is mortal." This classical example demonstrates two-hop reasoning, where a conclusion logically follows from two connected premises. While transformer-based Large Language Models (LLMs) can make two-hop reasoning, they tend to collapse to random guessing when faced with distracting premises. To understand the underlying mechanism, we train a three-layer transformer on synthetic two-hop reasoning tasks. The training dynamics show two stages: a slow learning phase, where the 3-layer transformer performs random guessing like LLMs, followed by an abrupt phase transitions, where the 3-layer transformer suddenly reaches $100%$ accuracy. Through reverse engineering, we explain the inner mechanisms for how models learn to randomly guess between distractions initially, and how they learn to ignore distractions eventually. We further propose a three-parameter model that supports the causal claims for the mechanisms to the training dynamics of the transformer. Finally, experiments on LLMs suggest that the discovered mechanisms generalize across scales. Our methodologies provide new perspectives for scientific understandings of LLMs and our findings provide new insights into how reasoning emerges during training.

Recent advances in context-augmented generation (CAG) techniques, particularly retrieval-augmented generation (RAG) (Gupta et al., 2024; Gao et al., 2023) and in-context learning (ICL) (Dong et al., 2022; Wei et al., 2022), have been widely adopted in large language models (LLMs) (Dubey et al., 2024; Achiam et al., 2023), improving their ability to generalize to unseen tasks with contextual information, as demonstrated in Figure 1 (top). These techniques employ a sequential encoding process to ground LLM inputs with knowledge from external sources: concatenating the retrieved texts into one sequence, and encoding the sequence into key-value (KV) states as the context for subsequent queries. While this new, significantly longer input improves performance, the increased latency in context prefilling becomes a bottleneck in tasks that require long inputs but generate short outputs (Bai et al., 2023; Agarwal et al., 2024; Jiang et al., 2024b). For example, prefilling a 128K context takes 17 seconds, whereas generating 256 tokens requires only 6 seconds. This discrepancy leaves significant room to improve the practical efficiency of CAG systems in real-world deployments (Liu, 2022; Chase, 2022).

Practitioners have consistently observed three puzzling phenomena in transformer-based large language models (LLMs): attention sinks, value-state drains, and residual-state peaks, collectively referred to as extreme-token phenomena. These phenomena are characterized by certain so-called "sink tokens" receiving disproportionately high attention weights, exhibiting significantly smaller value states, and having much larger residual-state norms than those of other tokens. These extreme tokens give rise to various challenges in LLM inference, quantization, and interpretability. We elucidate the mechanisms behind extreme-token phenomena. First, we show that these phenomena arise in very simple architectures -- transformers with one to three layers -- trained on a toy model, the Bigram-Backcopy (BB) task. In this setting, we identify an active-dormant mechanism, where attention heads become sinks for specific input domains while remaining non-sinks for others. Our theoretical analysis of the training dynamics reveals that these phenomena are driven by a mutual reinforcement mechanism. Building on these insights, we propose strategies to mitigate extreme-token phenomena during pretraining, including replacing softmax with ReLU and Adam with SGD. Next, we extend our analysis to pretrained LLMs, including Llama and OLMo, showing that many attention heads exhibit a similar active-dormant mechanism as in the BB task, and that the mutual reinforcement mechanism also governs the emergence of extreme-token phenomena during LLM pretraining. Our results reveal that many of the static and dynamic properties of extreme-token phenomena predicted by the BB task align with observations in pretrained LLMs.

How to efficiently serve Large Language Models (LLMs) has become a pressing issue because of their huge computational cost in their autoregressive generation process. To mitigate computational costs, LLMs often employ the KV Cache technique to improve the generation speed. While improving the computational efficiency, the storage requirements of the KV cache are substantial, particularly in long-context scenarios, leading to significant memory consumption. Existing KV cache eviction methods often degrade the performance of LLMs in long-context scenarios due to the information loss introduced by eviction. In this paper, we propose a novel KV cache merging approach, called KVMerger, to achieve adaptive KV cache compression for long-context tasks without significant performance degradation under constrained memory budgets. Our approach is inspired by the intriguing observation that key states exhibit high similarity at the token level within a single sequence. To facilitate merging, we develop an effective yet straightforward merging set identification algorithm to identify suitable KV states for merging. Our merging set identification algorithm stimulates the second observation that KV cache sparsity, from similarity perspective, is independent of the dataset and remains persistent at the model level. Subsequently, we propose a Gaussian kernel weighted merging algorithm to selectively merge all states within each merging set. We conduct extensive experiments to demonstrate the effectiveness of KVMerger for long-context tasks under constrained memory budgets, applying it to models including Llama2-7B-chat and Llama2-13B-chat. Using the LongBench and ZeroScroll benchmarks, we compare our method with other KV cache compression techniques, including H2O and CaM, showing that our method achieves superior performance across tasks with both 50% and 35% KV cache budgets.

Values are things that are important to us. Actions activate values - they either go against our values or they promote our values. Values themselves can either be conforming or conflicting depending on the action that is taken. In this short paper, we argue that values may be classified as one of two types - conflicting and inherently conflicting values. They are distinguished by the fact that the latter in some sense can be thought of as being independent of actions. This allows us to do two things: i) check whether a set of values is consistent and ii) check whether it is in conflict with other sets of values.

An agent's assessment of its trust in another agent is commonly taken to be a measure of the reliability/predictability of the latter's actions. It is based on the trustor's past observations of the behaviour of the trustee and requires no knowledge of the inner-workings of the trustee. However, in situations that are new or unfamiliar, past observations are of little help in assessing trust. In such cases, knowledge about the trustee can help. A particular type of knowledge is that of values - things that are important to the trustor and the trustee. In this paper, based on the premise that the more values two agents share, the more they should trust one another, we propose a simple approach to trust assessment between agents based on values, taking into account if agents trust cautiously or boldly, and if they depend on others in carrying out a task.

In many environments only a tiny subset of all states yield high reward. In these cases, few of the interactions with the environment provide a relevant learning signal. Hence, we may want to preferentially train on those high-reward states and the probable trajectories leading to them. To this end, we advocate for the use of a backtracking model that predicts the preceding states that terminate at a given high-reward state. We can train a model which, starting from a high value state (or one that is estimated to have high value), predicts and sample for which the (state, action)-tuples may have led to that high value state. These traces of (state, action) pairs, which we refer to as Recall Traces, sampled from this backtracking model starting from a high value state, are informative as they terminate in good states, and hence we can use these traces to improve a policy. We provide a variational interpretation for this idea and a practical algorithm in which the backtracking model samples from an approximate posterior distribution over trajectories which lead to large rewards. Our method improves the sample efficiency of both on- and off-policy RL algorithms across several environments and tasks.