We present a mechanistic case study of a format-dependent reasoning failure in Llama-3.1-8B-Instruct, where the model incorrectly judges "9.11" as larger than "9.8" in chat or Q&A formats, but answers correctly in simple format. Through systematic intervention, we discover transformers implement even/odd attention head specialization: even indexed heads handle numerical comparison, while odd heads serve incompatible functions. The bug requires exactly 8 even heads at Layer 10 for perfect repair. Any combination of 8+ even heads succeeds, while 7 or fewer completely fails, revealing sharp computational thresholds with perfect redundancy among the 16 even heads. SAE analysis reveals the mechanism: format representations separate (10% feature overlap at Layer 7), then re-entangle with different weightings (80% feature overlap at Layer 10), with specific features showing 1.5x amplification in failing formats. We achieve perfect repair using only 25% of attention heads and identify a 60% pattern replacement threshold, demonstrating that apparent full-module requirements hide sophisticated substructure with implications for interpretability and efficiency. All of our code is available at https://github.com/gussand/surgeon.

"straightforward" from simply looking at the equations, we maintain that the multi-layer extension is a significant However, note from Figure 5 (appendix) the pattern in which the layers are sequentially "added" by the We consider the direction of finding other optimizations for layer choice an important future work. From eqn 3, you are correct, it is possible for all layers to contribute differently. Intuitively, the most impactful layers are added first. The decoding for this layer notation is shown in Figure 5 (appendix). We will be sure to clarify these points in the final version.

Large language models (LLMs) have achieved remarkable success in contextual knowledge understanding. In this paper, we show that these concentrated massive values consistently emerge in specific regions of attention queries (Q) and keys (K) while not having such patterns in values (V) in various modern transformer-based LLMs (Q, K, and V mean the representations output by the query, key, and value layers respectively). Through extensive experiments, we further demonstrate that these massive values play a critical role in interpreting contextual knowledge (i.e., knowledge obtained from the current context window) rather than in retrieving parametric knowledge stored within the model's parameters. Our further investigation of quantization strategies reveals that ignoring these massive values leads to a pronounced drop in performance on tasks requiring rich contextual understanding, aligning with our analysis. Finally, we trace the emergence of concentrated massive values and find that such concentration is caused by Rotary Positional Encoding (RoPE), which has appeared since the first layers. These findings shed new light on how Q and K operate in LLMs and offer practical insights for model design and optimization.

This paper presents a pioneering exploration of the mechanisms underlying large foundation models' (LFMs) weights, aiming to simplify AI research. Through extensive observation and analysis on prevailing LFMs, we find that regardless of initialization strategies, their weights predominantly follow a Gaussian distribution, with occasional sharp, inverted T-shaped, or linear patterns. We further discover that the weights share the i.i.d. properties of Gaussian noise, and explore their direct relationship. We find that transformation weights can be derived from Gaussian noise, and they primarily serve to increase the standard deviation of pre-trained weights, with their standard deviation growing with layer depth. In other words, transformation weights broaden the acceptable deviation from the optimal weights, facilitating adaptation to downstream tasks. Building upon the above conclusions, we thoroughly discussed the nature of optimal weights, ultimately concluding that they should exhibit zero-mean, symmetry, and sparsity, with the sparse values being a truncated Gaussian distribution and a few outliers. Our experiments in LFM adaptation and editing demonstrate the effectiveness of these insights. We hope these findings can provide a foundational understanding to pave the way for future advancements in the LFM community.

Circuit discovery with edge-level ablation has become a foundational framework for mechanism interpretability of language models. However, its focus on individual edges often overlooks the sequential, path-level causal relationships that underpin complex behaviors, thus potentially leading to misleading or incomplete circuit discoveries. To address this issue, we propose a novel path-level circuit discovery framework capturing how behaviors emerge through interconnected linear chain and build towards complex behaviors. Our framework is constructed upon a fully-disentangled linear combinations of ``memory circuits'' decomposed from the original model. To discover functional circuit paths, we leverage a 2-step pruning strategy by first reducing the computational graph to a faithful and minimal subgraph and then applying causal mediation to identify common paths of a specific skill, termed as skill paths. In contrast to circuit graph from existing works, we focus on the complete paths of a generic skill rather than on the fine-grained responses to individual components of the input. To demonstrate this, we explore three generic language skills, namely Previous Token Skill, Induction Skill and In-Context Learning Skill using our framework and provide more compelling evidence to substantiate stratification and inclusiveness of these skills.

We present GIFT (Generative Interpretable Fine-tuning Transformers) for fine-tuning pretrained (often large) Transformer models at downstream tasks in a parameter-efficient way with built-in interpretability. Our GIFT is a deep parameter-residual learning method, which addresses two problems in fine-tuning a pretrained Transformer model: Where to apply the parameter-efficient fine-tuning (PEFT) to be extremely lightweight yet sufficiently expressive, and How to learn the PEFT to better exploit the knowledge of the pretrained model in a direct way? For the former, we select the final projection (linear) layer in the multi-head self-attention of a Transformer model, and verify its effectiveness. For the latter, in contrast to the prior art that directly introduce new model parameters (often in low-rank approximation form) to be learned in fine-tuning with downstream data, we propose a method for learning to generate the fine-tuning parameters. Our GIFT is a hyper-Transformer which take as input the pretrained parameters of the projection layer to generate its fine-tuning parameters using a proposed Parameter-to-Cluster Attention (PaCa). The PaCa results in a simple clustering-based forward explainer that plays the role of semantic segmentation in testing. In experiments, our proposed GIFT is tested on the VTAB benchmark and the fine-grained visual classification (FGVC) benchmark. It obtains significantly better performance than the prior art. Our code is available at https://github.com/savadikarc/gift

Investigating deep learning language models has always been a significant research area due to the ``black box" nature of most advanced models. With the recent advancements in pre-trained language models based on transformers and their increasing integration into daily life, addressing this issue has become more pressing. In order to achieve an explainable AI model, it is essential to comprehend the procedural steps involved and compare them with human thought processes. Thus, in this paper, we use simple, well-understood non-language tasks to explore these models' inner workings. Specifically, we apply a pre-trained language model to constrained arithmetic problems with hierarchical structure, to analyze their attention weight scores and hidden states. The investigation reveals promising results, with the model addressing hierarchical problems in a moderately structured manner, similar to human problem-solving strategies. Additionally, by inspecting the attention weights layer by layer, we uncover an unconventional finding that layer 10, rather than the model's final layer, is the optimal layer to unfreeze for the least parameter-intensive approach to fine-tune the model. We support these findings with entropy analysis and token embeddings similarity analysis. The attention analysis allows us to hypothesize that the model can generalize to longer sequences in ListOps dataset, a conclusion later confirmed through testing on sequences longer than those in the training set. Lastly, by utilizing a straightforward task in which the model predicts the winner of a Tic Tac Toe game, we identify limitations in attention analysis, particularly its inability to capture 2D patterns.

Simulating particle detector response is the single most expensive step in the Large Hadron Collider computational pipeline. Recently it was shown that normalizing flows can accelerate this process while achieving unprecedented levels of accuracy, but scaling this approach up to higher resolutions relevant for future detector upgrades leads to prohibitive memory constraints. To overcome this problem, we introduce Inductive CaloFlow (iCaloFlow), a framework for fast detector simulation based on an inductive series of normalizing flows trained on the pattern of energy depositions in pairs of consecutive calorimeter layers. We further use a teacher-student distillation to increase sampling speed without loss of expressivity. As we demonstrate with Datasets 2 and 3 of the CaloChallenge2022, iCaloFlow can realize the potential of normalizing flows in performing fast, high-fidelity simulation on detector geometries that are ~ 10 - 100 times higher granularity than previously considered.

Transformer networks have revolutionized NLP representation learning since they were introduced. Though a great effort has been made to explain the representation in transformers, it is widely recognized that our understanding is not sufficient. One important reason is that there lack enough visualization tools for detailed analysis. In this paper, we propose to use dictionary learning to open up these "black boxes" as linear superpositions of transformer factors. Through visualization, we demonstrate the hierarchical semantic structures captured by the transformer factors, e.g., word-level polysemy disambiguation, sentence-level pattern formation, and long-range dependency. While some of these patterns confirm the conventional prior linguistic knowledge, the rest are relatively unexpected, which may provide new insights. We hope this visualization tool can bring further knowledge and a better understanding of how transformer networks work. The code is available at https://github.com/zeyuyun1/TransformerVis