Circuits in Language Models

The "Locate-then-Update" paradigm has become a predominant approach in the post-training of large language models (LLMs), identifying critical components via mechanistic interpretability for targeted parameter updates. However, this paradigm rests on a fundamental yet unverified assumption: can mechanisms derived from current static parameters reliably guide future dynamic parameter updates? To investigate this, we systematically track the structural evolution of Transformer circuits throughout the supervised fine-tuning (SFT) process, revealing the underlying dynamics of task mechanisms. We introduce three novel metrics-Circuit Distance, Circuit Stability, and Circuit Conflict-to analyze circuit evolution across three dimensions: neural migration, semantic stability, and cross-task interference. Our empirical results reveal that circuits inherently exhibit "Free Evolution" during parameter updates. Consequently, static mechanisms extracted from current states inevitably suffer from temporal latency, making them fundamentally inadequate for guiding future states. Moreover, by deconstructing the "illusion of effectiveness" in existing methods, this work underscores the necessity of "foresight" in mechanistic localization and proposes a predictive framework for future research.

Automating analog circuit design remains a longstanding challenge in Electronic Design Automation (EDA). While Transformer-based Large Language Models (LLMs) have revolutionized software code generation, their application to analog hardware design is hindered by two critical limitations: (i) the scarcity of analog design datasets containing natural language description of a design and its corresponding netlist, and (ii) the inefficiency of general-purpose tokenizers (e.g., Byte Pair Encoding (BPE)) in capturing the inherent graph structure of circuits. To bridge this gap, first, we curate the largest annotated dataset of analog circuit netlists to date, comprising 31,341 netlist-natural language description pairs across all major circuit classes. Furthermore, we propose Circuit Tokenizer (CKT), a novel circuit graph tokenizer designed to encode netlist connectivity by explicitly mining frequent subcircuits. In terms of scalability, CKT overcomes the bottleneck of prior circuit graph serialization methods where vocabulary size scales linearly with maximum number of components in the dataset, n_max, (O(n_max)); instead, CKT decouples vocabulary growth from circuit complexity, achieving a constant O(1) complexity. Empirically, CKT outperforms standard BPE on circuit topology representation, reducing sequence length by 57% and achieving a 2.3x superior compression ratio using a compact, fixed vocabulary of size 512. Leveraging this optimized tokenization, we train a circuit-specific language model, CircuitFormer, a 511M parameter encoder-decoder transformer. Our model achieves 100% syntactic correctness and an 83% functional success rate across all major analog circuit categories, outperforming state-of-the-art open-source LLMs by 10% and 14%, respectively, while requiring 240x fewer parameters. The dataset is publicly available at https://huggingface.co/datasets/touhid314/cktformer-dataset.

Perturbation probing generates task-specific causal hypotheses for FFN neurons in large language models using two forward passes per prompt and no backpropagation, followed by a one-time intervention sweep of about 150 passes amortized across all identified neurons. Across eight behavioral circuits, 13 models, and four architecture families, we identify two circuit structures that organize LLM behavior. Opposition circuits appear when RLHF suppresses a pre-training tendency. In safety refusal, about 50 neurons, or 0.014 percent of all neurons, control the refusal template; ablating them changes 80 percent of response formats on 520 AdvBench prompts while producing near-zero harmful compliance, 3 of 520 cases, all with disclaimers. Routing circuits appear for pre-training behaviors distributed through attention. For language selection, residual-stream direction injection switches English to Chinese output on 99.1 percent of 580 benchmark prompts in the 3 of 19 tested models that satisfy three observed conditions: bilingual training, FFN-to-skip signal ratio between 0.3 and 1.1, and linear representability. The same intervention fails on the other 16 models and on math, code, and factual circuits, defining the limits of directional steering. The FFN-to-skip signal ratio, computed from the same two forward passes, distinguishes the two structures and predicts the appropriate intervention. Circuit topology varies by architecture, from Qwen's concentrated FFN bottleneck to Gemma's normalization-shielded circuit. In Qwen3.5-2B, ablating 20 neurons eliminates multi-turn sycophantic capitulation, while amplifying 10 related neurons improves factual correction from 52 percent to 88 percent on 200 TruthfulQA prompts. These results show that perturbation probing offers mechanistic insight into RLHF-organized behavior and a practical toolkit for precision template-layer editing.

Mechanistic interpretability has made it possible to localize circuits underlying specific behaviors in language models, but existing methods are expensive, model-specific, and difficult to scale to larger architectures. We introduce \textbf{Differentiable Faithfulness Alignment (DFA)}, a framework that transfers circuit information from a smaller source model to a larger target model through a learned differentiable alignment. DFA projects source-model node importance scores into the target model and trains this mapping with a soft faithfulness objective, avoiding full circuit discovery on the target model. We evaluate DFA on Llama-3 and Qwen-2.5 across six tasks spanning factual retrieval, multiple-choice reasoning, and arithmetic. The strongest results occur on Llama-3 $1$B$\rightarrow3$B, where aligned circuits are often competitive with direct node attribution and zero-shot transfer remains effective. Recovery weakens for larger source--target gaps and is substantially lower on Qwen-2.5, suggesting that transfer becomes harder as architectural and scaling differences increase. Overall, DFA consistently outperforms simple baselines and, in some settings, recovers target-model circuits with faithfulness comparable to or stronger than direct attribution. These results suggest that smaller models can provide useful mechanistic priors for larger ones, while highlighting both the promise and the limits of node-level cross-model circuit alignment.\footnote{Code is available at https://github.com/jasonshaoshun/dfa-circuits.

When a language model agrees with a user's false belief, is it failing to detect the error, or noticing and agreeing anyway? We show the latter. Across twelve open-weight models from five labs, spanning small to frontier scale, the same small set of attention heads carries a "this statement is wrong" signal, whether the model is evaluating a claim on its own or being pressured to agree with a user. Silencing these heads flips sycophantic behavior sharply while leaving factual accuracy intact, so the circuit controls deference rather than knowledge. Edge-level path patching confirms that the same head-to-head connections drive sycophancy, factual lying, and instructed lying. Opinion-agreement, where no factual ground truth exists, reuses these head positions but writes into an orthogonal direction, ruling out a simple "truth-direction" reading of the substrate. Alignment training leaves this circuit in place: an RLHF refresh cuts sycophantic behavior roughly tenfold while the shared heads persist or grow, a pattern that replicates on an independent model family and under targeted anti-sycophancy DPO. When these models sycophant, they register that the user is wrong and agree anyway.

Transformers commonly exhibit an attention sink: disproportionately high attention to the first position. We study this behavior in GPT-2-style models with learned query biases and absolute positional embeddings. Combining structural analysis with causal interventions, validated across natural-language, mathematical, and code inputs, we find that the sink arises from the interaction among (i) a learned query bias, (ii) the first-layer MLP transformation of the positional encoding, and (iii) structure in the key projection. Crucially, each component we identify is individually dispensable: architectures omitting each of them robustly exhibit sinks. This indicates that attention sinks may arise through distinct circuits across architectures. These findings inform mitigation of sinks, and motivate broader investigation into why sinks emerge.

Applying steering vectors to large language models (LLMs) is an efficient and effective model alignment technique, but we lack an interpretable explanation for how it works--specifically, what internal mechanisms steering vectors affect and how this results in different model outputs. To investigate the causal mechanisms underlying the effectiveness of steering vectors, we conduct a comprehensive case study on refusal. We propose a multi-token activation patching framework and discover that different steering methodologies leverage functionally interchangeable circuits when applied at the same layer. These circuits reveal that steering vectors primarily interact with the attention mechanism through the OV circuit while largely ignoring the QK circuit. Freezing all attention scores during steering drops performance by only 8.83% across three model families. A mathematical decomposition of the steered OV circuit further reveals semantically interpretable concepts, even in cases where the steering vector itself does not. Leveraging the activation patching results, we show that steering vectors can be sparsified by up to 85-96% while retaining most performance, and that different steering methodologies agree on a subset of important dimensions.

We localize the policy routing mechanism in alignment-trained language models. An intermediate-layer attention gate reads detected content and triggers deeper amplifier heads that boost the signal toward refusal. In smaller models the gate and amplifier are single heads; at larger scale they become bands of heads across adjacent layers. The gate contributes under 1% of output DLA, yet interchange testing (p < 0.001) and knockout cascade confirm it is causally necessary. Interchange screening at n >= 120 detects the same motif in twelve models from six labs (2B to 72B), though specific heads differ by lab. Per-head ablation weakens up to 58x at 72B and misses gates that interchange identifies; at scale, interchange is the only reliable audit. Modulating the detection-layer signal continuously controls policy from hard refusal through evasion to factual answering. On safety prompts the same intervention turns refusal into harmful guidance, showing that the safety-trained capability is gated by routing, not removed. Thresholds vary by topic and by input language, and the circuit relocates across generations within a family even while behavioral benchmarks register no change. Routing is early-commitment: the gate fires at its own layer before deeper layers finish processing the input. An in-context substitution cipher collapses gate interchange necessity by 70 to 99% across three models, and the model switches to puzzle-solving rather than refusal. Injecting the plaintext gate activation into the cipher forward pass restores 48% of refusals in Phi-4-mini, localizing the bypass to the routing interface. A second method, cipher contrast analysis, uses plain/cipher DLA differences to map the full cipher-sensitive routing circuit in O(3n) forward passes. Any encoding that defeats detection-layer pattern matching bypasses the policy regardless of whether deeper layers reconstruct the content.

Post-training pretrained autoregressive models (ARMs) into masked diffusion models (MDMs) provides an efficient route to diffusion language modeling, but it remains unclear whether the resulting models reuse inherited autoregressive computation or reorganize it for non-autoregressive generation. We compare two 7B ARM-MDM families across four controlled diagnostic tasks and find a task-dependent mechanism shift. On prefix-dominant tasks, MDMs largely preserve inherited high-attribution pathways or exhibit only modest changes in where computation occurs. On globally constrained tasks, the reorganization is substantially stronger, with task-relevant computation shifting toward earlier layers. This depth-wise pattern persists across prompt resampling, circuit budgets, and tested inference budgets, while targeted ablations support the functional importance of the identified structures under the tested intervention protocols. At the component level, diagnostic probes suggest that ARMs rely more strongly on sharply specialized components, whereas MDMs exhibit weaker single-component specialization and more diffuse output-space alignment. Together, these results suggest that diffusion post-training selectively preserves or reorganizes inherited computation according to task structure, rather than uniformly replacing autoregressive mechanisms.