Mechanistic interpretability aims to reverse-engineer large language models (LLMs) into human-understandable computational circuits. However, the complexity of pretrained models often obscures the minimal mechanisms required for specific reasoning tasks. In this work, we train small, attention-only transformers from scratch on a symbolic version of the Indirect Object Identification (IOI) task -- a benchmark for studying coreference -- like reasoning in transformers. Surprisingly, a single-layer model with only two attention heads achieves perfect IOI accuracy, despite lacking MLPs and normalization layers. Through residual stream decomposition, spectral analysis, and embedding interventions, we find that the two heads specialize into additive and contrastive subcircuits that jointly implement IOI resolution. Furthermore, we show that a two-layer, one-head model achieves similar performance by composing information across layers through query-value interactions. These results demonstrate that task-specific training induces highly interpretable, minimal circuits, offering a controlled testbed for probing the computational foundations of transformer reasoning.

Backdoor attacks present a substantial security concern for deep learning models, especially those utilized in applications critical to safety and security. These attacks manipulate model behavior by embedding a hidden trigger during the training phase, allowing unauthorized control over the model's output during inference time. Although numerous defenses exist for image classification models, there is a conspicuous absence of defenses tailored for time series data, as well as an end-to-end solution capable of training clean models on poisoned data. To address this gap, this paper builds upon Anti-Backdoor Learning (ABL) and introduces an innovative method, End-to-End Anti-Backdoor Learning (E2ABL), for robust training against backdoor attacks. Unlike the original ABL, which employs a two-stage training procedure, E2ABL accomplishes end-to-end training through an additional classification head linked to the shallow layers of a Deep Neural Network (DNN). This secondary head actively identifies potential backdoor triggers, allowing the model to dynamically cleanse these samples and their corresponding labels during training. Our experiments reveal that E2ABL significantly improves on existing defenses and is effective against a broad range of backdoor attacks in both image and time series domains.