Many recent studies have found evidence for emergent reasoning capabilities in large language models, but debate persists concerning the robustness of these capabilities, and the extent to which they depend on structured reasoning mechanisms. To shed light on these issues, we perform a comprehensive study of the internal mechanisms that support abstract rule induction in an open-source language model (Llama3-70B). We identify an emergent symbolic architecture that implements abstract reasoning via a series of three computations. In early layers, symbol abstraction heads convert input tokens to abstract variables based on the relations between those tokens. In intermediate layers, symbolic induction heads perform sequence induction over these abstract variables. Finally, in later layers, retrieval heads predict the next token by retrieving the value associated with the predicted abstract variable. These results point toward a resolution of the longstanding debate between symbolic and neural network approaches, suggesting that emergent reasoning in neural networks depends on the emergence of symbolic mechanisms.

Training-free guidance enables controlled generation in diffusion and flow models, but most existing methods assume differentiable objectives and rely on gradients. This work focuses on training-free guidance addressing challenges from non-differentiable objectives and discrete data distributions. We propose an algorithmic framework TreeG: Tree Search-Based Path Steering Guidance, applicable to both continuous and discrete settings in diffusion and flow models. TreeG offers a unified perspective on training-free guidance: proposing candidates for the next step, evaluating candidates, and selecting the best to move forward, enhanced by a tree search mechanism over active paths or parallelizing exploration. We comprehensively investigate the design space of TreeG over the candidate proposal module and the evaluation function, instantiating TreeG into three novel algorithms. Our experiments show that TreeG consistently outperforms the top guidance baselines in symbolic music generation, small molecule generation, and enhancer DNA design, all of which involve non-differentiable challenges. Additionally, we identify an inference-time scaling law showing TreeG's scalability in inference-time computation.

Diffusion models have demonstrated empirical successes in various applications and can be adapted to task-specific needs via guidance. This paper introduces a form of gradient guidance for adapting or fine-tuning diffusion models towards user-specified optimization objectives. We study the theoretic aspects of a guided score-based sampling process, linking the gradient-guided diffusion model to first-order optimization. We show that adding gradient guidance to the sampling process of a pre-trained diffusion model is essentially equivalent to solving a regularized optimization problem, where the regularization term acts as a prior determined by the pre-training data. Diffusion models are able to learn data's latent subspace, however, explicitly adding the gradient of an external objective function to the sample process would jeopardize the structure in generated samples. To remedy this issue, we consider a modified form of gradient guidance based on a forward prediction loss, which leverages the pre-trained score function to preserve the latent structure in generated samples. We further consider an iteratively fine-tuned version of gradient-guided diffusion where one can query gradients at newly generated data points and update the score network using new samples. This process mimics a first-order optimization iteration in expectation, for which we proved O(1/K) convergence rate to the global optimum when the objective function is concave.

Modern detection transformers (DETRs) use a set of object queries to predict a list of bounding boxes, sort them by their classification confidence scores, and select the top-ranked predictions as the final detection results for the given input image. A highly performant object detector requires accurate ranking for the bounding box predictions. For DETR-based detectors, the top-ranked bounding boxes suffer from less accurate localization quality due to the misalignment between classification scores and localization accuracy, thus impeding the construction of high-quality detectors. In this work, we introduce a simple and highly performant DETR-based object detector by proposing a series of rank-oriented designs, combinedly called Rank-DETR. Our key contributions include: (i) a rank-oriented architecture design that can prompt positive predictions and suppress the negative ones to ensure lower false positive rates, as well as (ii) a rank-oriented loss function and matching cost design that prioritizes predictions of more accurate localization accuracy during ranking to boost the AP under high IoU thresholds. We apply our method to improve the recent SOTA methods (e.g., H-DETR and DINO-DETR) and report strong COCO object detection results when using different backbones such as ResNet-$50$, Swin-T, and Swin-L, demonstrating the effectiveness of our approach. Code is available at \url{https://github.com/LeapLabTHU/Rank-DETR}.