We propose using mechanistic interpretability -- techniques for reverse engineering model weights into human-interpretable algorithms -- to derive and compactly prove formal guarantees on model performance.We prototype this approach by formally proving accuracy lower bounds for a small transformer trained on Max-of-$K$, validating proof transferability across 151 random seeds and four values of $K$.We create 102 different computer-assisted proof strategies and assess their length and tightness of bound on each of our models.Using quantitative metrics, we find that shorter proofs seem to require and provide more mechanistic understanding.Moreover, we find that more faithful mechanistic understanding leads to tighter performance bounds.We confirm these connections by qualitatively examining a subset of our proofs.Finally, we identify compounding structureless errors as a key challenge for using mechanistic interpretability to generate compact proofs on model performance.

Foundation models are becoming valuable tools in medicine. Yet despite their promise, the best way to leverage Large Language Models (LLMs) in complex medical tasks remains an open question. We introduce a novel multi-agent framework, named **M**edical **D**ecision-making **Agents** (**MDAgents**) that helps to address this gap by automatically assigning a collaboration structure to a team of LLMs. The assigned solo or group collaboration structure is tailored to the medical task at hand, a simple emulation inspired by the way real-world medical decision-making processes are adapted to tasks of different complexities. We evaluate our framework and baseline methods using state-of-the-art LLMs across a suite of real-world medical knowledge and clinical diagnosis benchmarks, including a comparison ofLLMs' medical complexity classification against human physicians. MDAgents achieved the **best performance in seven out of ten** benchmarks on tasks requiring an understanding of medical knowledge and multi-modal reasoning, showing a significant **improvement of up to 4.2\%** ($p$ < 0.05) compared to previous methods' best performances. Ablation studies reveal that MDAgents effectively determines medical complexity to optimize for efficiency and accuracy across diverse medical tasks. Notably, the combination of moderator review and external medical knowledge in group collaboration resulted in an average accuracy **improvement of 11.8\%**.

Fenchel-Young losses are a family of loss functions, encompassing the squared,logistic and sparsemax losses, among others. They are convex w.r.t. the modeloutput and the target, separately. Each Fenchel-Young loss is implicitly associatedwith a link function, that maps model outputs to predictions. For instance, thelogistic loss is associated with the soft argmax link function. Can we build newloss functions associated with the same link function as Fenchel-Young losses?In this paper, we introduce Fitzpatrick losses, a new family of separately convexloss functions based on the Fitzpatrick function. A well-known theoretical tool inmaximal monotone operator theory, the Fitzpatrick function naturally leads to arefined Fenchel-Young inequality, making Fitzpatrick losses tighter than Fenchel-Young losses, while maintaining the same link function for prediction. As anexample, we introduce the Fitzpatrick logistic loss and the Fitzpatrick sparsemaxloss, counterparts of the logistic and the sparsemax losses. This yields two newtighter losses associated with the soft argmax and the sparse argmax, two of themost ubiquitous output layers used in machine learning. We study in details theproperties of Fitzpatrick losses and, in particular, we show that they can be seen asFenchel-Young losses using a modified, target-dependent generating function.

To make sense of massive data, we often first fit simplified models and then interpret the parameters; for example, we cluster the text embeddings and then interpret the mean parameters of each cluster.However, these parameters are often high-dimensional and hard to interpret.To make model parameters directly interpretable, we introduce a family of statistical models---including clustering, time series, and classification models---parameterized by . For example, a cluster of text about COVID could be parameterized by the predicate `` ''.To learn these statistical models effectively, we develop a model-agnostic algorithm that optimizes continuous relaxations of predicate parameters with gradient descent and discretizes them by prompting language models (LMs).Finally, we apply our framework to a wide range of problems: taxonomizing user chat dialogues, characterizing how they evolve across time, finding categories where one language model is better than the other, clustering math problems based on subareas, and explaining visual features in memorable images.Our framework is highly versatile, applicable to both textual and visual domains, can be easily steered to focus on specific properties (e.g.

Incorporating biological neuronal properties into Artificial Neural Networks (ANNs) to enhance computational capabilities is under active investigation in the field of deep learning. Inspired by recent findings indicating that dendrites adhere to quadratic integration rule for synaptic inputs, this study explores the computational benefits of quadratic neurons. We theoretically demonstrate that quadratic neurons inherently capture correlation within structured data, a feature that grants them superior generalization abilities over traditional neurons. This is substantiated by few-shot learning experiments. Furthermore, we integrate the quadratic rule into Convolutional Neural Networks (CNNs) using a biologically plausible approach, resulting in innovative architectures--Dendritic integration inspired CNNs (Dit-CNNs). Our Dit-CNNs compete favorably with state-of-the-art models across multiple classification benchmarks, e.g., ImageNet-1K, while retaining the simplicity and efficiency of traditional CNNs.

We cast real-world humanoid control as a next token prediction problem, akin to predicting the next word in language. Our model is a causal transformer trained via autoregressive prediction of sensorimotor sequences. To account for the multi-modal nature of the data, we perform prediction in a modality-aligned way, and for each input token predict the next token from the same modality. This general formulation enables us to leverage data with missing modalities, such as videos without actions. We train our model on a dataset of sequences from a prior neural network policy, a model-based controller, motion capture, and YouTube videos of humans. We show that our model enables a real humanoid robot to walk in San Francisco zero-shot. Our model can transfer to the real world even when trained on only 27 hours of walking data, and can generalize to commands not seen during training. These findings suggest a promising path toward learning challenging real-world control tasks by generative modeling of sensorimotor sequences.

Graph regression is a fundamental task that has gained significant attention invarious graph learning tasks. However, the inference process is often not easilyinterpretable. Current explanation techniques are limited to understanding GraphNeural Network (GNN) behaviors in classification tasks, leaving an explanation gapfor graph regression models. In this work, we propose a novel explanation methodto interpret the graph regression models (XAIG-R). Our method addresses thedistribution shifting problem and continuously ordered decision boundary issuesthat hinder existing methods away from being applied in regression tasks. Weintroduce a novel objective based on the graph information bottleneck theory (GIB)and a new mix-up framework, which can support various GNNs and explainersin a model-agnostic manner. Additionally, we present a self-supervised learningstrategy to tackle the continuously ordered labels in regression tasks. We evaluateour proposed method on three benchmark datasets and a real-life dataset introducedby us, and extensive experiments demonstrate its effectiveness in interpreting GNNmodels in regression tasks.

However, training EBMs on data in discrete or mixed state spaces poses significant challenges due to the lack of robust and fast sampling methods. In this work, we propose to train discrete EBMs with Energy Discrepancy, a loss function which only requires the evaluation of the energy function at data points and their perturbed counterparts, thus eliminating the need for Markov chain Monte Carlo. We introduce perturbations of the data distribution by simulating a diffusion process on the discrete state space endowed with a graph structure. This allows us to inform the choice of perturbation from the structure of the modelled discrete variable, while the continuous time parameter enables fine-grained control of the perturbation. Empirically, we demonstrate the efficacy of the proposed approaches in a wide range of applications, including the estimation of discrete densities with non-binary vocabulary and binary image modelling. We also introduce the first application of EBMs to tabular data sets with applications in synthetic data generation and calibrated classification.

Widely adopted in modern Vision Transformer designs, Softmax attention can effectively capture long-range visual information; however, it incurs excessive computational cost when dealing with high-resolution inputs. In contrast, linear attention naturally enjoys linear complexity and has great potential to scale up to higher-resolution images. Nonetheless, the unsatisfactory performance of linear attention greatly limits its practical application in various scenarios. In this paper, we take a step forward to close the gap between the linear and Softmax attention with novel theoretical analyses, which demystify the core factors behind the performance deviations. Specifically, we present two key perspectives to understand and alleviate the limitations of linear attention: the injective property and the local modeling ability. Firstly, we prove that linear attention is not injective, which is prone to assign identical attention weights to different query vectors, thus adding to severe semantic confusion since different queries correspond to the same outputs. Secondly, we confirm that effective local modeling is essential for the success of Softmax attention, in which linear attention falls short. The aforementioned two fundamental differences significantly contribute to the disparities between these two attention paradigms, which is demonstrated by our substantial empirical validation in the paper. In addition, more experiment results indicate that linear attention, as long as endowed with these two properties, can outperform Softmax attention across various tasks while maintaining lower computation complexity.

We propose a novel family of decision-aware surrogate losses, called Perturbation Gradient (PG) losses, for the predict-then-optimize framework. These losses directly approximate the downstream decision loss and can be optimized using off-the-shelf gradient-based methods. Importantly, unlike existing surrogate losses, the approximation error of our PG losses vanishes as the number of samples grows. This implies that optimizing our surrogate loss yields a best-in-class policy asymptotically, even in misspecified settings. This is the first such result in misspecified settings and we provide numerical evidence confirming our PG losses substantively outperform existing proposals when the underlying model is misspecified and the noise is not centrally symmetric. Insofar as misspecification is commonplace in practice -- especially when we might prefer a simpler, more interpretable model -- PG losses offer a novel, theoretically justified, method for computationally tractable decision-aware learning.