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Interpretability

Jiachang Liu, Rui Zhang, Cynthia Rudin

Survival analysis is an important research topic with applications in healthcare, business, and manufacturing. One essential tool in this area is the Cox proportional hazards (CPH) model, which is widely used for its interpretability, flexibility, and predictive performance. However, for modern data science challenges such as high dimensionality (both $n$ and $p$) and high feature correlations, current algorithms to train the CPH model have drawbacks, preventing us from using the CPH model at its full potential. The root cause is that the current algorithms, based on the Newton method, have trouble converging due to vanishing second order derivatives when outside the local region of the minimizer. To circumvent this problem, we propose new optimization methods by constructing and minimizing surrogate functions that exploit hidden mathematical structures of the CPH model. Our new methods are easy to implement and ensure monotonic loss decrease and global convergence. Empirically, we verify the computational efficiency of our methods. As a direct application, we show how our optimization methods can be used to solve the cardinality-constrained CPH problem, producing very sparse high-quality models that were not previously practical to construct. We list several extensions that our breakthrough enables, including optimization opportunities, theoretical questions on CPH's mathematical structure, as well as other CPH-related applications.

Interpretability

Vivien Cabannes, Charles Arnal, Wassim Bouaziz, Xingyu Yang, Francois Charton, Julia Kempe

Chain-of-Thought (CoT) reasoning is known to improve Large Language Models both empirically and in terms of theoretical approximation power.However, our understanding of the inner workings and conditions of apparition of CoT capabilities remains limited.This paper helps fill this gap by demonstrating how CoT reasoning emerges in transformers in a controlled and interpretable setting.In particular, we observe the appearance of a specialized attention mechanism dedicated to iterative reasoning, which we coined "iteration heads".We track both the emergence and the precise working of these iteration heads down to the attention level, and measure the transferability of the CoT skills to which they give rise between tasks.

Generative Models · In Context Learning

Akshay Krishnamurthy, Keegan Harris, Dylan J Foster, Cyril Zhang, Aleksandrs Slivkins

We investigate the extent to which contemporary Large Language Models (LLMs) can engage in exploration, a core capability in reinforcement learning and decision making. We focus on native performance of existing LLMs, without training interventions. We deploy LLMs as agents in simple multi-armed bandit environments, specifying the environment description and interaction history entirely in-context, i.e., within the LLM prompt. We experiment with GPT-3.5, GPT-4, and Llama2, using a variety of prompt designs, and find that the models do not robustly engage in exploration without substantial interventions: i) Only one configuration resulted in satisfactory exploratory behavior: GPT-4 with chain-of-thought reasoning and an externally summarized interaction history; ii) All other configurations did not result in robust exploratory behavior, including those with chain-of-thought reasoning but unsummarized history. While these findings can be interpreted positively, they suggest that external summarization—which may not be possible in more complex settings—is essential for desirable LLM behavior. We conclude that non-trivial algorithmic interventions, such as fine-tuning or dataset curation, may be required to empower LLM-based decision making agents in complex settings.

Interpretability

Pulkit Gopalani, Ekdeep S Lubana, Wei Hu

Recent analysis on the training dynamics of Transformers has unveiled an interesting characteristic: the training loss plateaus for a significant number of training steps, and then suddenly (and sharply) drops to near--optimal values. To understand this phenomenon in depth, we formulate the low-rank matrix completion problem as a masked language modeling (MLM) task, and show that it is possible to train a BERT model to solve this task to low error. Furthermore, the loss curve shows a plateau early in training followed by a sudden drop to near-optimal values, despite no changes in the training procedure or hyper-parameters. To gain interpretability insights into this sudden drop, we examine the model's predictions, attention heads, and hidden states before and after this transition. Concretely, we observe that (a) the model transitions from simply copying the masked input to accurately predicting the masked entries; (b) the attention heads transition to interpretable patterns relevant to the task; and (c) the embeddings and hidden states encode information relevant to the problem. We also analyze the training dynamics of individual model components to understand the sudden drop in loss.

Interpretability

Xinyue Luo, Jin Cheng, Yu Chen

Lossless compression of large-scale scientific floating-point data is critical yet challenging due to the presence of high-order information and noise that arises from model truncation and discretization errors. Existing entropy coding techniques fail to effectively leverage the mechanisms underlying the data generation process. This paper introduces MeLLoC(Mechanism Learning for Lossless Compression), a novel approach that combines high-order mechanism learning with classical encoding to enhance lossless compression for scientific data. The key idea is to treat the data as discrete samples from an underlying physical field described by differential equations and solve an inverse problem to identify the governing equation coefficients exhibiting more compressible numeric representations. Periodic extension techniques are employed to accelerate the decompression. Through extensive experiments on various scientific datasets, MeLLoC consistently outperforms state-of-the-art lossless compressors while offering compelling trade-offs between compression ratios and computational costs. This work opens up new avenues for exploiting domain knowledge and high-order information to improve data compression in scientific computing.

Pierre Colombo, Telmo Pessoa Pires, Malik Boudiaf, Rui Melo, Gabriel Hautreux, Etienne Malaboeuf, Johanne Charpentier, Dominic Culver, Michael Desa

In this paper, we introduce SaulLM-medium and SaulLM-large, two large language models (LLMs) families tailored for the legal sector. These models, which feature architectures of 54 billion and 140 billion parameters, respectively, are based on the Mixtral architecture. The development of SaulLM-54B and SaulLM-140B is guided by large-scale domain adaptation, divided into strategies: (1) the exploitation of continued pretaining involving a legal corpus that includes over $400$ billion tokens, (2) the implementation of a specialized legal instruction-following protocol, and (3) the alignment of model outputs with human preferences in legal interpretations. The integration of synthetically generated data in the second and third steps enhances the models' capabilities in interpreting and processing legal texts, effectively reaching state-of-the-art performance and outperforming all previous open-source models on LegalBench Instruct. This research thoroughly explores the trade-offs involved in domain-specific adaptation at this scale, offering insights that may inform future studies on domain adaptation using strong decoder models. Building upon SaulLM-7B, this study refines the approach to produce an LLM better equipped for legal tasks and domains. Additionally, we release base, instruct and aligned versions on top of SaulLM-medium and SaulLM-large under the MIT License to facilitate reuse and collaborative research.

Statistical Methods

Weichao Yang, Hongwei Shi, Xu Guo, Changliang Zou

The high-dimensional single index model (SIM), which assumes that the response is independent of the predictors given a linear combination of predictors, has drawn attention due to its flexibility and interpretability, but its efficiency is adversely affected by outlying observations and heavy-tailed distributions. This paper introduces a robust procedure by recasting the SIM into a pseudo-linear model with transformed responses. It relaxes the distributional conditions on random errors from sub-Gaussian to more general distributions and thus it is robust with substantial efficiency gain for heavy-tailed random errors. Under this paradigm, we provide asymptotically honest group inference procedures based on the idea of orthogonalization, which enjoys the feature that it does not require the zero and nonzero coefficients to be well-separated. Asymptotic null distribution and bootstrap implementation are both established. Moreover, we develop a multiple testing procedure for determining if the individual coefficients are relevant simultaneously, and show that it is able to control the false discovery rate asymptotically. Numerical results indicate that the new procedures can be highly competitive among existing methods, especially for heavy-tailed errors.

Generative Models

Jingwei Zhao, Gus Xia, Ziyu Wang, Ye Wang

In the realm of music AI, arranging rich and structured multi-track accompaniments from a simple lead sheet presents significant challenges. Such challenges include maintaining track cohesion, ensuring long-term coherence, and optimizing computational efficiency. In this paper, we introduce a novel system that leverages prior modelling over disentangled style factors to address these challenges. Our method presents a two-stage process: initially, a piano arrangement is derived from the lead sheet by retrieving piano texture styles; subsequently, a multi-track orchestration is generated by infusing orchestral function styles into the piano arrangement. Our key design is the use of vector quantization and a unique multi-stream Transformer to model the long-term flow of the orchestration style, which enables flexible, controllable, and structured music generation. Experiments show that by factorizing the arrangement task into interpretable sub-stages, our approach enhances generative capacity while improving efficiency. Additionally, our system supports a variety of music genres and provides style control at different composition hierarchies. We further show that our system achieves superior coherence, structure, and overall arrangement quality compared to existing baselines.

Causality

Ryan Welch, Jiaqi Zhang, Caroline Uhler

Causal disentanglement aims to learn about latent causal factors behind data, hold- ing the promise to augment existing representation learning methods in terms of interpretability and extrapolation. Recent advances establish identifiability results assuming that interventions on (single) latent factors are available; however, it re- mains debatable whether such assumptions are reasonable due to the inherent nature of intervening on latent variables. Accordingly, we reconsider the fundamentals and ask what can be learned using just observational data.We provide a precise characterization of latent factors that can be identified in nonlinear causal models with additive Gaussian noise and linear mixing, without any interventions or graphical restrictions. In particular, we show that the causal variables can be identified up to a _layer_-wise transformation and that further disen- tanglement is not possible. We transform these theoretical results into a practical algorithm consisting of solving a quadratic program over the score estimation of the observed data. We provide simulation results to support our theoretical guarantees and demonstrate that our algorithm can derive meaningful causal representations from purely observational data.

Data-centric AI · Data augmentation

Minui Hong, Junhyeog Yun, Insu Jeon, Gunhee Kim

Federated Learning (FL) allows multiple clients to collaboratively train models without directly sharing their private data. While various data augmentation techniques have been actively studied in the FL environment, most of these methods share input-level or feature-level data information over communication, posing potential privacy leakage. In response to this challenge, we introduce a federated data augmentation algorithm named FedAvP that shares only the augmentation policies, not the data-related information. For data security and efficient policy search, we interpret the policy loss as a meta update loss in standard FL algorithms and utilize the first-order gradient information to further enhance privacy and reduce communication costs. Moreover, we propose a meta-learning method to search for adaptive personalized policies tailored to heterogeneous clients. Our approach outperforms existing best performing augmentation policy search methods and federated data augmentation methods, in the benchmarks for heterogeneous FL.

Multimodal Models

Mingrui Wu, Xinyue Cai, Jiayi Ji, Jiale Li, Oucheng Huang, Gen Luo, Hao Fei, GUANNAN JIANG, Xiaoshuai Sun, Rongrong Ji

In this work, we propose a training-free method to inject visual prompts into Multimodal Large Language Models (MLLMs) through learnable latent variable optimization. We observe that attention, as the core module of MLLMs, connects text prompt tokens and visual tokens, ultimately determining the final results. Our approach involves adjusting visual tokens from the MLP output during inference, controlling the attention response to ensure text prompt tokens attend to visual tokens in referring regions. We optimize a learnable latent variable based on an energy function, enhancing the strength of referring regions in the attention map. This enables detailed region description and reasoning without the need for substantial training costs or model retraining. Our method offers a promising direction for integrating referring abilities into MLLMs, and supports referring with box, mask, scribble and point. The results demonstrate that our method exhibits out-of-domain generalization and interpretability.

Computational Biology

Lingxiang Jia, Yuchen Ying, Zunlei Feng, Zipeng Zhong, Shaolun Yao, Jiacong Hu, Mingjiang Duan, Xingen Wang, Jie Song, Mingli Song

Deep learning-based methods significantly advance the exploration of associations among triple-wise biological entities (e.g., drug-target protein-adverse reaction), thereby facilitating drug discovery and safeguarding human health. However, existing researches only focus on entity-centric information mapping and aggregation, neglecting the crucial role of potential association patterns among different entities. To address the above limitation, we propose a novel association pattern-aware fusion method for biological entity relationship prediction, which effectively integrates the related association pattern information into entity representation learning. Additionally, to enhance the missing information of the low-order message passing, we devise a bind-relation module that considers the strong bind of low-order entity associations. Extensive experiments conducted on three biological datasets quantitatively demonstrate that the proposed method achieves about 4%-23% hit@1 improvements compared with state-of-the-art baselines. Furthermore, the interpretability of association patterns is elucidated in detail, thus revealing the intrinsic biological mechanisms and promoting it to be deployed in real-world scenarios. Our data and code are available at https://github.com/hry98kki/PatternBERP.

Interpretability

Deqing Fu, Tian-qi Chen, Robin Jia, Vatsal Sharan

Transformers excel at *in-context learning* (ICL)---learning from demonstrations without parameter updates---but how they do so remains a mystery. Recent work suggests that Transformers may internally run Gradient Descent (GD), a first-order optimization method, to perform ICL. In this paper, we instead demonstrate that Transformers learn to approximate second-order optimization methods for ICL. For in-context linear regression, Transformers share a similar convergence rate as *Iterative Newton's Method*, both *exponentially* faster than GD. Empirically, predictions from successive Transformer layers closely match different iterations of Newton’s Method linearly, with each middle layer roughly computing 3 iterations; thus, Transformers and Newton’s method converge at roughly the same rate. In contrast, Gradient Descent converges exponentially more slowly. We also show that Transformers can learn in-context on ill-conditioned data, a setting where Gradient Descent struggles but Iterative Newton succeeds. Finally, to corroborate our empirical findings, we prove that Transformers can implement $k$ iterations of Newton's method with $k + \mathcal O(1)$ layers.

Deep Learning · Theory

Boyao Li, Alexander Thomson, houssam nassif, Matthew Engelhard, David Page

Deep neural networks (DNNs) lack the precise semantics and definitive probabilistic interpretation of probabilistic graphical models (PGMs). In this paper, we propose an innovative solution by constructing infinite tree-structured PGMs that correspond exactly to neural networks. Our research reveals that DNNs, during forward propagation, indeed perform approximations of PGM inference that are precise in this alternative PGM structure. Not only does our research complement existing studies that describe neural networks as kernel machines or infinite-sized Gaussian processes, it also elucidates a more direct approximation that DNNs make to exact inference in PGMs. Potential benefits include improved pedagogy and interpretation of DNNs, and algorithms that can merge the strengths of PGMs and DNNs.

Interpretability

Sonia Laguna, Ričards Marcinkevičs, Moritz Vandenhirtz, Julia Vogt

Recently, interpretable machine learning has re-explored concept bottleneck models (CBM). An advantage of this model class is the user's ability to intervene on predicted concept values, affecting the downstream output. In this work, we introduce a method to perform such concept-based interventions on *pretrained* neural networks, which are not interpretable by design, only given a small validation set with concept labels. Furthermore, we formalise the notion of *intervenability* as a measure of the effectiveness of concept-based interventions and leverage this definition to fine-tune black boxes. Empirically, we explore the intervenability of black-box classifiers on synthetic tabular and natural image benchmarks. We focus on backbone architectures of varying complexity, from simple, fully connected neural nets to Stable Diffusion. We demonstrate that the proposed fine-tuning improves intervention effectiveness and often yields better-calibrated predictions. To showcase the practical utility of our techniques, we apply them to deep chest X-ray classifiers and show that fine-tuned black boxes are more intervenable than CBMs. Lastly, we establish that our methods are still effective under vision-language-model-based concept annotations, alleviating the need for a human-annotated validation set.

Interpretability

Justin Kang, Yigit Efe Erginbas, Landon Butler, Ramtin Pedarsani, Kannan Ramchandran

One of the key challenges in machine learning is to find interpretable representations of learned functions. The Möbius transform is essential for this purpose, as its coefficients correspond to unique *importance scores* for *sets of input variables*. This transform is closely related to widely used game-theoretic notions of importance like the *Shapley* and *Bhanzaf value*, but it also captures crucial higher-order interactions. Although computing the Möbius Transform of a function with $n$ inputs involves $2^n$ coefficients, it becomes tractable when the function is *sparse* and of *low-degree* as we show is the case for many real-world functions. Under these conditions, the complexity of the transform computation is significantly reduced. When there are $K$ non-zero coefficients, our algorithm recovers the Möbius transform in $O(Kn)$ samples and $O(Kn^2)$ time asymptotically under certain assumptions, the first non-adaptive algorithm to do so. We also uncover a surprising connection between group testing and the Möbius transform. For functions where all interactions involve at most $t$ inputs, we use group testing results to compute the Möbius transform with $O(Kt\log n)$ sample complexity and $O(K\mathrm{poly}(n))$ time. A robust version of this algorithm withstands noise and maintains this complexity. This marks the first $n$ sub-linear query complexity, noise-tolerant algorithm for the Möbius transform. While our algorithms are conceptualized in an idealized setting, they indicate that the Möbius transform is a potent tool for interpreting deep learning models.

Deep Learning · Representation Learning

Jacopo Dapueto, Nicoletta Noceti, Francesca Odone

Developing meaningful and efficient representations that separate the fundamental structure of the data generation mechanism is crucial in representation learning. However, Disentangled Representation Learning has not fully shown its potential on real images, because of correlated generative factors, their resolution and limited access to ground truth labels. Specifically on the latter, we investigate the possibility of leveraging synthetic data to learn general-purpose disentangled representations applicable to real data, discussing the effect of fine-tuning and what properties of disentanglement are preserved after the transfer. We provide an extensive empirical study to address these issues. In addition, we propose a new interpretable intervention-based metric, to measure the quality of factors encoding in the representation. Our results indicate that some level of disentanglement, transferring a representation from synthetic to real data, is possible and effective.

Interpretability

Yiyang Sun, Tong Wang, Cynthia Rudin

Sparsity is a central aspect of interpretability in machine learning. Typically, sparsity is measured in terms of the size of a model globally, such as the number of variables it uses. However, this notion of sparsity is not particularly relevant for decision making; someone subjected to a decision does not care about variables that do not contribute to the decision. In this work, we dramatically expand a notion of *decision sparsity* called the *Sparse Explanation Value* (SEV) so that its explanations are more meaningful. SEV considers movement along a hypercube towards a reference point. By allowing flexibility in that reference and by considering how distances along the hypercube translate to distances in feature space, we can derive sparser and more meaningful explanations for various types of function classes. We present cluster-based SEV and its variant tree-based SEV, introduce a method that improves credibility of explanations, and propose algorithms that optimize decision sparsity in machine learning models.

Deep Learning · Representation Learning

Yuan He, Moy Yuan, Jiaoyan Chen, Ian Horrocks

Interpreting hierarchical structures latent in language is a key limitation of current language models (LMs). While previous research has implicitly leveraged these hierarchies to enhance LMs, approaches for their explicit encoding are yet to be explored. To address this, we introduce a novel approach to re-train transformer encoder-based LMs as Hierarchy Transformer encoders (HiTs), harnessing the expansive nature of hyperbolic space. Our method situates the output embedding space of pre-trained LMs within a Poincaré ball with a curvature that adapts to the embedding dimension, followed by re-training on hyperbolic clustering and centripetal losses. These losses are designed to effectively cluster related entities (input as texts) and organise them hierarchically. We evaluate HiTs against pre-trained LMs, standard fine-tuned LMs, and several hyperbolic embedding baselines, focusing on their capabilities in simulating transitive inference, predicting subsumptions, and transferring knowledge across hierarchies. The results demonstrate that HiTs consistently outperform all baselines in these tasks, underscoring the effectiveness and transferability of our re-trained hierarchy encoders.

Interpretability

Pietro Barbiero, Francesco Giannini, Gabriele Ciravegna, Michelangelo Diligenti, Giuseppe Marra

The design of interpretable deep learning models working in relational domains poses an open challenge: interpretable deep learning methods, such as Concept Bottleneck Models (CBMs), are not designed to solve relational problems, while relational deep learning models, such as Graph Neural Networks (GNNs), are not as interpretable as CBMs. To overcome these limitations, we propose Relational Concept Bottleneck Models (R-CBMs), a family of relational deep learning methods providing interpretable task predictions. As special cases, we show that R-CBMs are capable of both representing standard CBMs and message passing GNNs. To evaluate the effectiveness and versatility of these models, we designed a class of experimental problems, ranging from image classification to link prediction in knowledge graphs. In particular we show that R-CBMs (i) match generalization performance of existing relational black-boxes, (ii) support the generation of quantified concept-based explanations, (iii) effectively respond to test-time interventions, and (iv) withstand demanding settings including out-of-distribution scenarios, limited training data regimes, and scarce concept supervisions.