The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications

Causal discovery aims to automatically uncover causal relationships from data, a capability with significant potential across many scientific disciplines. However, its real-world applications remain limited. Current methods often rely on unrealistic assumptions and are evaluated only on simple synthetic toy datasets, often with inadequate evaluation metrics. In this paper, we substantiate these claims by performing a systematic review of the recent causal discovery literature. We present applications in biology, neuroscience, and Earth sciences - fields where causal discovery holds promise for addressing key challenges. We highlight available simulated and real-world datasets from these domains and discuss common assumption violations that have spurred the development of new methods. Our goal is to encourage the community to adopt better evaluation practices by utilizing realistic datasets and more adequate metrics.

Empirical influence functions to understand the logic of fine-tuning

Understanding the process of learning in neural networks is crucial for improving their performance and interpreting their behavior. This can be approximately understood by asking how a model's output is influenced when we fine-tune on a new training sample. There are desiderata for such influences, such as decreasing influence with semantic distance, sparseness, noise invariance, transitive causality, and logical consistency. Here we use the empirical influence measured using fine-tuning to demonstrate how individual training samples affect outputs. We show that these desiderata are violated for both for simple convolutional networks and for a modern LLM. We also illustrate how prompting can partially rescue this failure. Our paper presents an efficient and practical way of quantifying how well neural networks learn from fine-tuning stimuli. Our results suggest that popular models cannot generalize or perform logic in the way they appear to.

A large language model-assisted education tool to provide feedback on open-ended responses

Open-ended questions are a favored tool among instructors for assessing student understanding and encouraging critical exploration of course material. Providing feedback for such responses is a time-consuming task that can lead to overwhelmed instructors and decreased feedback quality. Many instructors resort to simpler question formats, like multiple-choice questions, which provide immediate feedback but at the expense of personalized and insightful comments. Here, we present a tool that uses large language models (LLMs), guided by instructor-defined criteria, to automate responses to open-ended questions. Our tool delivers rapid personalized feedback, enabling students to quickly test their knowledge and identify areas for improvement. We provide open-source reference implementations both as a web application and as a Jupyter Notebook widget that can be used with instructional coding or math notebooks. With instructor guidance, LLMs hold promise to enhance student learning outcomes and elevate instructional methodologies.

Neural Networks as Paths through the Space of Representations

Deep neural networks implement a sequence of layer-by-layer operations that are each relatively easy to understand, but the resulting overall computation is generally difficult to understand. We develop a simple idea for interpreting the layer-by-layer construction of useful representations: the role of each layer is to reformat information to reduce the "distance" to the target outputs. We formalize this intuitive idea of "distance" by leveraging recent work on metric representational similarity, and show how it leads to a rich space of geometric concepts. With this framework, the layer-wise computation implemented by a deep neural network can be viewed as a path in a high-dimensional representation space. We develop tools to characterize the geometry of these in terms of distances, angles, and geodesics. We then ask three sets of questions of residual networks trained on CIFAR-10: (1) how straight are paths, and how does each layer contribute towards the target? (2) how do these properties emerge over training? and (3) how similar are the paths taken by wider versus deeper networks? We conclude by sketching additional ways that this kind of representational geometry can be used to understand and interpret network training, or to prescriptively improve network architectures to suit a task.

Clustering units in neural networks: upstream vs downstream information

It has been hypothesized that some form of "modular" structure in artificial neural networks should be useful for learning, compositionality, and generalization. However, defining and quantifying modularity remains an open problem. We cast the problem of detecting functional modules into the problem of detecting clusters of similar-functioning units. This begs the question of what makes two units functionally similar. For this, we consider two broad families of methods: those that define similarity based on how units respond to structured variations in inputs ("upstream"), and those based on how variations in hidden unit activations affect outputs ("downstream"). We conduct an empirical study quantifying modularity of hidden layer representations of simple feedforward, fully connected networks, across a range of hyperparameters. For each model, we quantify pairwise associations between hidden units in each layer using a variety of both upstream and downstream measures, then cluster them by maximizing their "modularity score" using established tools from network science. We find two surprising results: first, dropout dramatically increased modularity, while other forms of weight regularization had more modest effects. Second, although we observe that there is usually good agreement about clusters within both upstream methods and downstream methods, there is little agreement about the cluster assignments across these two families of methods. This has important implications for representation-learning, as it suggests that finding modular representations that reflect structure in inputs (e.g. disentanglement) may be a distinct goal from learning modular representations that reflect structure in outputs (e.g. compositionality).

Prospective Learning: Back to the Future

Research on both natural intelligence (NI) and artificial intelligence (AI) generally assumes that the future resembles the past: intelligent agents or systems (what we call 'intelligence') observe and act on the world, then use this experience to act on future experiences of the same kind. We call this 'retrospective learning'. For example, an intelligence may see a set of pictures of objects, along with their names, and learn to name them. A retrospective learning intelligence would merely be able to name more pictures of the same objects. We argue that this is not what true intelligence is about. In many real world problems, both NIs and AIs will have to learn for an uncertain future. Both must update their internal models to be useful for future tasks, such as naming fundamentally new objects and using these objects effectively in a new context or to achieve previously unencountered goals. This ability to learn for the future we call 'prospective learning'. We articulate four relevant factors that jointly define prospective learning. Continual learning enables intelligences to remember those aspects of the past which it believes will be most useful in the future. Prospective constraints (including biases and priors) facilitate the intelligence finding general solutions that will be applicable to future problems. Curiosity motivates taking actions that inform future decision making, including in previously unmet situations. Causal estimation enables learning the structure of relations that guide choosing actions for specific outcomes, even when the specific action-outcome contingencies have never been observed before. We argue that a paradigm shift from retrospective to prospective learning will enable the communities that study intelligence to unite and overcome existing bottlenecks to more effectively explain, augment, and engineer intelligences.

Object Based Attention Through Internal Gating

Object-based attention is a key component of the visual system, relevant for perception, learning, and memory. Neurons tuned to features of attended objects tend to be more active than those associated with non-attended objects. There is a rich set of models of this phenomenon in computational neuroscience. However, there is currently a divide between models that successfully match physiological data but can only deal with extremely simple problems and models of attention used in computer vision. For example, attention in the brain is known to depend on top-down processing, whereas self-attention in deep learning does not. Here, we propose an artificial neural network model of object-based attention that captures the way in which attention is both top-down and recurrent. Our attention model works well both on simple test stimuli, such as those using images of handwritten digits, and on more complex stimuli, such as natural images drawn from the COCO dataset. We find that our model replicates a range of findings from neuroscience, including attention-invariant tuning, inhibition of return, and attention-mediated scaling of activity. Understanding object based attention is both computationally interesting and a key problem for computational neuroscience.

An adversarial algorithm for variational inference with a new role for acetylcholine

Sensory learning in the mammalian cortex has long been hypothesized to involve the objective of variational inference (VI). Likely the most well-known algorithm for cortical VI is the Wake-Sleep algorithm (Hinton et al. 1995). However Wake-Sleep problematically assumes that neural activities are independent given lower-layers during generation. Here, we construct a VI system that is both compatible with neurobiology and avoids this assumption. The core of the system is a wake-sleep discriminator that classifies network states as inferred or self-generated. Inference connections learn by opposing this discriminator. This adversarial dynamic solves a core problem within VI, which is to match the distribution of stimulus-evoked (inference) activity to that of self-generated activity. Meanwhile, generative connections learn to predict lower-level activity as in standard VI. We implement this algorithm and show that it can successfully train the approximate inference network for generative models. Our proposed algorithm makes several biological predictions that can be tested. Most importantly, it predicts a teaching signal that is remarkably similar to known properties of the cholinergic system.

Spike-based causal inference for weight alignment

In artificial neural networks trained with gradient descent, the weights used for processing stimuli are also used during backward passes to calculate gradients. For the real brain to approximate gradients, gradient information would have to be propagated separately, such that one set of synaptic weights is used for processing and another set is used for backward passes. This produces the so-called "weight transport problem" for biological models of learning, where the backward weights used to calculate gradients need to mirror the forward weights used to process stimuli. This weight transport problem has been considered so hard that popular proposals for biological learning assume that the backward weights are simply random, as in the feedback alignment algorithm. However, such random weights do not appear to work well for large networks. Here we show how the discontinuity introduced in a spiking system can lead to a solution to this problem. The resulting algorithm is a special case of an estimator used for causal inference in econometrics, regression discontinuity design. We show empirically that this algorithm rapidly makes the backward weights approximate the forward weights. As the backward weights become correct, this improves learning performance over feedback alignment on tasks such as Fashion-MNIST and CIFAR-10. Our results demonstrate that a simple learning rule in a spiking network can allow neurons to produce the right backward connections and thus solve the weight transport problem.

Identifying Weights and Architectures of Unknown ReLU Networks

The output of a neural network depends on its parameters in a highly nonlinear way, and it is widely assumed that a network's parameters cannot be identified from its outputs. Here, we show that in many cases it is possible to reconstruct the architecture, weights, and biases of a deep ReLU network given the ability to query the network. ReLU networks are piecewise linear and the boundaries between pieces correspond to inputs for which one of the ReLUs switches between inactive and active states. Thus, first-layer ReLUs can be identified (up to sign and scaling) based on the orientation of their associated hyperplanes. Later-layer ReLU boundaries bend when they cross earlier-layer boundaries and the extent of bending reveals the weights between them. Our algorithm uses this to identify the units in the network and weights connecting them (up to isomorphism). The fact that considerable parts of deep networks can be identified from their outputs has implications for security, neuroscience, and our understanding of neural networks.