Task Discovery: Finding the Tasks that Neural Networks Generalize on
Authors: Andrei Atanov
Andrey Filatov
Teresa Yeo
Ajay Sohmshetty
Amir Zamir
Venue: NeurIPS 2022 Accept (2022)
Keywords: Generalization
Understanding Neural Networks
Deep Learning

Abstract: When developing deep learning models, we usually decide what task we want to solve then search for a model that generalizes well on the task. An intriguing question would be: what if, instead of fixing the task and searching in the model space, we fix the model and search in the task space? Can we find tasks that the model generalizes on? How do they look, or do they indicate anything? These are the questions we address in this paper. 

We propose a task discovery framework that automatically finds examples of such tasks via optimizing a generalization-based quantity called agreement score. We demonstrate that one set of images can give rise to many tasks on which neural networks generalize well. These tasks are a reflection of the inductive biases of the learning framework and the statistical patterns present in the data, thus they can make a useful tool for analyzing the neural networks and their biases. As an example, we show that the discovered tasks can be used to automatically create ''adversarial train-test splits'' which make a model fail at test time, without changing the pixels or labels, but by only selecting how the datapoints should be split between the train and test sets. We end with a discussion on human-interpretability of the discovered tasks.


Task Discovery: Finding the Tasks that Neural Networks Generalize on
Andrei Atanov Andrei Filatov
Teresa Yeo Ajay Sohmshetty Amir Zamir
Swiss Federal Institute of Technology (EPFI.)
attps://aaekdiscovrry.p...
Abstract
When developing deep learning models, usually decide what task want to solve then search for a model that generalizes well on the task. An intriguing question would be: what if. instead of fixing the task and searching in the model space, we fix the model and search in the task space? Can we find tasks that the model generalizes on? How do they look, or do they indicate anything? These are the questions we address in this paper.
We propose task discovery framework that automatically finds examples of such tasks via optimizing a generalization based quantity called agreement score. We demonstrate that one of images can give rise many tasks on which neural networks generalize well. These tasks are a reflection of the inductive biases the learning framework and the statistical patterns present in the data, thus they can make a useful tool for analysing the neural networks and their biases. As an example, show that the discovered tasks be used to automatically create "adversarial train-test splits" " which make model fail at test time, without changing the pixels or labels, but by only selecting how the datapoints should be split between the train and test sets. We end with a discussion on human- intrrrrttttrrr of the discovered tasks.
Introduction
Deep learning models are found generalize well, i.e., exhibit low test when trained human-labelled tasks. This can be seen as a consequence of the models' inductive biases that favor solutions with low test error over those which also have low training loss but higher test error. In this paper, we aim to find what are examples other tasks]] that are favored by neural networks, i.c., on which they generalize well. We will also discuss some of the consequences of such findings.
We start by defining quantity called agreement score (AS) to measure how well network generalizes on a task. It quantifies whether two networks trained on the same task with different training stochasticity (e.g., initialization) make similar predictions AS can be seen as a necessary condition for generalization, as there cannot be generalization if the AS is low and networks converge to different solutions. On the other hand, if the AS is high, then there a stable solution that different networks converge to, and, therefore, generalization is possible (see Appendix D.. We show that the AS indeed makes for useful metric and differentiates between human- and handom-labelled tasks (see Fig. center).
test images. Intuitively, high
Given the AS as a prerequisite of generalization, we develop a task discovery framework that optimizes it and finds new tasks which neural networks generalize well. Experimentally. found that the same images can allow for many different tasks on which different network architectures generalize (see an example in Fig. rightt.
In the context of this paper, generally, "task" is labelling of a dataset, and any label set defines a "task".
36th Conference on Neural Information Processing Systems (NeurIPS 2022).

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Figure 1: Left: The agreement score (AS) measures whether two networks trained the task with different optimization stochasticity (e.g., initialization) make the same prediction on a image f. f(ă, w) denotes network with weights w applied to an input é. v and w" denote initial and converged weights, respectively, The agreement score successfully differentiates between human-labellne original labels and random-lahelled tasks. The task discovery framework finds novel tasks with high agreement scores. Right: Examples of a discovered, buman-labelles (animals vs. non-animals) and mandom-labellie tasks CIFAR-10. This particular discovered task looks visually distinct and seems to be based on the image background.
Center:
tasks based on CIFAR-I0
Finally, we discuss how the proposed framework can help us understand deep learning better, for example, by demonstrating its biases and failure modes. We the discovered tasks to split dataset into train test sets in an adversarial way instead of random splitting. After training on the train set, the network fails make correct predictions on the test set. The adversarial splits can be seen as using the "spurious" correlations that exist in the datasets via discovered tasks. We conjecture that these tasks provide strong adversarial splits since task discovery finds tasks that are "favored" by the network the most. Unlike manually curated benchmarks that reveal similar failing behaviours (67 47 777, pixel-level adversarial attacks (71 40 [11, the proposed approach finds the adversarial split automatically and does not need to change any pixels or labels or collect new difficult or ad adversarial images.
2 Related Work
Deep learning generalization. is not well understood yet why deep neural networks generalize well in practice while being overparameterized and having large complexity 26 21
80 75). A line of work approaches this question by investigating the role the different components of deep learning [M] 15 2 II [53] [22) [72] 19 and developing novel complexity measures that could explain The proposed task discovery framework can serve as an experimental tool to shed more light on when and how deep learning models generalize. Also, compared to existing quantities for studying generalization, namely [II, which is based on the training process only, our agreement score is directly based on test data and generalization.
59
neural networks' generalization
46
54 69].
Similarity measures between networks. Measuring the similar between two networks is challenging and depends a particular application. Two common approaches
measure the similarity and the predictions made on unseen data (70]. agreement score measure. In contrast these works, which mainly use the AS as metric, we turn it into an optimization objective to find new tasks with the desired property of good generalization.
between hidden representations
45
38
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Similar to work, [19 29 also
Maas-variance decomposition. The AS used in this work can be seen as a measure of the variance term in the bias-variance decomposition of the test error 18
75 [4]. Recent works investigate how this term behaves in deep learning models [ 55 79 56 In contrast, we characterize its dependence on the task being learned instead of the model's 's complexity and find those that maximize the AS.
Creating distribution shifts. Distributions shifts can result from e.g. spurious correlations, under- 5. To create such shifts to study the failure modes of networks, one needs to define them manually 67 47]. We show that it is possible to automaicaally
sampling (77 adversarial attacks 71 40
create many such shifts that lead to significant accuracy drop on a given dataset using the discovered tasks (see Sec. 6 and Fig. left). In contrast to other automatic methods to find such shifts, the proposed approach allows creates many of them for learning algorithm rather than for a single trained model [16], does not require additional prior knowledge [12] or adversarial optimization [2]. and does not change pixel values 44) or labels.

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Data-centric analyses of learning. Multiple works study how training data influences the final model. Common approaches are to measure the effect of removing, adding or mislabelling individual data points or group of them E6 37 27 28 Instead of choosing which objects to train on, in task discovery, we choose how to label a fixed set of objects (i.e., tasks), s.t. network generalizes well.
3 Agreement Score: Measuring Consistency of Labeling Unseen Data
In this section, we introduce the basis for the task discovery framework: the definition of a task and the agreement score, measure of the task's generalizability. We then provide an empirical analysis of this score and demonstrate that it differentiates human- and random-labelled tasks.
Notation and definitions. Given a set of N images X {a x E X, we define task as a binary labelling of this set X + {0. 1) (a multi-class extension is straightforward) We denote the corresponding labelled dataset as ( 7) {(x, (())) E X} and the set of all possible tasks (i.e., label sets) on X as Tx. We consider a learning algorithm A to be a neural network f(; w) : X + [0. 1] with weights w trained by SGD with cross-entropy loss. Due the inherent stochasticity, such as random initialization and mini-batching, this learning algorithm induces a distribution over the weights given dataset w A(D(X,T)) T)).
3.1 Agreement Score as Measure of Generalization
standard approach measure the generalization of learning algorithm A trained on D(Xers 7) is to measure the test error on
T). The test error can be decomposed into bias and variance terms 4 7 14. where, in our case, the stochasticity is due to A while the train-test split is fixed. We now examine how this decomposition depends on the task т. The bias term measures how much the average prediction deviates from and mostly depends variance term captures how predictions of different models agree with each other and does not depend on the task's 's test labels but only on training labels through D(Xer, T). We suggest measuring the generalizability of a task T with an agreement score, as defined below.
what are the test labels on Xto- The
For a given train-test split Xtr, Xte and a task T, we define the agreement score (AS) as: AS(T: Xtr, Xte) = Em (...-AA((X..)).BBxx......
w1) f(z; w2)],
(1)
where the first expectation is over different models trained on D(Xir; 7) and the inner expectation is averaging over the test set. Practically, this corresponds to training two networks from different initializations on the training dataset labelled by r and measuring the agreement between these two models' predictions on the test set (see Fig. left and the inner-loop in Fig. left).
The AS depends only on the task's 's training labels, thus, test labels are not required. However, it is tightly connected to the test error, as having a high-AS task T that labels training data, one can construct task with a high test accuracy. We note, however, that when the task is given and fixed, the high-AS provides only a necessary but not sufficient condition for high test accuracy as test labels can take any values in general (e.g., be adversarial as in Sec. 5) thus, it cannot be used to predict the
test accuracy, in this case 20 35| Refer to Appendix T for a more in-depth discussion.
3.2 Agreement Score Behaviour for Random- and Human-Labeller Tasks
Here, we demonstrate that the AS exhibits the desired behaviour of differentiating human-labelled from labelle tasks. We take the set of images X from the CIFAR- 10 dataset 339 and
split the original training set into 45K images for Xxx and 5K for X1e. We split 10 original classes differently into two sets of classes to construct 5-vs-5 binary classification tasks Tal Out of all (20) tasks, we randomly sub-sample 20 ones to form the set of human-labelled tasks THL. We construct the set of 20 candom-labelled tasks TRL by generating binary labels for all images randomly and fixing them throughout the training, similar to [1 We use ResNet-18 [24] architecture and Adam [34] optimizer as the learning algorithm A. unless otherwise specified. We measure the AS by training two networks for 100 epochs, which is enough to achieve zero training error for all considered tasks.
AS differentiates human- from random-labelled tasks. Fig. [centr shows that haman-labelled tasks have a higher AS than random-labelled ones. This coincides with our intuition that one should not expect generalization on a random task, for which AS is close to the chance level of 0.5. Note, that the empirical distribution of the AS for of the AS distribution over all possible tasks, as TRL are uniform samples from Tx..- This suggests that high-AS tasks do not make for large fraction of all tasks. A high AS of human- label-laaeeled tasks
tasks (Fig. left) is unbiased estimation
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Figure 2: Agreement score for human- and random-labelled tasks. Left: AS measured on three architectures: ResNet-18, MI. and ViT. Center: AS measured on ResNet-18 for different numbers of training images N. The standard deviation over present in A. Each row shows when one of the 1) initialization, 2) data-order or 3) CUDA is stochastic and the other two sources are fixed, and the bottom is when all the sources are fixed (sec Sec. 3.2 The differentiation between human- and lanele-labelled tasks stably persists across different architectures, data sizes and sources of randomness.
random tasks and three data splits. Right: Ablating the sources of stochasticity
also consistent with the understanding that network is able generalize when trained on the original CIFAR-10 labels.
How does the AS differ across architectures? In addition to ResNet-18, 18, we measure the AS using
MIP 700 and ViT architectures [3] (see Appendix I I.3 Fig. -left shows that the AS for all the architectures distinguishes tasks from TRL. and THL well. MLP and ViT have lower AS than ResNet- 18, aligned with our understanding that convolutional networks should exhibit better generalization on this small dataset due to their architectural inductive biases. Similar to the architectural analysis, we provide the analysis on the data-dependency of the AS in Appendix
How does the AS depend on the training size? When only too little data is available for training, one could expect the stochasticity in A to play bigger role than data, i.e., the agreement score decreases with less data. This intuition is consistent with empirical evidence for labelel tasks, as seen in Fig. center. However, for mandom-labellee tasks, the AS increases with less data (but they still remain distinguishable from human- labelled tasks). One possible reason is that when the training dataset is very small, and the labels are random, the two networks do not deviate much from their initializations. This results in similar networks and consequently high AS, but basically irrelevant to the data and uninformative.
Any stochasticity is enough to provide differentiation. We ablate the three sources of stochasticity in A: 1) initialization, 2) data-order and 3) CUDA stochasticity [31] The system fully deterministic with all three sources fixed, thus, AS=1. Interestingly, when any of these variables change between two runs, the AS drops. creating separation between human- and mandom-labelles tasks.
These empirical observations show that the AS well differentiates between human- and random- labelled tasks across multiple architectures, dataset sizes and sources of stochasticity.
Task Discovery via Meta-Optimization of the Agreement Score
As the previous section shows, AS is a useful measure network's generalization on a given task. A natural question then arises: there high-AS tasks other than human- mabell-l ones, and what are they? In this section, we establish a task discovery framework to automatically search for these tasks and study this question computationally.
4.1 Task Space Parametrization and Agreement Score Meta-Optimization
Our goal is to find a task T that maximizes AS(T). is a high- ditenssinnii discrete optimization problem which is computationally hard to solve. In order to make it differentiable and utilize more efficient first-order optimization methods, we, first, substitute the 0-1 loss Eq, | with the cross- entropy loss lee- Then, we parameterize the space of tasks with task network Lo X + [0. and treat the AS as function of its parameters This basically means that we view the labelled training dataset D(Xue, T) and network to with the same labels on X as being equivalent, as one can always train network fit the training dataset.
Given that all the components are now differentiable. we can calculate the gradient of the AS w.r.t. task parameters (ta)((t) by unrolling the inner-loop optimization and use it for gradient-baut

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optimization over the task parameters 8. This results in meta-optimization problem where the inner-loop optimization over parameters w1, W2 and the outer-loop optimization is over (see Fig. left).
Evaluating the meta- geta-ggrdieet w.r.t. 0 has high memory and computational costs, we need to train two networks from scratch in the inner-loop. To make feasible, we limit the number of inner-loop optimization steps to 50, which we found to be enough to separate the AS between random and tasks and provide a useful learning signal (see Appendix L.1 We additionally use gradient checkpointing [ after every inner-loop step to avoid linear memory consumption in the number of steps. This allows us to run the discovery process for the ResNet-18 model on the CIFAR-10 10 dataset using a single 40GB A100, See Appendix L.2 for more details.
4.2 Discovering Set of Dissimilar Tasks with High Agreement Scores
The described AS meta- meta-optimization results in only single Aigh-AS task, whereas there are poten- tially many of them. Therefore, we would like to discover a set of tasks T (to,.....,t. ,,x ). A naive approach to finding such a set would be to run the meta-optimization from K different intializations of task parameters 0. However, this results in set of similar (or even the same) tasks, in the preliminary experiments. Therefore, we aim to discover dissimilar tasks to better represent the set of all high-AS tasks. We measure the similarity between two tasks set X as follows:
observed
( T2) max {EE=~x [Ti (a) T2(2)) E. (x) = (=(()))
(2)
where the maximum accounts for the labels' flipping. Since this metric is not differentiable, we, instead, use a differentiable loss Laim to minimize the similarity (defined later Sec. 4.3 Eq. 5)
Finally, we formulate the task discovery framework as the following optimization problem over T:
arg max AS((t) X Leim (T).
T- ("ae.""
We show the influence of À task discovery in Appendix H discovering trivial solutions that are highly imbalanced (e.g., labelling all objects with class 0) due to the similarity loss, as these tasks are similar each other, and set T that includes them will be penalized.
Note that this naturally avoids
In practice, we could solve this optimization sequentially - i.e., first find fe freeze it and add it to T, then optimize for le., and so on. However, we found this to be slow. In the next Sec. 4.3 we provide a solution that is more efficient, i.e., can find more tasks with less compute.
Regulated task discovery. The task discovery formulation above only concerns with finding high- AS tasks- which the minimum requirement for having generalizable tasks. One can introduce additional constraints to regulate the discovery process, e.g., by adding regularizer to Eq. 3 or via the task network's 's architectural biases. This approach can allow for guided task discovery to favor the discovery of particular tasks. We provide an example of a regulated discovery in Sec. 5. by using self-supervised trained embeddings the input to the task network.
4.3 Modelling The Set of Tasks with an Embedding Space
Modelling every task by separate network increases memory and computational costs. In order to amortize these costs, we adopt an approach popular in multi-task learning and model task networks with a shared encoder e(-; 0z) X' + Rd and task-specific linear head 0, Rd, so that (a(x) e(x; ).)TT. 0j. See Fig. 3 right for visualization. Then, instead of learning fixed set of different task-specific heads, we aim to learn an embedding space where any linear hyperplane gives rise to a high-AS task. Thus, an encoder with parameters 0g defines the following set of tasks:
Tg. (to 0 (0,, 01), B₁ E ER.)
(4)
This set is not infinite as it might seem at first since many linear layers will correspond to the same shattering of X. The size of To, as measured by the number of unique tasks on X is only limited by the dimensionality of the embedding space d and the encoder's expressivity. Potentially. it can be as big as the set of all shatterings when d = | - and the encoder e is flexible enough [74].
We adopt a uniformity loss over the embedding space 776 to induce dissimilarity between tasks:
e(21; 0e) e(x2; 0c)
Laim (To.) = (0m) = log Ex,,, exp a [Te(; 0-)1l -1 [|e(22 0.)11
(5)
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Figure 3: Left: Agreement score meta-optimization. Inner-lopp: given the task to T. two networks wi), W2 optimize the cross-entropy loss lee on the training set labelled by the task to (Sec. H.J). After training, the agreement between two networks is calculated on the test set. Outer-loop: the task parameters 9 are updated with the meta-gradient of the AS. Right: the task-space paramertrization with the shared encoder (Sec. 4.3) The encoder e(- (1; 02) (after projection) distributes images uniformly on the sphere in the embedding space. Different tasks are then formed by applying a linear classifier with weights, c.g., 0f and of. passing through the origin. The corresponding set of tasks To, consists of all such linear classifiers in this space. This results in a more efficient task discovery framework than modelling each task with separate network.
where the expectation is taken w.r.t pairs of images randomly sampled from the training set. It favours the embeddings to be uniformly distributed on sphere, and, if the encoder satisfies this property, any two orthogonal hyper-planes 0/ .. 8² (passing through origin) give rise to two tasks with the low similarity of 0.5 as measured by Eq. (see Fig. right).
In order to optimize the AS averaged over To, in Eq. we can use a Monte-Casn Carlo gradient estimator and sample one hyper-plane 6₁ at each step, e.g., w.r.t. an isotropic Gaussian distribution, which, on average, results in dissimilar tasks given that the uniformity is high. As result of running the task discovery framework, we find the encoder parameters 0" that optimize the objective Eq. 3 and gives rise to the corresponding set of tasks Ta: (see Eq. and Fig. B-right).
Note that the framework outlined above can be straightforwardly extended to the case of discovering multi-way classification tasks as we show in Appendix [ where instead of sampling hyperplane that divides the embedding space into two parts, we sample K hyperplanes that divide the embedding space into K regions and give rise to K classes.
Towards the space of high-AS tasks. Instead of creating set of tasks, one could seek to define space of high-AS tasks. That to define a basis set of tasks and binary operation on a set of tasks that constructs new task and preserves the AS. The proposed formulation with shared embedding space can be seen as a step toward this direction. Indeed, in this case, the structure over Tp: is imposed implicitly by the space of liner hyperplanes 0 E Rdd each of which gives rise to a high-AS task.
4.4 Discovering High-AS Tasks on CIFAR-10 Dataset
In this section, we demonstrate that the proposed framework successfully finds dissimilar tasks with high AS. We consider the same setting as in Sec. 3.2 We use the encoder-based discovery described in Sec. 4.3 and use the ResNet-18 architecture for e(:; 0z) with linear layer mapping to Rd (with d = 32) instead of the last classification layer. We use Adam the meta-optimizer and SGD optimizer for the inner-loop optimization. Please refer to Appendix L.2 for more details.
We optimize Eq. to find 0 and sample 32 tasks from Ta- by taking d orthogonal hyper-planes 0, We refer these 32 tasks RessNet. The average similarity (Eq. 2 between all pairs of tasks from this set is 0.51, close to the smallest possible value of 0.5. For each discovered task, we evaluate its AS in the same way as in Sec. 3.2 (according to Eq. [b. Fig. center demonstrates that the proposed task discovery framework successfully finds tasks with high AS. See more visualizations and analyses of these discovered tasks in Sec. 5 and Appendix B
Random networks give rise to high-AS tasks. Interestingly, in our experiments, we found that if we initialize a task network randomly (standard uniform initialization from PyTorch [3]]. the corresponding task (after applying softmax) will have high AS, on par with human-labelled and discovered ones (+s 0.85). Different random initializations, however, give rise to very similar tasks (c.g., 32 randomly sampled networks have an average similarity of 0.68 compared to 0.51 for the discovered tasks. See Appendix for a more detailed comparison). Therefore, a naive approach of sampling random networks does not result in efficient task discovery framework, as one needs to

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Figure 4: Left: The AS for tasks from THL, TReseet, TLP,, TuT measured all three architcctures (z and y axis). Right: Sample images for each class our discovered tasks are shown in the first two columns. We show some unlabelled examples in the third column for the reader to guess the label. The answers are in the Appendix B These images have been sampled to be the most discriminative, as measured by the network predicted probability. Right (top): Some of the discovered tasks from the unregulated version of task discovery seem to be based on color patterns, e.g. (2) 1 are images with similar blue color, which make sense as learnahle task and are expected (see Sec. [..I). Right (bottom): The same, hut for regulated version where the encoder was pretrained with SimCLR. The tasks seems to correspond more to semantic tasks e.g. r (x) 1 are images of vehicles with different backgrounds. As the pretraining encourages the encoder to be invariant to color, it seems to be biased towards semantic information. Thus, the framework is able to pick up on the inductive biases from SimCLR pretraining, via the discovered tasks.
draw prohibitively many of them to get sufficiently dissimilar tasks. Note, that this result is specific to the initialization scheme used and not any instantiation of the network's weights necessarily results in a high-AS task.
5 Empirical Study of the Discovered Tasks
In this section, we first perform a qualitative analysis of the discovered tasks in See. 5.1 Second in Sec. Sec.6.2 we discuss the human- inteaananterrrttabiitty of the discovered tasks and whether tasks should be expected to be discovered. Then, we analyze how discovered tasks differ for three different architectures in Sec. 5.3 We also study the dependency of the AS on the test data domain and show the results in Appendix in the interest of space.
5.1 Qualitative Analyses of the Discovered Tasks
Here we attempt to analyze the tasks discovered by the proposed discovery framework. Fig. 4 top-right shows examples of images for three sample discovered tasks found in Sec. 4.4 For ease of visualization, we selected the most discriminative images from each class measured by the network's predicted probability. In the interest of space, the visuals for all tasks are in the Appendix B alongside some post hoc interpretability analysis.
Some of these tasks seem be based on color, e.g. the class 1 of Tı includes images with blue (sky or water) color, and the class O includes images with orange color. Other tasks seem to pick up other cues. These are basically reflections of the statistical patterns present in the data and the inductive biases of the learning architecture.
Regulated task discovery described in Sec. 4.2 allows us to incorporate additional information to favor the discovery of specific tasks, e.g., ones based on more high-level concepts. As an example, we use self-supervised contrastive pre-training that learns embeddings invariant to the employed set
embeddings of the ResNet-50 24 trained with SimCLR 9 as the input to the encoder e instead of raw images, which in this case is a 2-layer
of augmentations (20 22 B 52). Specifically,
fully-connected network. Note that the AS is still computed using the raw pixels.
Fig. bottoo--iight shows the resulting tasks. Since the encoder is now more invariant to colour information due to the colour jittering augmentation employed during pre-training D. the discovered tasks seem to be more aligned with CIFAR- classes; e.g. samples from 7 reggs class show vehicles against different backgrounds. Note that task discovery regulated by contrastive pre-training only provides tool to discover tasks invariant to the set of employed augmentations. The choice of augmentations, however, depends on the set tasks one wants to discover. For example, one should not employ rotation augmentation if they need to discover dew-ddepeddent tasks (78).
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5.2 On Human-lnterpretabbllty and Human-Labelled Tasks
In this section, we discuss i) if the discovered tasks should be visually interpretable to humans, ii) if one should expect them to contain human-labelled tasks and if they do in practice, and iii) an example of how the discovery of human-labelled tasks can be promoted.
Should the discovered high-AS tasks be human-inter numan-interpretablee In this work, by "human- interpretable tasks", we generally refer to those classifications that humans can visually understand or learn sufficiently conveniently. Human-labelles, tasks are examples of such tasks. While we found in Sec. 3.2 that such interpretable tasks have a high AS, the opposite is not true, i.e., not all high-AS tasks should be visually interpretable by a human as they reflect the inductive biases of the particular learning algorithm used, which are not necessarily aligned with human perception. The following "green pixel task" is an example of such a high-AS task that is learnable and generalizable in statistical learning sense but not convenient for humans to learn visually.
The "green pixel task". Consider the following simple task: the label for æ 1 the pixel p at a fixed position has the green channel intensity above certain threshold and 0 otherwise. The threshold is chosen to split images evenly into two classes. This simple task has the AS of approximately 0.98, and a network trained to solve it has a high test accuracy of 0.96. Moreover, the network indeed seems to make the predictions based on this rule rather than other cues: the accuracy remains almost the same when we set all pixels but p to random noise and, on the flip side, drops to the chance level of 0.5 when randomly sample p and keep the rest of the image untouched. This suggests that the network captured the underlying rule for the task and generalizes well in the statistical learning sense. However, it would be hard for a human infer this pattern by only looking examples of images from both classes, and consequently, it would appear like an uninterpretablerrandoo task to human eyes.
It is sensible that many of the discovered tasks belong such a category. This indicates that finding more iumernliterrpeetable tasks would essentially require bringing in additional constraints and biases that the current neural network architectures do not include. We provide an example of such promotion using the SSL regulated task discovery results below.
Do discovered tasks contain human-labelled tasks? We observe that the similarity between the discovered and most human-labelle tasks is relatively low (see Fig. Ieft and Appendix for more details). As mentioned above, human-labelled tasks make up only a small subset of all tasks with high AS. The task discovery framework aims to find different (i.e., dissimilar) tasks from this set and not necessarily all of them. In other words, there are many tasks with a high AS other than human labelled ones, which the proposed discovery framework successfully finds.
As mentioned above, introducing additional inductive biases would be necessary to promote finding more human-labelled tasks. We demonstrate this by using the tasks discovered with the SimCLR pre-trained encoder (see Sec. 5. Fig. rigght shows that the recall of human-labelled tasks among the discovered ones increases notably due to the inductive biases that SimCLR data augmentations bring in.
5.3 The Dependency of the Agreement Score and Discovered Tasks on the Architecture
In this section, we study how the AS of a task depends on the neural network architecture used for measuring the AS. We include human-labelled tasks as well as a set of tasks discovered using different architectures in this study. We consider the same architectures as in Sec. 3.2 ResNet- 18, MLP, and ViT. We change both f and Sec. H.4 As a result, we obtain three sets: Tiee TMLLP, T Tvrr, each with 32 tasks. For each task, evaluate its AS on all three architectures. Fig. left shows that high-AS tasks for one architecture do not necessary have similar AS when measured on another architecture (e.g., TResNet on ViT). For MLP and ViT architectures, we find that ASs correlate well for all groups for tasks, which is aligned with the understanding that these architectures are more similar to each other than to ResNet-
be one of MLP or ViT and run the same discovery process in
More importantly, we note that comparing architectures on any single group of tasks is not enough. For example, if comparing the AS for R8 and MLP only on human-labelled tasks Tin., one might conclude that they correlate well (p = 0.8), suggesting they generalize on similar tasks. However, when the set Te is taken into account, the conclusion changes (p 0.17). Thus, it is important to analyse the different architectures on a broader set of tasks not to bias our understanding. and the proposed task discovery framework allows for more complete analyses.
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0.8
Tafa
123%
Tafa)
(279)
Test accuracy W.F.t.
Test Accuracy
0.6
X
(S0PS)
0.4
?h
R2(2)
(279)
0.2
Adversanial spllt
Random
-0.10 -0.05 0.00
0,05
0.10
spil
AS(TT) AS(72)
Figure 5: Adversarial splits on CIFAR-10. Left: Test accuracy for human-lahelled tasks Tu on random and adversarial splits. The boxplot distribution is over four tasks for the random split and 24 (Ta, ra) pairs for the adversarial one. Training with the adversarial split results in significant test performance drop. Center: Example of adversarial split, constructed such that images from train and sets have the opposite correlation between The and ra (the percentage of images in each group shown in brackets). The model seems to learn to make its predictions based on Ta instcad of Th (hence, the significant test accuracy drop). Right: Each dot corresponds to a pair of tasks (TI, r2). where the y-axis is the test accuracy after training on the corresponding adversarial split to predict Tı, and the a-axis is the difference in the AS of these two tasks. The plot suggests that Ti is, the higher the accuracy w.r.t TI is. Thus, for adversarial split to be successful, the AS of the target task 71 should be lower than the AS of 72.
the network favors learning the task with higher AS: the higher the AS of
6 Adversarial Dataset Splits
In this section, we demonstrate how the discovered tasks can be used to reveal biases and failure modes of a given network architecture (and training pipeline). In particular, we introduce an adversarial split - which a train-test dataset split such that the test accuracy of the yielded network significantly drops, compared to random train-test split. This is because the AS can reveal what tasks network favors learn, and thus, the discovered tasks can be used to construct such adversarial splits.
6.1 Creating Adversarial Train-Test Dataset Partitions Using Discovered High-AS Tasks
For given human-labelled task Thi let us consider the standard procedure of training network on D(Xir; Thi) and testing it D(Xee Thi). The network usually achieves high test accuracy when the dataset is split into train and test sets randomly. Using discovered tasks, we show how to construct adversarial splits on which the test accuracy drops significantly after training. To do that, we take discovered task Ta with a high AS and construct the split, s.t. Thi and Ta have the same labels on the training set Xadv and the opposite ones on the test set Xaavv (see Fig, center):
(6) Fig. left shows that for various pairs of (Thi, Ta); the test accuracy on D(Xaddv Thi) drops signifi- cantly after training on D(Xadv, na). This suggests the network chooses to learn the cue in Ta rather than Thi as it predicts 1 - Thi on X which coincides with Ta- We note that we keep the class balance and sizes of the random and adversarial splits approximately the same (see Fig. 5 center).
Xadv {ar ma(r)) Ta(x), x E X), X far (1) + Ta( x EX.
33 and the adversarial split creates a spurious correlation between Tal and Ta on Xaady that fools the network. Similar behaviour was observed before on datasets where spurious correlations were curated manually [67 47 777 In
discovered task Ta. in this case, can be seen as a spurious feature 68]
contrast, the described approach using the discovered tasks allows us to find such spurious features, to which networks are vulnerable, automatically. It can potentially find spurious correlations on datasets where none was known to exist or find new ones on existing benchmarks, as shown below.
In Appendix [ we show how to extend this approach to multi-class classification, and provide results for the results for the original 10-way classification task of the CIFAR-10 dataset. We also construct and present adversarial adversarial splits for ImageNet and CelebA datasets in Appendix G
6.2 Neural Networks Favor Learning the Task with a Higher AS.
The empirical observation made in the previous section demonstrates that network trained dataset where 7h and 7a coincide predicts the latter. While theoretical analysis is needed to understand the cause of this phenomenon, here, we provide an empirical clue towards its understanding.
We consider a of 10 discovered tasks and 4 human-labelled tasks. For all pairs of tasks (Ti, T2) from this set, construct the adversarial split according to Eq. 6 train network on D D(Xadv .1)
and test it on D (xxadv TT). Fig. 5 right shows the test accuracy against the difference in the agreement

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score of these two tasks A AS(rt). ). We find that the test accuracy w.r.t 71 correlates well with the difference in the agreement: when AS(T1) is sufficiently larger than AS(r)), the network makes predictions according to T1, and vice-versa. When the agreement scores are similar, the network makes test predictions according to neither of them (see Appendix [ for further discussion). This observation suggests that an adversarial split is successful, i.e., causes the network to fail, if the AS of the target task 71 is lower than that of the task 72 used to create the split.
7 Conclusion
In this work, we introduce task discovery, a framework that finds tasks on which a given network architecture generalizes well. It uses the Agreement Score (AS) as the measure of generalization and optimizes it over the space of tasks to find generalizable ones. We show the effectiveness of this approach and demonstrate multiple examples of such generalizable tasks. We find that these tasks are not limited to human-labelled ones and can be based on other patterns in the data. This framework provides an empirical tool analyze neural networks through the lens of the tasks they generalize on and can potentially help us better understand deep learning. Below we outline a few research directions that can benefit from the proposed task discovery framework.
Understanding neural networks' inductive biases. Discovered tasks can be seen as a reflection of the inductive biases of a learning algorithm (network architectures, optimization with SGD, etc.), i.e., a set of preferences that allow them to generalize on these tasks. Therefore, having access to these biases in the form of concrete tasks could help us understand them better and guide the development of deep learning frameworks.
Understanding data. As discussed and shown, task discovery depends on, not only the learning model, but also the data in hand. Through the analysis of discovered tasks, one can, for example, find patterns in data that interact with a model's inductive biases and affect its performance, thus use the insights to guide dataset collection.
Generalization under distribution shifts. The AS turned out to be predictive of the cues/tasks network favors in learning. The consequent adversarial splits (Sec. () provide a tool for studying the biases and gencralization of neural networks under distribution shifts. They can be constructed automatically for datasets where no adverse distribution shifts are known and help us to build more broad-scale benchmarks and more robust models.
8 Limitations
The proposed instantiation of a more general task discovery framework has several limitations, which we outline below, along with potential approaches to address them.
Completeness: the set of discovered tasks does not necessarily include all of the tasks with a high AS. Novel optimization methods that better traverse different optima of the optimization objective Eq. 3. e.g., 61 500 and further scaling are needed to address this aspect. Also, while the proposed encoder- based parametrization yields an efficient task discovery method, it imposes some constraints on the discovered tasks, as there might not exist an encoder such that the corresponding set of tasks Te, contains all and only high-AS ones.
Scalability: the task discovery framework relies expensive meta-optimization which limits its applicability to large-scale datasets. This problem can be potentially addressed in future works with recent advances in efficient meta-optimization methods [4] 651 as well as employing effective approximations of the current processes.
Interpretability: As we discussed and demonstrated, analysis of discovered high-AS tasks can shed more light how the neural networks work. However, it is the expected behavior that not all of these tasks may be easily interpretable or "useful" in the conventional sense (c.g. as an unsupervised pre-training task). This is more of consequence of the learning model under discovery, rather than the task discovery framework itself. Having discovered tasks that exhibit such properties requires additional inductive biases to be incorporated in the learning model. This was discussed in Sec. 5.2
Acknowledgment: We thank Alexander Sax, Pang Wei Koh, Roman Bachmann, David Mizrahi and Oğuzhan Fatih Kar for the feedback on carlier drafts of this manuscript. We also thank Onur Beker and Polina Kirichenko for the helpful discussions.
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Reviews:
[{"review_id": "upILLVyDJJI", "reviewer": "Reviewer_QpNg", "summary": "This paper studies the problem of discovering the generalizable tasks over the models.\nIn this context, the image label assignment of labels is considered a different task. \nThen, the method proposed in the paper seeks to find different assignments of label sets over images such that desired generalizability is ensured. In a way, the labels are merged to create new labels to simulate new tasks. Such fusion may or may not be semantically meaningful. In this work, the authors wonder if a meaningful fusion (thus the derivation of a new task) can be performed by seeking the generalizability of the derived task over the test set. The authors propose a framework for task discovery that automatically finds generalizable tasks using the proposed agreement score. Furthermore, a case of “adversarial train-test splits' ' where a split of datapoints between training and testing leads to the failure of the model is also studied.\n\n", "questions": "* Trivial solution: to avoid the trivial solution the proposed formulation of (3) makes a trade off between tasks and agreement. This trade-off makes it unclear what is indeed being searched, as the hypaerparameter \\lambda plays the role. Obviously, the presence of hypaerparameter in itself is not a problem. In this context of this paper however, the discovery of the generalizable tasks which is unknown, becomes the function of the hyperparameter that needs to be tuned. I wonder how this hypaerparameter can be selected meaningfully as there is no ground truth (or any interpretable measure as far as I can see). \n\n* Regulated discovery: In line 236, the figure Fig.5.2 (bottom right) is incorrectly referred (also in line 225). The regularization of simCLR is as a matter of fact simply a better visual extractor.  Such pre-training learns the some desired invariances thereby leading to similar invariances in the discovered tasks. Such regularization however needs to be task dependent. For example, if one wishes to perform rotation estimation, features learned for rotation invariance are not desired. This particular case is justified for the image classification by object class (in the used case here). However, a broader discussion on what kind of regulated discovery is meaningful needs to be provided. Here again, this question arises as one is unaware beforehand what task is being searched, which is instead searched merely based on some objective which is effectively only vaguely interpretable. \n\n* Embedding space: Monte-Carlo gradient estimator technique resulting uniformity in dissimilar tasks, and rest of the discussion is unclear. This may either require references or more details. Is the presented claim coupled with the choice of embedding space for the task?\n\n* Training size in the context of utility: discovery of the generalizable tasks can potentially be used for knowledge transfer across tasks. This however is meaningful in practice when only a limited amount of data from the target task is available. The proposed method appears to be heavily biased from the pretraining in the case of limited data.\n\n", "limitations": "There is no obvious severe limitation of this paper besides what the authors have already mentioned in the paper. I can say nothing regarding the negative social impact of this paper from my reading.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "\nStrengths:\n\n* This paper studied an interesting problem to uncover the nature of the deep learning models by means of agreement in the test set, in the context of the multi-task learning setup for task discovery for generalization.\n\n* The proposed hypothesis and developed framework are intuitive and convincing.\n\n* The paper is well written and easy to follow. The unconventional writing of the abstract and the discussion-rich paper make it an interesting read.\n\n* Experimental results, both quantitative and qualitative, validate the significance of the proposed method.\n\n* The studied case of adversarial train-test splits for the setup of the proposed setup is particularly interesting (although not very surprising).\n\n* Experimental results in Fig 7 in the supp. Material is meaningful. I suggest that to be included in the main paper.\n\n* Supp. Material provided with the submission (document, code, and video) are helpful.\n\n\nWeakness: \n\n* Conclusion: The conclusion of the paper is not really helpful. It reads as few comments of discussion and largely limitation in rather a short paragraph. The conclusion does not summarize the discovery of the paper in terms of theoretical or experimental results. In fact, the conclusion provided in the supp. Video is rather more meaningful.\n\n* Experimental setup: The experimental setup used in this paper is rather limiting. Although already highlighted in the limitation section, this becomes rather a serious concern to gauge the effectiveness of the proposed method in more practical task discovery.\n\n* Future work: Authors' thought processes behind formulating the problem, beside understanding the neural networks, is not clear. In particular, how the proposed framework can potentially be utilized beyond the experimental setup of this paper.\n\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "obzHW5bYoal", "reviewer": "Reviewer_G4XU", "summary": "This paper introduces task discovery, which aims to find tasks that the model can generalize on.\n", "questions": "see Weaknesses", "limitations": "see Weaknesses", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**\n\n1. The task is interesting. Compared to existing works that mostly focus on optimizing models to achieve SOTA performance on several benchmarks, this task is more interesting and can help us understand NN more deeply.\n\n2. I think the construction of  ``adversarial train-test splits’’ is valuable for understanding current out-of-distribution generalization or domain generalization problems.\n\n3. The experiments are pretty good and basically answer most of my questions about the proposed task.\n\n**Weaknesses**\n\n1. Just as the author mentioned, one of my main concerns of me is the expensive meta-optimization.\n2. I think the proposed task discovery task is relevant to domain generalization without demographics [1], optimal experimental design [2], and data-centric machine learning. Maybe more discussion should be included.\n\n[1] Environment Inference for Invariant Learning, ICML, 2021\n\n[2] Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design, ICML, 2021", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "Im1StNnKAT", "reviewer": "Reviewer_YjqC", "summary": "This paper proposes a new paradigm in which given a fixed model architecture (with learnable parameters and different initializations) the goal is to automatically discover a \"task\", or rather a binary label for inputs in a given dataset. This is achieved by learning a task network via optimizing a proposed metric termed the agreement score. This metric assesses on average how often two different models of the same class trained on the same task will agree with one another on unseen data, with the premise being that if the class of models generalize well then they should be in agreement more often on unseen data. This metric is proposed for both automatically learning tasks as mentioned before as well as being a investigatory tool for analyzing different biases and settings.", "questions": "I was wondering if the authors could speak more to their decisions regarding the approach taken for learning multiple tasks simultaneously. In your findings, was having a shared encoder with task-specific linear discriminators sufficiently flexible? Did you happen to notice the embeddings to be particularly sparse in high-dimensions? I am curious if a more flexible task-specific operation was considered, such as a network that accepts the shared encoding and a learned task-specific embedding or even just learning a task-specific shallow network that accepts the shared encoding? \n\nFinally, just to confirm my own intuition, when discovering a new task an entire dataset is essentially being partitioned into two classes ($t_\\theta(x)\\approx 1$ and $t_\\theta(x)\\approx 0$). In your findings, was is common that this process had a preference for discovering tasks with high rates of separability or decisiveness (meaning for a random $x\\sim X$ it is highly likely for $t_\\theta(x)$ to be close to 0 or 1) or did it also allow for instances where there are larger subsets of the data where the class is unsure ($t_\\theta(x)\\approx 0.5$)? Additionally, would you say that this process tended to prefer discovering tasks with roughly equal class balance? It would be interesting to be able to control or target the degrees of class imbalance exhibited within a class as I could see that leading to uncovering some uncommon but distinct traits or features within a dataset.", "limitations": "The authors have adequately discussed the limitations of their approach and findings.", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The proposal is novel and interesting as both a tool for analysis as well as for automatic task discovery. The paper has a good mix of technical contributions, ablation studies / investigations, as well as qualitative demonstrations. The methodology developed is well supported and motivated. I found the premise, proposed techniques, and experiments to all be clear and concise. \n\nOne slight correction should be made to the equations throughout the paper. Often within an expected value there is something like $\\tau_1(x)=\\tau_2(x)$ such as Eq. 2. These all need to be inputs to an indicator function to be proper.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "E6ZEvpF-xv", "reviewer": "Reviewer_RNrr", "summary": "The authors formulate an agreement score that scores how well two networks from different initializations, etc converge to a common solution on a task. They claim that the agreement score is a proxy measure for how generalizable a task is. They use this agreement score to find tasks that networks can generalize on. ", "questions": "- How exactly is the AS being used to discover adversarial splits? \n- Can the authors provide some qualitative examples for the tasks being discovered? Are they useful tasks? ", "limitations": "The authors did include a paragraph on limitations. ", "rating": 6, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n- The problem formulation is unique and probably interesting. The agreement score is also interesting since it shows how robust a network is on a task. \n\nConcerns/weaknesses:\n- I am mostly concerned about the practicality of such a problem definition. Why would one want to fix a network and find a task? Tasks are defined by practical demand and we find a solution to them, not the other way around. I believe this would be interesting if we were to find the set of tasks a network is good at, but that is rarely the use case. Searching in the opposite way makes more practical sense - which networks are good for my task? \n- I am not convinced why the agreement score is a proxy measure for generalizability. It seems like it is a proxy measure for robustness of a network for a task. If a network can converge a good solution from different initializations, it means that the task space is well defined and convex and easy for the network. Doesn't necessarily mean generalization - which in my knowledge is defined as performance on unseen and novel combinations of data. \n- The authors say that the agreement score based search doesn't discover any real tasks. This further convinces me that the searching in the task space is probably unnecessary. \n- Discovering the adversarial splits seems like an interesting direction to me here, but I didn't quite understand how the AS is being used here. To me, it seems like we can do this with any dataset and split it in a way where test labels are starkly different or opposite to train labels for a certain feature or feature combinations.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept