Standard training metrics like loss fail to explain the emergence of complex capabilities in large language models. We take a spectral approach to investigate the geometry of learned representations across pretraining and post-training, measuring effective rank (RankMe) and eigenspectrum decay (αReQ). With OLMo (1B-7B) and Pythia (160M-12B) models, we uncover a consistent non-monotonic sequence of three geometric phases during autoregressive pretraining. The initial “warmup” phase exhibits rapid representational collapse. This is followed by an “entropy-seeking” phase, where the manifold’s dimensionality expands substantially, coinciding with peak n-gram memorization. Subsequently, a “compression-seeking” phase imposes anisotropic consolidation, selectively preserving variance along dominant eigendirections while contracting others, a transition marked with significant improvement in downstream task performance. We show these phases can emerge from a fundamental interplay of cross-entropy optimization under skewed token frequencies and representational bottlenecks (d ≪ |V|). Post-training further transforms geometry: SFT and DPO drive “entropy-seeking” dynamics to integrate specific instructional or preferential data, improving in-distribution performance while degrading out-of-distribution robustness. Conversely, RLVR induces “compression-seeking” , enhancing reward alignment but reducing generation diversity.

Although modern neural networks often generalize to new combinations of familiar concepts, the conditions that enable such compositionality have long been an open question.In this work, we study the systematicity gap in visual question answering: the performance difference between reasoning on previously seen and unseen combinations of object attributes.To test, we introduce a novel diagnostic dataset, CLEVR-HOPE.We find that the systematicity gap is not reduced by increasing the quantity of training data, but is reduced by increasing the diversity of training data.In particular, our experiments suggest that the more distinct attribute type combinations are seen during training, the more systematic we can expect the resulting model to be.We release our data and code at https://github.com/ ikb-a/systematicity-gap-in-vqa.

Recent progress in self-supervised (SSL) visual representation learning has led to the development of several different proposed frameworks that rely on augmentations of images but use different loss functions. However, there are few theoretically grounded principles to guide practice, so practical implementation of each SSL framework requires several heuristics to achieve competitive performance. In this work, we build on recent analytical results to design practical recommendations for competitive and efficient SSL that are grounded in theory. Specifically, recent theory tells us that existing SSL frameworks are actually minimizing the same idealized loss, which is to learn features that best match the data similarity kernel defined by the augmentations used. We show how this idealized loss can be reformulated to a functionally equivalent loss that is more efficient to compute. We study the implicit bias of using gradient descent to minimize our reformulated loss function, and find that using a stronger orthogonalization constraint with a reduced projector dimensionality should yield good representations. Furthermore, the theory tells us that approximating the reformulated loss should be improved by increasing the number of augmentations, and as such using multiple augmentations should lead to improved convergence. We empirically verify our findings on CIFAR, STL and Imagenet datasets, wherein we demonstrate an improved linear readout performance when training a ResNet-backbone using our theoretically grounded recommendations. Remarkably, we also demonstrate that by leveraging these insights, we can reduce the pretraining dataset size by up to 2$\times$ while maintaining downstream accuracy simply by using more data augmentations. Taken together, our work provides theoretically grounded recommendations that can be used to improve SSL convergence and efficiency.

We introduce the “inverse bandit” problem of estimating the rewards of a multi-armed bandit instance from observing the learning process of a low-regret demonstrator. Existing approaches to the related problem of inverse reinforcement learning assume the execution of an optimal policy, and thereby suffer from an identifiability issue. In contrast, we propose to leverage the demonstrator’s behavior en route to optimality, and in particular, the exploration phase, for reward estimation. We begin by establishing a general information-theoretic lower bound under this paradigm that applies to any demonstrator algorithm, which characterizes a fundamental tradeoff between reward estimation and the amount of exploration of the demonstrator. Then, we develop simple and efficient reward estimators for upper-confidence-based demonstrator algorithms that attain the optimal tradeoff, showing in particular that consistent reward estimation—free of identifiability issues—is possible under our paradigm. Extensive simulations on both synthetic and semi-synthetic data corroborate our theoretical results.

Self-Supervised Learning (SSL) with large-scale unlabelled datasets enables learning useful representations for multiple downstream tasks. However, assessing the quality of such representations efficiently poses nontrivial challenges. Existing approaches train linear probes (with frozen features) to evaluate performance on a given task. This is expensive both computationally, since it requires retraining a new prediction head for each downstream task, and statistically, requires task-specific labels for multiple tasks. This poses a natural question, how do we efficiently determine the "goodness" of representations learned with SSL across a wide range of potential downstream tasks? In particular, a task-agnostic statistical measure of representation quality, that predicts generalization without explicit downstream task evaluation, would be highly desirable. In this work, we analyze characteristics of learned representations $\mathbf{f_\theta}$, in well-trained neural networks with canonical architectures \& across SSL objectives. We observe that the eigenspectrum of the empirical feature covariance $\mathrm{Cov}(\mathbf{f_\theta}$) can be well approximated with the family of power-law distribution. We analytically and empirically (using multiple datasets, e.g. CIFAR, STL10, MIT67, ImageNet) demonstrate that the decay coefficient $\alpha$ serves as a measure of representation quality for tasks that are solvable with a linear readout, i.e. there exist well-defined intervals for $\alpha$ where models exhibit excellent downstream generalization. Furthermore, our experiments suggest that key design parameters in SSL algorithms, such as BarlowTwins, implicitly modulate the decay coefficient of the eigenspectrum ($\alpha$). As $\alpha$ depends only on the features themselves, this measure for model selection with hyperparameter tuning for BarlowTwins enables search with less compute.

The Model AI Assignments session seeks to gather and disseminate the best assignment designs of the Artificial Intelligence (AI) Education community. Recognizing that assignments form the core of student learning experience, we here present abstracts of nine AI assignments from the 2020 session that are easily adoptable, playfully engaging, and flexible for a variety of instructor needs. Assignment specifications and supporting resources may be found at http://modelai.gettysburg.edu.

The Model AI Assignments session seeks to gather and disseminate the best assignment designs of the Artificial Intelligence (AI) Education community. Recognizing that assignments form the core of student learning experience, we here present abstracts of ten AI assignments from the 2019 session that are easily adoptable, playfully engaging, and flexible for a variety of instructor needs. Assignment specifications and supporting resources may be found at http: //modelai.gettysburg.edu.

While normalizing flows have led to significant advances in modeling high-dimensional continuous distributions, their applicability to discrete distributions remains unknown. In this paper, we show that flows can in fact be extended to discrete events---and under a simple change-of-variables formula not requiring log-determinant-Jacobian computations. Discrete flows have numerous applications. We consider two flow architectures: discrete autoregressive flows that enable bidirectionality, allowing, for example, tokens in text to depend on both left-to-right and right-to-left contexts in an exact language model; and discrete bipartite flows that enable efficient non-autoregressive generation as in RealNVP. Empirically, we find that discrete autoregressive flows outperform autoregressive baselines on synthetic discrete distributions, an addition task, and Potts models; and bipartite flows can obtain competitive performance with autoregressive baselines on character-level language modeling for Penn Tree Bank and text8.