Physical computing systems provide a promising route toward hardware-native machine learning, but their computational capabilities remain difficult to characterize in a principled, task-independent, and data-efficient way. We extend the Information Processing Capacity (IPC) framework to stationary physical computing systems and establish several fundamental results: individual capacities are bounded between zero and one, their sum over a complete basis is bounded by the number of readouts, and noise strictly reduces this bound. We address the finite-sample estimation of IPC and derive the asymptotic form of the systematic positive bias affecting naive estimators. Building on these results, we introduce data-efficient estimation methods based on Richardson extrapolation and Sobol quasi-random sampling. We validate the framework experimentally using a photonic computing system based on picosecond laser pulses propagating through a nonlinear optical fibre. By varying the laser power and fibre length, we observe systematic shifts of the IPC distribution toward higher-order nonlinear capacities induced by the Kerr effect. Finally, we demonstrate that the total IPC strongly correlates with performance on benchmark machine-learning tasks and provides a reliable estimate of the effective dimensionality of the system. These results establish IPC as a practical bridge between the intrinsic dynamics of physical computing systems and their machine-learning performance.

However, in practice, new reconstruction methods could improve performance for at least three other reasons: learning more about the distribution of stimuli, becoming better at reconstructing text or images in general, or exploiting weaknesses in current image and/or text evaluation metrics. Here we disentangle how much of the reconstruction is due to these other factors vs. productively using the neural recordings.

Estimating the dimensionality of the latent representation needed for prediction-- the task-relevant dimension--is a difficult, largely unsolved problem with broad scientific applications. We cast it as an Information Bottleneck question: what embedding bottleneck dimension is sufficient to compress predictor and predicted views while preserving their mutual information (MI). We show that standard neural estimators with separable/bilinear critics systematically inflate the inferred dimension, and we address this by introducing a hybrid critic that retains an explicit dimensional bottleneck while allowing flexible nonlinear cross-view interactions, thereby preserving the latent geometry. We further propose a one-shot protocol that reads off the effective dimension from a single over-parameterized hybrid model, without sweeping over bottleneck sizes. We validate the approach on synthetic problems with known task-relevant dimension. We extend the approach to intrinsic dimensionality by constructing paired views of a single dataset, enabling comparison with classical geometric dimension estimators. In noisy regimes where those estimators degrade, our approach remains reliable. Finally, we demonstrate the utility of the method on multiple physics datasets. Before "low-dimensional latent embeddings" became a rallying cry of AI, they were already a basic aim of science: identify a low-dimensional state--a small set of degrees of freedom constructed from observations--that suffices to predict the quantities of interest. The long road from Aristotelian to Newtonian mechanics illustrates that determining the number of such state variables--the relevant latent dimensionality--can be hard, even before one argues about the right variables or the laws that relate them.

Feature learning strength (FLS), i.e., the inverse of the effective output scaling of a model, plays a critical role in shaping the optimization dynamics of neural nets. While its impact has been extensively studied under the asymptotic regimes -- both in training time and FLS -- existing theory offers limited insight into how FLS affects generalization in practical settings, such as when training is stopped upon reaching a target training risk. In this work, we investigate the impact of FLS on generalization in deep networks under such practical conditions. Through empirical studies, we first uncover the emergence of an $\textit{optimal FLS}$ -- neither too small nor too large -- that yields substantial generalization gains. This finding runs counter to the prevailing intuition that stronger feature learning universally improves generalization. To explain this phenomenon, we develop a theoretical analysis of gradient flow dynamics in two-layer ReLU nets trained with logistic loss, where FLS is controlled via initialization scale. Our main theoretical result establishes the existence of an optimal FLS arising from a trade-off between two competing effects: An excessively large FLS induces an $\textit{over-alignment}$ phenomenon that degrades generalization, while an overly small FLS leads to $\textit{over-fitting}$.

How and where does a transformer notice that a sentence has gone semantically off the rails? To explore this question, we evaluated the causal language model (phi-2) using a carefully curated corpus, with sentences that concluded plausibly or implausibly. Our analysis focused on the hidden states sampled at each model layer. To investigate how violations are encoded, we utilized two complementary probes. First, we conducted a per-layer detection using a linear probe. Our findings revealed that a simple linear decoder struggled to distinguish between plausible and implausible endings in the lowest third of the model's layers. However, its accuracy sharply increased in the middle blocks, reaching a peak just before the top layers. Second, we examined the effective dimensionality of the encoded violation. Initially, the violation widens the representational subspace, followed by a collapse after a mid-stack bottleneck. This might indicate an exploratory phase that transitions into rapid consolidation. Taken together, these results contemplate the idea of alignment with classical psycholinguistic findings in human reading, where semantic anomalies are detected only after syntactic resolution, occurring later in the online processing sequence.

This work explores transfer learning from several synthetic languages to English. We investigate the structure of the embeddings in the fine-tuned models, the information they contain, and the capabilities of the fine-tuned models on simple linguistic tasks. We also introduce a new synthetic language that leads to better transfer to English than the languages used in previous research. Finally, we introduce Tiny-Cloze Benchmark - a new synthetic benchmark for natural language understanding that is more informative for less powerful models. We use Tiny-Cloze Benchmark to evaluate fine-tuned models in several domains demonstrating that fine-tuning on a new synthetic language allows for better performance on a variety of tasks.

Deep neural networks are often seen as different from other model classes by defying conventional notions of generalization. Popular examples of anomalous generalization behaviour include benign overfitting, double descent, and the success of overparametrization. We argue that these phenomena are not distinct to neural networks, or particularly mysterious. Moreover, this generalization behaviour can be intuitively understood, and rigorously characterized using long-standing generalization frameworks such as PAC-Bayes and countable hypothesis bounds. We present soft inductive biases as a key unifying principle in explaining these phenomena: rather than restricting the hypothesis space to avoid overfitting, embrace a flexible hypothesis space, with a soft preference for simpler solutions that are consistent with the data. This principle can be encoded in many model classes, and thus deep learning is not as mysterious or different from other model classes as it might seem. However, we also highlight how deep learning is relatively distinct in other ways, such as its ability for representation learning, phenomena such as mode connectivity, and its relative universality.

When evaluating stimuli reconstruction results it is tempting to assume that higher fidelity text and image generation is due to an improved understanding of the brain or more powerful signal extraction from neural recordings. However, in practice, new reconstruction methods could improve performance for at least three other reasons: learning more about the distribution of stimuli, becoming better at reconstructing text or images in general, or exploiting weaknesses in current image and/or text evaluation metrics. Here we disentangle how much of the reconstruction is due to these other factors vs. productively using the neural recordings. We introduce BrainBits, a method that uses a bottleneck to quantify the amount of signal extracted from neural recordings that is actually necessary to reproduce a method's reconstruction fidelity. We find that it takes surprisingly little information from the brain to produce reconstructions with high fidelity. In these cases, it is clear that the priors of the methods' generative models are so powerful that the outputs they produce extrapolate far beyond the neural signal they decode. Given that reconstructing stimuli can be improved independently by either improving signal extraction from the brain or by building more powerful generative models, improving the latter may fool us into thinking we are improving the former. We propose that methods should report a method-specific random baseline, a reconstruction ceiling, and a curve of performance as a function of bottleneck size, with the ultimate goal of using more of the neural recordings.

Quantifying robustness in a single measure for the purposes of model selection, development of adversarial training methods, and anticipating trends has so far been elusive. The simplest metric to consider is the number of trainable parameters in a model but this has previously been shown to be insufficient at explaining robustness properties. A variety of other metrics, such as ones based on boundary thickness and gradient flatness have been proposed but have been shown to be inadequate proxies for robustness. In this work, we investigate the relationship between a model's effective dimensionality, which can be thought of as model complexity, and its robustness properties. We run experiments on commercial-scale models that are often used in real-world environments such as YOLO and ResNet. We reveal a near-linear inverse relationship between effective dimensionality and adversarial robustness, that is models with a lower dimensionality exhibit better robustness. We investigate the effect of a variety of adversarial training methods on effective dimensionality and find the same inverse linear relationship present, suggesting that effective dimensionality can serve as a useful criterion for model selection and robustness evaluation, providing a more nuanced and effective metric than parameter count or previously-tested measures.