Advances in brain decoding, particularly in visual image reconstruction, have sparked discussions about the societal implications and ethical considerations of neurotechnology. As reconstruction methods aim to recover visual experiences from brain activity and achieve prediction beyond training samples (zero-shot prediction), it is crucial to assess their capabilities and limitations to inform public expectations and regulations. Our case study of recent text-guided reconstruction methods, which leverage a large-scale dataset (Natural Scenes Dataset, NSD) and text-to-image diffusion models, reveals critical limitations in their generalizability, demonstrated by poor reconstructions on a different dataset. UMAP visualization of the text features from NSD images shows limited diversity with overlapping semantic and visual clusters between training and test sets. We identify that clustered training samples can lead to "output dimension collapse," restricting predictable output feature dimensions. While diverse training data improves generalization over the entire feature space without requiring exponential scaling, text features alone prove insufficient for mapping to the visual space. Our findings suggest that the apparent realism in current text-guided reconstructions stems from a combination of classification into trained categories and inauthentic image generation (hallucination) through diffusion models, rather than genuine visual reconstruction. We argue that careful selection of datasets and target features, coupled with rigorous evaluation methods, is essential for achieving authentic visual image reconstruction. These insights underscore the importance of grounding interdisciplinary discussions in a thorough understanding of the technology's current capabilities and limitations to ensure responsible development.

Contrastive representation learning encourages data representation to make semantically similar pairs closer than randomly drawn negative samples, which has been successful in various domains such as vision, language, and graphs. Recent theoretical studies have attempted to explain the benefit of the large negative sample size by upper-bounding the downstream classification loss with the contrastive loss. However, the previous surrogate bounds have two drawbacks: they are only legitimate for a limited range of negative sample sizes and prohibitively large even within that range. Due to these drawbacks, there still does not exist a consensus on how negative sample size theoretically correlates with downstream classification performance. Following the simplified setting where positive pairs are drawn from the true distribution (not generated by data augmentation; as supposed in previous studies), this study establishes surrogate upper and lower bounds for the downstream classification loss for all negative sample sizes that best explain the empirical observations on the negative sample size in the earlier studies. Our bounds suggest that the contrastive loss can be viewed as a surrogate objective of the downstream loss and larger negative sample sizes improve downstream classification because the surrogate gap between contrastive and supervised losses decays. We verify that our theory is consistent with experiments on synthetic, vision, and language datasets.

Adaptation and invariance to multiple environments are both crucial abilities for intelligent systems. Model-agnostic meta-learning (MAML) is a meta-learning algorithm to enable such adaptability, and invariant risk minimization (IRM) is a problem setting to achieve the invariant representation across multiple environments. We can formulate both methods as optimization problems with the environment-dependent constraint and this constraint is known to hamper optimization. Therefore, understanding the effect of the constraint on the optimization is important. In this paper, we provide a conceptual insight on how the constraint affects the optimization of MAML and IRM by analyzing the trainability of the gradient descent on the loss with the gradient norm penalty, which is easier to study but is related to both MAML and IRM. We conduct numerical experiments with practical datasets and architectures for MAML and IRM and validate that the analysis of the gradient norm penalty loss captures well the empirical relationship between the constraint and the trainability of MAML and IRM.

Hyperbolic space is a geometry that is known to be well-suited for representation learning of data with an underlying hierarchical structure. In this paper, we present a novel hyperbolic distribution called hyperbolic wrapped distribution, a wrapped normal distribution on hyperbolic space whose density can be evaluated analytically and differentiated with respect to the parameters. Our distribution enables the gradient-based learning of the probabilistic models on hyperbolic space that could never have been considered before. Also, we can sample from this hyperbolic probability distribution without resorting to auxiliary means like rejection sampling. As applications of our distribution, we develop a hyperbolic-analog of variational autoencoder and a method of probabilistic word embedding on hyperbolic space. We demonstrate the efficacy of our distribution on various datasets including MNIST, Atari 2600 Breakout, and WordNet.