Coordinate-based networks, usually in the forms of MLPs, have been successfully applied to the task of predicting high-frequency but low-dimensional signals using coordinate inputs. To scale them to model large-scale signals, previous works resort to hybrid representations, combining a coordinate-based network with a grid-based representation, such as sparse voxels. However, such approaches lack a compact global latent representation in its grid, making it difficult to model a distribution of signals, which is important for generalization tasks. To address the limitation, we propose the Levels-of-Experts (LoE) framework, which is a novel coordinate-based representation consisting of an MLP with periodic, positiondependent weights arranged hierarchically. For each linear layer of the MLP, multiple candidate values of its weight matrix are tiled and replicated across the input space, with different layers replicating at different frequencies. Based on the input, only one of the weight matrices is chosen for each layer. This greatly increases the model capacity without incurring extra computation or compromising generalization capability. We show that the new representation is an efficient and competitive drop-in replacement for a wide range of tasks, including signal fitting, novel view synthesis, and generative modeling.

To understand neural network behavior, recent works quantitatively compare different networks' learned representations using canonical correlation analysis (CCA), centered kernel alignment (CKA), and other dissimilarity measures. Unfortunately, these widely used measures often disagree on fundamental observations, such as whether deep networks differing only in random initialization learn similar representations. These disagreements raise the question: which, if any, of these dissimilarity measures should we believe? We provide a framework to ground this question through a concrete test: measures should have sensitivity to changes that affect functional behavior, and specificity against changes that do not. We quantify this through a variety of functional behaviors including probing accuracy and robustness to distribution shift, and examine changes such as varying random initialization and deleting principal components. We find that current metrics exhibit different weaknesses, note that a classical baseline performs surprisingly well, and highlight settings where all metrics appear to fail, thus providing a challenge set for further improvement.

To understand neural network behavior, recent works quantitatively compare different networks' learned representations using canonical correlation analysis (CCA), centered kernel alignment (CKA), and other dissimilarity measures. Unfortunately, these widely used measures often disagree on fundamental observations, such as whether deep networks differing only in random initialization learn similar representations. These disagreements raise the question: which, if any, of these dissimilarity measures should we believe? We provide a framework to ground this question through a concrete test: measures should have sensitivity to changes that affect functional behavior, and specificity against changes that do not. We quantify this through a variety of functional behaviors including probing accuracy and robustness to distribution shift, and examine changes such as varying random initialization and deleting principal components. We find that current metrics exhibit different weaknesses, note that a classical baseline performs surprisingly well, and highlight settings where all metrics appear to fail, thus providing a challenge set for further improvement.

It is important to properly tune the kernel scale/bandwidth σb, which determines its scale of connectivity. Several studies have proposed schemes for tuning σb, see for example [10, 3, 12, 5]. Here, we focus on two schemes, a global bandwidth and a local bandwidth. The local bandwidth proposed in [12], involves setting a local-scale σi for each data point xi,i= 1,...,n. The scale is chosen using the L1 distance from the k-th nearest neighbor of the point xi.

What are Russia's gains from the Iran war? 'We are not losers; we are winners' But the calm is deceptive. Two soldiers scour the skies, hands firmly gripping anti-aircraft guns mounted on pick-up trucks parked on a small, dilapidated bridge on a tributary of the Pripyat River. Danger is all around, both in the surrounding land, which still carries the legacy of the 1986 Chornobyl nuclear disaster, with pockets of intense radioactive contamination, and above, where Russian drones and missiles launched from just across the border in Belarus, a short distance to the north, regularly pass overhead. The area is known as the Chornobyl Exclusion Zone (CEZ), a restricted area of approximately 30km (19 miles) in diameter, comparable in size to Luxembourg, established to contain the spread of contamination. Since Russia launched its full-scale invasion of Ukraine on February 24, 2022, briefly occupying the CEZ and the surrounding area, large swaths of it have become militarised, adding another layer of restriction to an already tightly controlled and hazardous environment. Yet despite the CEZ's many dangers, four decades on from the Chornobyl disaster, small communities of scientists, elderly returnees and soldiers have carved out lives among its abandoned buildings, while wildlife thrives in the surrounding forests.

When answering a question, humans utilize the information available across different modalities to synthesize a consistent and complete chain of thought (CoT). This process is normally a black box in the case of deep learning models like large-scale language models. Recently, science question benchmarks have been used to diagnose the multi-hop reasoning ability and interpretability of an AI system. However, existing datasets fail to provide annotations for the answers, or are restricted to the textual-only modality, small scales, and limited domain diversity. To this end, we present Science Question Answering (SCIENCEQA), a new benchmark that consists of 21k multimodal multiple choice questions with diverse science topics and annotations of their answers with corresponding lectures and explanations. We further design language models to learn to generate lectures and explanations as the chain of thought (CoT) to mimic the multi-hop reasoning process when answering SCIENCEQA questions. SCIENCEQA demonstrates the utility of CoT in language models, as CoT improves the question answering performance by 1.20% in fewshot GPT-3 and 3.99% in fine-tuned UnifiedQA. We also explore the upper bound for models to leverage explanations by feeding those in the input; we observe that it improves the few-shot performance of GPT-3 by 18.96%. Our analysis further shows that language models, similar to humans, benefit from explanations to learn from fewer data and achieve the same performance with just 40% of the data.1