Rosanne Liu

Sarah Pratt, Ian Covert, Rosanne Liu et al. · allen-ai, uw

Open-vocabulary models are a promising new paradigm for image classification. Unlike traditional classification models, open-vocabulary models classify among any arbitrary set of categories specified with natural language during inference. This natural language, called "prompts", typically consists of a set of hand-written templates (e.g., "a photo of a {}") which are completed with each of the category names. This work introduces a simple method to generate higher accuracy prompts, without relying on any explicit knowledge of the task domain and with far fewer hand-constructed sentences. To achieve this, we combine open-vocabulary models with large language models (LLMs) to create Customized Prompts via Language models (CuPL, pronounced "couple"). In particular, we leverage the knowledge contained in LLMs in order to generate many descriptive sentences that contain important discriminating characteristics of the image categories. This allows the model to place a greater importance on these regions in the image when making predictions. We find that this straightforward and general approach improves accuracy on a range of zero-shot image classification benchmarks, including over one percentage point gain on ImageNet. Finally, this simple baseline requires no additional training and remains completely zero-shot. Code available at https://github.com/sarahpratt/CuPL.

Aarohi Srivastava, Abhinav Rastogi, Abhishek Rao et al. · allen-ai, amazon-science

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 450 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting.

Rosanne Liu, Dan Garrette, Chitwan Saharia et al. · deepmind

Current image generation models struggle to reliably produce well-formed visual text. In this paper, we investigate a key contributing factor: popular text-to-image models lack character-level input features, making it much harder to predict a word's visual makeup as a series of glyphs. To quantify this effect, we conduct a series of experiments comparing character-aware vs. character-blind text encoders. In the text-only domain, we find that character-aware models provide large gains on a novel spelling task (WikiSpell). Applying our learnings to the visual domain, we train a suite of image generation models, and show that character-aware variants outperform their character-blind counterparts across a range of novel text rendering tasks (our DrawText benchmark). Our models set a much higher state-of-the-art on visual spelling, with 30+ point accuracy gains over competitors on rare words, despite training on far fewer examples.

Jiri Hron, Laura Culp, Gamaleldin Elsayed et al. · anthropic, deepmind

While many capabilities of language models (LMs) improve with increased training budget, the influence of scale on hallucinations is not yet fully understood. Hallucinations come in many forms, and there is no universally accepted definition. We thus focus on studying only those hallucinations where a correct answer appears verbatim in the training set. To fully control the training data content, we construct a knowledge graph (KG)-based dataset, and use it to train a set of increasingly large LMs. We find that for a fixed dataset, larger and longer-trained LMs hallucinate less. However, hallucinating on $\leq5$% of the training data requires an order of magnitude larger model, and thus an order of magnitude more compute, than Hoffmann et al. (2022) reported was optimal. Given this costliness, we study how hallucination detectors depend on scale. While we see detector size improves performance on fixed LM's outputs, we find an inverse relationship between the scale of the LM and the detectability of its hallucinations.

C. Daniel Freeman, Laura Culp, Aaron Parisi et al. · anthropic, deepmind

We introduce and study the problem of adversarial arithmetic, which provides a simple yet challenging testbed for language model alignment. This problem is comprised of arithmetic questions posed in natural language, with an arbitrary adversarial string inserted before the question is complete. Even in the simple setting of 1-digit addition problems, it is easy to find adversarial prompts that make all tested models (including PaLM2, GPT4, Claude2) misbehave, and even to steer models to a particular wrong answer. We additionally provide a simple algorithm for finding successful attacks by querying those same models, which we name "prompt inversion rejection sampling" (PIRS). We finally show that models can be partially hardened against these attacks via reinforcement learning and via agentic constitutional loops. However, we were not able to make a language model fully robust against adversarial arithmetic attacks.

Andrija Djurisic, Nebojsa Bozanic, Arjun Ashok et al.

The separation between training and deployment of machine learning models implies that not all scenarios encountered in deployment can be anticipated during training, and therefore relying solely on advancements in training has its limits. Out-of-distribution (OOD) detection is an important area that stress-tests a model's ability to handle unseen situations: Do models know when they don't know? Existing OOD detection methods either incur extra training steps, additional data or make nontrivial modifications to the trained network. In contrast, in this work, we propose an extremely simple, post-hoc, on-the-fly activation shaping method, ASH, where a large portion (e.g. 90%) of a sample's activation at a late layer is removed, and the rest (e.g. 10%) simplified or lightly adjusted. The shaping is applied at inference time, and does not require any statistics calculated from training data. Experiments show that such a simple treatment enhances in-distribution and out-of-distribution distinction so as to allow state-of-the-art OOD detection on ImageNet, and does not noticeably deteriorate the in-distribution accuracy. Video, animation and code can be found at: https://andrijazz.github.io/ash

Bernd Bohnet, Pierre-Alexandre Kamienny, Hanie Sedghi et al.

We demonstrate an approach for LLMs to critique their \emph{own} answers with the goal of enhancing their performance that leads to significant improvements over established planning benchmarks. Despite the findings of earlier research that has cast doubt on the effectiveness of LLMs leveraging self critique methods, we show significant performance gains on planning datasets in the Blocksworld domain through intrinsic self-critique, without external source such as a verifier. We also demonstrate similar improvements on Logistics and Mini-grid datasets, exceeding strong baseline accuracies. We employ a few-shot learning technique and progressively extend it to a many-shot approach as our base method and demonstrate that it is possible to gain substantial improvement on top of this already competitive approach by employing an iterative process for correction and refinement. We illustrate how self-critique can significantly boost planning performance. Our empirical results present new state-of-the-art on the class of models considered, namely LLM model checkpoints from October 2024. Our primary focus lies on the method itself, demonstrating intrinsic self-improvement capabilities that are applicable regardless of the specific model version, and we believe that applying our method to more complex search techniques and more capable models will lead to even better performance.

Michael C. Mozer, Shoaib Ahmed Siddiqui, Rosanne Liu

Transformers encode structure in sequences via an expanding contextual history. However, their purely feedforward architecture fundamentally limits dynamic state tracking. State tracking -- the iterative updating of latent variables reflecting an evolving environment -- involves inherently sequential dependencies that feedforward networks struggle to maintain. Consequently, feedforward models push evolving state representations deeper into their layer stack with each new input step, rendering information inaccessible in shallow layers and ultimately exhausting the model's depth. While this depth limit can be bypassed by dynamic depth models and by explicit or latent thinking that externalizes state representations, these solutions are computationally and memory inefficient. In this article, we argue that temporally extended cognition requires refocusing from explicit thought traces to implicit activation dynamics via recurrent architectures. We introduce a taxonomy of recurrent and continuous-thought transformer architectures, categorizing them by their recurrence axis (depth versus step) and their ratio of input tokens to recurrence steps. Finally, we outline promising research directions, including enhanced state-space models and coarse-grained recurrence, to better integrate state tracking into modern foundation models.

Andrija Djurisic, Rosanne Liu, Mladen Nikolic

The safe deployment of machine learning and AI models in open-world settings hinges critically on the ability to detect out-of-distribution (OOD) data accurately, data samples that contrast vastly from what the model was trained with. Current approaches to OOD detection often require further training the model, and/or statistics about the training data which may no longer be accessible. Additionally, many existing OOD detection methods struggle to maintain performance when transferred across different architectures. Our research tackles these issues by proposing a simple, post-hoc method that does not require access to the training data distribution, keeps a trained network intact, and holds strong performance across a variety of architectures. Our method, Logit Scaling (LTS), as the name suggests, simply scales the logits in a manner that effectively distinguishes between in-distribution (ID) and OOD samples. We tested our method on benchmarks across various scales, including CIFAR-10, CIFAR-100, ImageNet and OpenOOD. The experiments cover 3 ID and 14 OOD datasets, as well as 9 model architectures. Overall, we demonstrate state-of-the-art performance, robustness and adaptability across different architectures, paving the way towards a universally applicable solution for advanced OOD detection.

Gemini Team, Petko Georgiev, Ving Ian Lei et al. · deepmind, mila

In this report, we introduce the Gemini 1.5 family of models, representing the next generation of highly compute-efficient multimodal models capable of recalling and reasoning over fine-grained information from millions of tokens of context, including multiple long documents and hours of video and audio. The family includes two new models: (1) an updated Gemini 1.5 Pro, which exceeds the February version on the great majority of capabilities and benchmarks; (2) Gemini 1.5 Flash, a more lightweight variant designed for efficiency with minimal regression in quality. Gemini 1.5 models achieve near-perfect recall on long-context retrieval tasks across modalities, improve the state-of-the-art in long-document QA, long-video QA and long-context ASR, and match or surpass Gemini 1.0 Ultra's state-of-the-art performance across a broad set of benchmarks. Studying the limits of Gemini 1.5's long-context ability, we find continued improvement in next-token prediction and near-perfect retrieval (>99%) up to at least 10M tokens, a generational leap over existing models such as Claude 3.0 (200k) and GPT-4 Turbo (128k). Finally, we highlight real-world use cases, such as Gemini 1.5 collaborating with professionals on completing their tasks achieving 26 to 75% time savings across 10 different job categories, as well as surprising new capabilities of large language models at the frontier; when given a grammar manual for Kalamang, a language with fewer than 200 speakers worldwide, the model learns to translate English to Kalamang at a similar level to a person who learned from the same content.

Avi Singh, John D. Co-Reyes, Rishabh Agarwal et al. · anthropic, deepmind

Fine-tuning language models~(LMs) on human-generated data remains a prevalent practice. However, the performance of such models is often limited by the quantity and diversity of high-quality human data. In this paper, we explore whether we can go beyond human data on tasks where we have access to scalar feedback, for example, on math problems where one can verify correctness. To do so, we investigate a simple self-training method based on expectation-maximization, which we call ReST$^{EM}$, where we (1) generate samples from the model and filter them using binary feedback, (2) fine-tune the model on these samples, and (3) repeat this process a few times. Testing on advanced MATH reasoning and APPS coding benchmarks using PaLM-2 models, we find that ReST$^{EM}$ scales favorably with model size and significantly surpasses fine-tuning only on human data. Overall, our findings suggest self-training with feedback can substantially reduce dependence on human-generated data.

Pooyan Rahmanzadehgervi, Hung Huy Nguyen, Rosanne Liu et al.

Multi-head self-attention (MHSA) is a key component of Transformers, a widely popular architecture in both language and vision. Multiple heads intuitively enable different parallel processes over the same input. Yet, they also obscure the attribution of each input patch to the output of a model. We propose a novel 1-head Transformer Attention Bottleneck (TAB) layer, inserted after the traditional MHSA architecture, to serve as an attention bottleneck for interpretability and intervention. Unlike standard self-attention, TAB constrains the total attention over all patches to $\in [0, 1]$. That is, when the total attention is 0, no visual information is propagated further into the network, and the vision-language model (VLM) would default to a generic, image-independent response. To demonstrate the advantages of TAB, we train VLMs with TAB to perform image-difference captioning. Over three datasets, our models perform similarly to baseline VLMs in captioning but the bottleneck is superior in localizing changes and in identifying when no changes occur. TAB is the first architecture to enable users to debug by editing attention, which often produces expected outputs by VLMs.

Liangchen Luo, Yinxiao Liu, Rosanne Liu et al.

Complex multi-step reasoning tasks, such as solving mathematical problems or generating code, remain a significant hurdle for even the most advanced large language models (LLMs). Verifying LLM outputs with an Outcome Reward Model (ORM) is a standard inference-time technique aimed at enhancing the reasoning performance of LLMs. However, this still proves insufficient for reasoning tasks with a lengthy or multi-hop reasoning chain, where the intermediate outcomes are neither properly rewarded nor penalized. Process supervision addresses this limitation by assigning intermediate rewards during the reasoning process. To date, the methods used to collect process supervision data have relied on either human annotation or per-step Monte Carlo estimation, both prohibitively expensive to scale, thus hindering the broad application of this technique. In response to this challenge, we propose a novel divide-and-conquer style Monte Carlo Tree Search (MCTS) algorithm named \textit{OmegaPRM} for the efficient collection of high-quality process supervision data. This algorithm swiftly identifies the first error in the Chain of Thought (CoT) with binary search and balances the positive and negative examples, thereby ensuring both efficiency and quality. As a result, we are able to collect over 1.5 million process supervision annotations to train Process Reward Models (PRMs). This fully automated process supervision alongside the weighted self-consistency algorithm is able to enhance LLMs' math reasoning performances. We improved the success rates of the instruction-tuned Gemini Pro model from 51\% to 69.4\% on MATH500 and from 86.4\% to 93.6\% on GSM8K. Similarly, we boosted the success rates of Gemma2 27B from 42.3\% to 58.2\% on MATH500 and from 74.0\% to 92.2\% on GSM8K. The entire process operates without any human intervention or supervision, making our method both financially and ...

Robin Tibor Schirrmeister, Rosanne Liu, Sara Hooker et al.

How do neural network image classifiers respond to simpler and simpler inputs? And what do such responses reveal about the learning process? To answer these questions, we need a clear measure of input simplicity (or inversely, complexity), an optimization objective that correlates with simplification, and a framework to incorporate such objective into training and inference. Lastly we need a variety of testbeds to experiment and evaluate the impact of such simplification on learning. In this work, we measure simplicity with the encoding bit size given by a pretrained generative model, and minimize the bit size to simplify inputs in training and inference. We investigate the effect of such simplification in several scenarios: conventional training, dataset condensation and post-hoc explanations. In all settings, inputs are simplified along with the original classification task, and we investigate the trade-off between input simplicity and task performance. For images with injected distractors, such simplification naturally removes superfluous information. For dataset condensation, we find that inputs can be simplified with almost no accuracy degradation. When used in post-hoc explanation, our learning-based simplification approach offers a valuable new tool to explore the basis of network decisions.

Felix Lau, Nishant Subramani, Sasha Harrison et al.

Although state-of-the-art object detection methods have shown compelling performance, models often are not robust to adversarial attacks and out-of-distribution data. We introduce a new dataset, Natural Adversarial Objects (NAO), to evaluate the robustness of object detection models. NAO contains 7,934 images and 9,943 objects that are unmodified and representative of real-world scenarios, but cause state-of-the-art detection models to misclassify with high confidence. The mean average precision (mAP) of EfficientDet-D7 drops 74.5% when evaluated on NAO compared to the standard MSCOCO validation set. Moreover, by comparing a variety of object detection architectures, we find that better performance on MSCOCO validation set does not necessarily translate to better performance on NAO, suggesting that robustness cannot be simply achieved by training a more accurate model. We further investigate why examples in NAO are difficult to detect and classify. Experiments of shuffling image patches reveal that models are overly sensitive to local texture. Additionally, using integrated gradients and background replacement, we find that the detection model is reliant on pixel information within the bounding box, and insensitive to the background context when predicting class labels. NAO can be downloaded at https://drive.google.com/drive/folders/15P8sOWoJku6SSEiHLEts86ORfytGezi8.

Genta Indra Winata, Andrea Madotto, Zhaojiang Lin et al.

General-purpose language models have demonstrated impressive capabilities, performing on par with state-of-the-art approaches on a range of downstream natural language processing (NLP) tasks and benchmarks when inferring instructions from very few examples. Here, we evaluate the multilingual skills of the GPT and T5 models in conducting multi-class classification on non-English languages without any parameter updates. We show that, given a few English examples as context, pre-trained language models can predict not only English test samples but also non-English ones. Finally, we find the in-context few-shot cross-lingual prediction results of language models are significantly better than random prediction, and they are competitive compared to the existing state-of-the-art cross-lingual models.

Niel Teng Hu, Xinyu Hu, Rosanne Liu et al.

Not all examples are created equal, but standard deep neural network training protocols treat each training point uniformly. Each example is propagated forward and backward through the network the same amount of times, independent of how much the example contributes to the learning protocol. Recent work has proposed ways to accelerate training by deviating from this uniform treatment. Popular methods entail up-weighting examples that contribute more to the loss with the intuition that examples with low loss have already been learned by the model, so their marginal value to the training procedure should be lower. This view assumes that updating the model with high loss examples will be beneficial to the model. However, this may not hold for noisy, real world data. In this paper, we theorize and then empirically demonstrate that loss-based acceleration methods degrade in scenarios with noisy and corrupted data. Our work suggests measures of example difficulty need to correctly separate out noise from other types of challenging examples.

Sahib Singh, Rosanne Liu

Recent studies assessing the efficacy of pruning neural networks methods uncovered a surprising finding: when conducting ablation studies on existing pruning-at-initialization methods, namely SNIP, GraSP, SynFlow, and magnitude pruning, performances of these methods remain unchanged and sometimes even improve when randomly shuffling the mask positions within each layer (Layerwise Shuffling) or sampling new initial weight values (Reinit), while keeping pruning masks the same. We attempt to understand the reason behind such network immunity towards weight/mask modifications, by studying layer-wise statistics before and after randomization operations. We found that under each of the pruning-at-initialization methods, the distribution of unpruned weights changed minimally with randomization operations.

Mitchell Wortsman, Vivek Ramanujan, Rosanne Liu et al.

We present the Supermasks in Superposition (SupSup) model, capable of sequentially learning thousands of tasks without catastrophic forgetting. Our approach uses a randomly initialized, fixed base network and for each task finds a subnetwork (supermask) that achieves good performance. If task identity is given at test time, the correct subnetwork can be retrieved with minimal memory usage. If not provided, SupSup can infer the task using gradient-based optimization to find a linear superposition of learned supermasks which minimizes the output entropy. In practice we find that a single gradient step is often sufficient to identify the correct mask, even among 2500 tasks. We also showcase two promising extensions. First, SupSup models can be trained entirely without task identity information, as they may detect when they are uncertain about new data and allocate an additional supermask for the new training distribution. Finally the entire, growing set of supermasks can be stored in a constant-sized reservoir by implicitly storing them as attractors in a fixed-sized Hopfield network.

Ashley D. Edwards, Himanshu Sahni, Rosanne Liu et al.

In this paper, we introduce a novel form of value function, $Q(s, s')$, that expresses the utility of transitioning from a state $s$ to a neighboring state $s'$ and then acting optimally thereafter. In order to derive an optimal policy, we develop a forward dynamics model that learns to make next-state predictions that maximize this value. This formulation decouples actions from values while still learning off-policy. We highlight the benefits of this approach in terms of value function transfer, learning within redundant action spaces, and learning off-policy from state observations generated by sub-optimal or completely random policies. Code and videos are available at http://sites.google.com/view/qss-paper.

Sumanth Dathathri, Andrea Madotto, Janice Lan et al.

Large transformer-based language models (LMs) trained on huge text corpora have shown unparalleled generation capabilities. However, controlling attributes of the generated language (e.g. switching topic or sentiment) is difficult without modifying the model architecture or fine-tuning on attribute-specific data and entailing the significant cost of retraining. We propose a simple alternative: the Plug and Play Language Model (PPLM) for controllable language generation, which combines a pretrained LM with one or more simple attribute classifiers that guide text generation without any further training of the LM. In the canonical scenario we present, the attribute models are simple classifiers consisting of a user-specified bag of words or a single learned layer with 100,000 times fewer parameters than the LM. Sampling entails a forward and backward pass in which gradients from the attribute model push the LM's hidden activations and thus guide the generation. Model samples demonstrate control over a range of topics and sentiment styles, and extensive automated and human annotated evaluations show attribute alignment and fluency. PPLMs are flexible in that any combination of differentiable attribute models may be used to steer text generation, which will allow for diverse and creative applications beyond the examples given in this paper.

Janice Lan, Rosanne Liu, Hattie Zhou et al.

Neural networks enjoy widespread use, but many aspects of their training, representation, and operation are poorly understood. In particular, our view into the training process is limited, with a single scalar loss being the most common viewport into this high-dimensional, dynamic process. We propose a new window into training called Loss Change Allocation (LCA), in which credit for changes to the network loss is conservatively partitioned to the parameters. This measurement is accomplished by decomposing the components of an approximate path integral along the training trajectory using a Runge-Kutta integrator. This rich view shows which parameters are responsible for decreasing or increasing the loss during training, or which parameters "help" or "hurt" the network's learning, respectively. LCA may be summed over training iterations and/or over neurons, channels, or layers for increasingly coarse views. This new measurement device produces several insights into training. (1) We find that barely over 50% of parameters help during any given iteration. (2) Some entire layers hurt overall, moving on average against the training gradient, a phenomenon we hypothesize may be due to phase lag in an oscillatory training process. (3) Finally, increments in learning proceed in a synchronized manner across layers, often peaking on identical iterations.

Hattie Zhou, Janice Lan, Rosanne Liu et al.

The recent "Lottery Ticket Hypothesis" paper by Frankle & Carbin showed that a simple approach to creating sparse networks (keeping the large weights) results in models that are trainable from scratch, but only when starting from the same initial weights. The performance of these networks often exceeds the performance of the non-sparse base model, but for reasons that were not well understood. In this paper we study the three critical components of the Lottery Ticket (LT) algorithm, showing that each may be varied significantly without impacting the overall results. Ablating these factors leads to new insights for why LT networks perform as well as they do. We show why setting weights to zero is important, how signs are all you need to make the reinitialized network train, and why masking behaves like training. Finally, we discover the existence of Supermasks, masks that can be applied to an untrained, randomly initialized network to produce a model with performance far better than chance (86% on MNIST, 41% on CIFAR-10).

Felipe Petroski Such, Vashisht Madhavan, Rosanne Liu et al.

Much human and computational effort has aimed to improve how deep reinforcement learning algorithms perform on benchmarks such as the Atari Learning Environment. Comparatively less effort has focused on understanding what has been learned by such methods, and investigating and comparing the representations learned by different families of reinforcement learning (RL) algorithms. Sources of friction include the onerous computational requirements, and general logistical and architectural complications for running Deep RL algorithms at scale. We lessen this friction, by (1) training several algorithms at scale and releasing trained models, (2) integrating with a previous Deep RL model release, and (3) releasing code that makes it easy for anyone to load, visualize, and analyze such models. This paper introduces the Atari Zoo framework, which contains models trained across benchmark Atari games, in an easy-to-use format, as well as code that implements common modes of analysis and connects such models to a popular neural network visualization library. Further, to demonstrate the potential of this dataset and software package, we show initial quantitative and qualitative comparisons between the performance and representations of several deep RL algorithms, highlighting interesting and previously unknown distinctions between them.

Rosanne Liu, Joel Lehman, Piero Molino et al.

Few ideas have enjoyed as large an impact on deep learning as convolution. For any problem involving pixels or spatial representations, common intuition holds that convolutional neural networks may be appropriate. In this paper we show a striking counterexample to this intuition via the seemingly trivial coordinate transform problem, which simply requires learning a mapping between coordinates in (x,y) Cartesian space and one-hot pixel space. Although convolutional networks would seem appropriate for this task, we show that they fail spectacularly. We demonstrate and carefully analyze the failure first on a toy problem, at which point a simple fix becomes obvious. We call this solution CoordConv, which works by giving convolution access to its own input coordinates through the use of extra coordinate channels. Without sacrificing the computational and parametric efficiency of ordinary convolution, CoordConv allows networks to learn either complete translation invariance or varying degrees of translation dependence, as required by the end task. CoordConv solves the coordinate transform problem with perfect generalization and 150 times faster with 10--100 times fewer parameters than convolution. This stark contrast raises the question: to what extent has this inability of convolution persisted insidiously inside other tasks, subtly hampering performance from within? A complete answer to this question will require further investigation, but we show preliminary evidence that swapping convolution for CoordConv can improve models on a diverse set of tasks. Using CoordConv in a GAN produced less mode collapse as the transform between high-level spatial latents and pixels becomes easier to learn. A Faster R-CNN detection model trained on MNIST showed 24% better IOU when using CoordConv, and in the RL domain agents playing Atari games benefit significantly from the use of CoordConv layers.

Chunyuan Li, Heerad Farkhoor, Rosanne Liu et al.

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.