Estimating uncertainty in Large Language Models (LLMs) is important for properly evaluating LLMs, and ensuring safety for users. However, prior approaches to uncertainty estimation focus on the final answer in generated text, ignoring intermediate steps that might dramatically impact the outcome. We hypothesize that there exist key forking tokens, such that re-sampling the system at those specific tokens, but not others, leads to very different outcomes. To test this empirically, we develop a novel approach to representing uncertainty dynamics across individual tokens of text generation, and applying statistical models to test our hypothesis. Our approach is highly flexible: it can be applied to any dataset and any LLM, without fine tuning or accessing model weights. We use our method to analyze LLM responses on 7 different tasks across 4 domains, spanning a wide range of typical use cases. We find many examples of forking tokens, including surprising ones such as a space character instead of a colon, suggesting that LLMs are often just a single token away from saying something very different.

Increase in data, size, or compute can lead to sudden learning of specific capabilities by a neural network---a phenomenon often called "emergence". Beyond scientific understanding, establishing the causal factors underlying such emergent capabilities is crucial to enable risk regulation frameworks for AI. In this work, we seek inspiration from study of emergent properties in other fields and propose a phenomenological definition for the concept in the context of neural networks. Our definition implicates the acquisition of general regularities underlying the data-generating process as a cause of sudden performance growth for specific, narrower tasks. We empirically investigate this definition by proposing an experimental system grounded in a context-sensitive formal language, and find that Transformers trained to perform tasks on top of strings from this language indeed exhibit emergent capabilities. Specifically, we show that once the language's underlying grammar and context-sensitivity inducing regularities are learned by the model, performance on narrower tasks suddenly begins to improve. We then analogize our network's learning dynamics with the process of percolation on a bipartite graph, establishing a formal phase transition model that predicts the shift in the point of emergence observed in our experiments when intervening on the data regularities. Overall, our experimental and theoretical frameworks yield a step towards better defining, characterizing, and predicting emergence in neural networks.

Recent work demonstrates that structured patterns in pretraining data influence how representations of different concepts are organized in a large language model’s (LLM) internals, with such representations then driving downstream abilities. Given the open-ended nature of LLMs, e.g., their ability to in-context learn novel tasks, we ask whether models can flexibly alter their semantically grounded organization of concepts. Specifically, if we provide in-context exemplars wherein a concept plays a different role than what the pretraining data suggests, can models infer these novel semantics and reorganize representations in accordance with them? To answer this question, we define a toy “graph tracing” task wherein the nodes of the graph are referenced via concepts seen during training (e.g., apple, bird, etc.), and the connectivity of the graph is defined via some predefined structure (e.g., a square grid). Given exemplars that indicate traces of random walks on the graph, we analyze intermediate representations of the model and find that as the amount of context is scaled, there is a sudden re-organization of representations according to the graph’s structure. Further, we find that when reference concepts have correlations in their semantics (e.g., Monday, Tuesday, etc.), the context-specified graph structure is still present in the representations, but is unable to dominate the pretrained structure. To explain these results, we analogize our task to energy minimization for a predefined graph topology, which shows getting non-trivial performance on the task requires for the model to infer a connected component. Overall, our findings indicate context-size may be an underappreciated scaling axis that can flexibly re-organize model representations, unlocking novel capabilities.

In-Context Learning (ICL) has significantly expanded the general-purpose nature of large language models, allowing them to adapt to novel tasks using merely the inputted context. This has motivated a series of papers that analyze tractable synthetic domains and postulate precise mechanisms that may underlie ICL. However, the use of relatively distinct setups that often lack a sequence modeling nature to them makes it unclear how general the reported insights from such studies are. Motivated by this, we propose a synthetic sequence modeling task that involves learning to simulate a finite mixture of Markov chains. As we show, models trained on this task reproduce most well-known results on ICL, hence offering a unified setting for studying the concept. Building on this setup, we demonstrate we can explain a model’s behavior by decomposing it into four broad algorithms that combine a fuzzy retrieval vs. inference approach with either unigram or bigram statistics of the context. These algorithms engage in a competitive dynamics to dominate model behavior, with the precise experimental conditions dictating which algorithm ends up superseding others: e.g., we find merely varying context size or amount of training yields (at times sharp) transitions between which algorithm dictates the model behavior, revealing a mechanism that explains the transient nature of ICL. In this sense, we argue ICL is best thought of as a mixture of different algorithms, each with its own peculiarities, instead of a monolithic capability. This also implies that making general claims about ICL that hold universally across all settings may be infeasible.

Prior work has shown that text-conditioned diffusion models can learn to identify and manipulate primitive concepts underlying a compositional data-generating process, enabling generalization to entirely novel, out-of-distribution compositions. Beyond performance evaluations, these studies develop a rich empirical phenomenology of learning dynamics, showing that models generalize sequentially, respecting the compositional hierarchy of the data-generating process. Moreover, concept-centric structures within the data significantly influence a model's speed of learning the ability to manipulate a concept. In this paper, we aim to better characterize these empirical results from a theoretical standpoint. Specifically, we propose an abstraction of prior work's compositional generalization problem by introducing a structured identity mapping (SIM) task, where a model is trained to learn the identity mapping on a Gaussian mixture with structurally organized centroids. We mathematically analyze the learning dynamics of neural networks trained on this SIM task and show that, despite its simplicity, SIM's learning dynamics capture and help explain key empirical observations on compositional generalization with diffusion models identified in prior work. Our theory also offers several new insights---e.g., we find a novel mechanism for non-monotonic learning dynamics of test loss in early phases of training. We validate our new predictions by training a text-conditioned diffusion model, bridging our simplified framework and complex generative models. Overall, this work establishes the SIM task as a meaningful theoretical abstraction of concept learning dynamics in modern generative models.

Short-term memory is essential for cognitive processing, yet our understanding of its neural mechanisms remains unclear. Neuroscience has long focused on how sequential activity patterns, where neurons fire one after another within large networks, can explain how information is maintained. While recurrent connections were shown to drive sequential dynamics, a mechanistic understanding of this process still remains unknown. In this work, we introduce two unique mechanisms that can support this form of short-term memory: slow-point manifolds generating direct sequences or limit cycles providing temporally localized approximations. Using analytical models, we identify fundamental properties that govern the selection of each mechanism. Precisely, on short-term memory tasks (delayed cue-discrimination tasks), we derive theoretical scaling laws for critical learning rates as a function of the delay period length, beyond which no learning is possible. We empirically verify these results by training and evaluating approximately 80,000 recurrent neural networks (RNNs), which are publicly available for further analysis. Overall, our work provides new insights into short-term memory mechanisms and proposes experimentally testable predictions for systems neuroscience.

Knowledge Editing (KE) algorithms alter models’ weights to perform targeted updates to incorrect, outdated, or otherwise unwanted factual associations. However, recent work has shown that applying KE can adversely affect models’ broader factual recall accuracy and diminish their reasoning abilities. Although these studies give insights into the potential harms of KE algorithms, e.g., performance evaluations on benchmarks, little is understood about why such destructive failures occur. Motivated by this, we define a novel synthetic task in which a Transformer is trained from scratch to internalize a "structured" knowledge graph. The structure enforces relationships between entities of the graph, such that editing a factual association has "trickling effects" on other entities (e.g., altering X’s parent is Y to Z affects who X’s siblings’ parent is). Through evaluations of edited models on this task, we show that KE inadvertently affects representations of entities beyond the targeted one, distorting relevant structures that allow a model to infer unseen knowledge about an entity. We call this phenomenon representation shattering and demonstrate that it degrades models’ factual recall and reasoning performance. We further corroborate our findings in naturalistic settings with pre-trained Llama and Mamba models as well. Overall, our work yields a precise mechanistic hypothesis to explain why KE has adverse effects on model abilities.

Recent work analyzing in-context learning (ICL) has identified a broad set of strategies that describe model behavior in different experimental conditions. We aim to unify these findings by asking why a model learns these disparate strategies in the first place. Specifically, we start with the observation that when trained to learn a mixture of tasks, as is popular in the literature, the strategies learned by a model for performing ICL can be captured by a family of Bayesian predictors: a memorizing predictor, which assumes a discrete prior on the set of seen tasks, and a generalizing predictor, where the prior matches the underlying task distribution. Adopting the normative lens of rational analysis, where a learner’s behavior is explained as an optimal adaptation to data given computational constraints, we develop a hierarchical Bayesian framework that almost perfectly predicts Transformer next- token predictions throughout training—without assuming access to its weights. Under this framework, pretraining is viewed as a process of updating the posterior probability of different strategies, and inference-time behavior as a posterior- weighted average over these strategies’ predictions. Our framework draws on common assumptions about neural network learning dynamics, which make explicit a tradeoff between loss and complexity among candidate strategies: beyond how well it explains the data, a model’s preference towards implementing a strategy is dictated by its complexity. This helps explain well-known ICL phenomena, while offering novel predictions: e.g., we show a superlinear trend in the timescale for transitioning from generalization to memorization as task diversity increases. Overall, our work advances an explanatory and predictive account of ICL grounded in tradeoffs between strategy loss and complexity.

Large language models (LLMs) trained on huge text datasets demonstrate intriguing capabilities, achieving state-of-the-art performance on tasks they were not explicitly trained for. The precise nature of LLM capabilities is often mysterious, and different prompts can elicit different capabilities through in-context learning. We propose a framework that enables us to analyze in-context learning dynamics to understand latent concepts underlying LLMs’ behavioral patterns. This provides a more nuanced understanding than success-or-failure evaluation benchmarks, but does not require observing internal activations as a mechanistic interpretation of circuits would. Inspired by the cognitive science of human randomness perception, we use random binary sequences as context and study dynamics of in-context learning by manipulating properties of context data, such as sequence length. In the latest GPT-3.5+ models, we find emergent abilities to generate seemingly random numbers and learn basic formal languages, with striking in-context learning dynamics where model outputs transition sharply from seemingly random behaviors to deterministic repetition.

Fine-tuning large pre-trained models has become the de facto strategy for developing both task-specific and general-purpose machine learning systems, including developing models that are safe to deploy. Despite its clear importance, there has been minimal work that explains how fine-tuning alters the underlying capabilities learned by a model during pretraining: does fine-tuning yield entirely novel capabilities or does it just modulate existing ones? We address this question empirically in synthetic, controlled settings where we can use mechanistic interpretability tools (e.g., network pruning and probing) to understand how the model's underlying capabilities are changing. We perform an extensive analysis of the effects of fine-tuning in these settings, and show that: (i) fine-tuning rarely alters the underlying model capabilities; (ii) a minimal transformation, which we call a `wrapper', is typically learned on top of the underlying model capabilities, creating the illusion that they have been modified; and (iii) further fine-tuning on a task where such ``wrapped capabilities'' are relevant leads to sample-efficient revival of the capability, i.e., the model begins reusing these capabilities after only a few gradient steps. This indicates that practitioners can unintentionally remove a model's safety wrapper merely by fine-tuning it on a, e.g., superficially unrelated, downstream task. We additionally perform analysis on language models trained on the TinyStories dataset to support our claims in a more realistic setup.

Stepwise inference protocols, such as scratchpads and chain-of-thought, help language models solve complex problems by decomposing them into a sequence of simpler subproblems. To unravel the underlying mechanisms of stepwise inference we propose to study autoregressive Transformer models on a synthetic task that embodies the multi-step nature of problems where stepwise inference is generally most useful. Specifically, we define a graph navigation problem wherein a model is tasked with traversing a path from a start to a goal node on the graph. We find we can empirically reproduce and analyze several phenomena observed at scale: (i) the stepwise inference reasoning gap, the cause of which we find in the structure of the training data; (ii) a diversity-accuracy trade-off in model generations as sampling temperature varies; (iii) a simplicity bias in the model’s output; and (iv) compositional generalization and a primacy bias with in-context exemplars. Overall, our work introduces a grounded, synthetic framework for studying stepwise inference and offers mechanistic hypotheses that can lay the foundation for a deeper understanding of this phenomenon.

Transformers trained on huge text corpora exhibit a remarkable set of capabilities, e.g., performing simple logical operations. Given the inherent compositional nature of language, one can expect the model to learn to compose these capabilities, potentially yielding a combinatorial explosion of what operations it can perform on an input. Motivated by the above, we aim to assess in this paper “how capable can a transformer become?”. Specifically, we train autoregressive Transformer models on a data-generating process that involves compositions of a set of well-defined monolithic capabilities. Through a series of extensive and systematic experiments on this data-generating process, we show that: (1) autoregressive Transformers can learn compositional structures from small amounts of training data and generalize to exponentially or even combinatorially many functions; (2) composing functions by generating intermediate outputs is more effective at generalizing to unseen compositions, compared to generating no intermediate outputs; (3) biases in the order of the compositions in the training data, results in Transformers that fail to compose some combinations of functions; and (4) the attention layers seem to select the capability to apply while the feed-forward layers execute the capability.

Modern generative models demonstrate impressive capabilities, likely stemming from an ability to identify and manipulate abstract concepts underlying their training data. However, fundamental questions remain: what determines the concepts a model learns, the order in which it learns them, and its ability to manipulate those concepts? To address these questions, we propose analyzing a model’s learning dynamics via a framework we call the concept space, where each axis represents an independent concept underlying the data generating process. By characterizing learning dynamics in this space, we identify how the speed at which a concept is learned, and hence the order of concept learning, is controlled by properties of the data we term concept signal. Further, we observe moments of sudden turns in the direction of a model’s learning dynamics in concept space. Surprisingly, these points precisely correspond to the emergence of hidden capabilities, i.e., where latent interventions show the model possesses the capability to manipulate a concept, but these capabilities cannot yet be elicited via naive input prompting. While our results focus on synthetically defined toy datasets, we hypothesize a general claim on emergence of hidden capabilities may hold: generative models possess latent capabilities that emerge suddenly and consistently during training, though a model might not exhibit these capabilities under naive input prompting.

In this work, we explore the limiting dynamics of deep neural networks trained with stochastic gradient descent (SGD). As observed previously, long after performance has converged, networks continue to move through parameter space by a process of anomalous diffusion in which distance traveled grows as a power law in the number of gradient updates with a nontrivial exponent. We reveal an intricate interaction among the hyperparameters of optimization, the structure in the gradient noise, and the Hessian matrix at the end of training that explains this anomalous diffusion. To build this understanding, we first derive a continuous-time model for SGD with finite learning rates and batch sizes as an underdamped Langevin equation. We study this equation in the setting of linear regression, where we can derive exact, analytic expressions for the phase-space dynamics of the parameters and their instantaneous velocities from initialization to stationarity. Using the Fokker-Planck equation, we show that the key ingredient driving these dynamics is not the original training loss but rather the combination of a modified loss, which implicitly regularizes the velocity, and probability currents that cause oscillations in phase space. We identify qualitative and quantitative predictions of this theory in the dynamics of a ResNet-18 model trained on ImageNet. Through the lens of statistical physics, we uncover a mechanistic origin for the anomalous limiting dynamics of deep neural networks trained with SGD. Understanding the limiting dynamics of SGD, and its dependence on various important hyperparameters like batch size, learning rate, and momentum, can serve as a basis for future work that can turn these insights into algorithmic gains.

We study neural network loss landscapes through the lens of mode connectivity, the observation that minimizers of neural networks retrieved via training on a dataset are connected via simple paths of low loss. Specifically, we ask the following question: are minimizers that rely on different mechanisms for making their predictions connected via simple paths of low loss? We provide a definition of mechanistic similarity as shared invariances to input transformations and demonstrate that lack of linear connectivity between two models implies they use dissimilar mechanisms for making their predictions. Relevant to practice, this result helps us demonstrate that naive fine-tuning on a downstream dataset can fail to alter a model’s mechanisms, e.g., fine-tuning can fail to eliminate a model’s reliance on spurious attributes. Our analysis also motivates a method for targeted alteration of a model’s mechanisms, named connectivity-based fine-tuning (CBFT), which we analyze using several synthetic datasets for the task of reducing a model’s reliance on spurious attributes.

Advances in optical and electrophysiological recording technologies have made it possible to record the dynamics of thousands of neurons, opening up new possibilities for interpreting and controlling large neural populations in behaving animals. A promising way to extract computational principles from these large datasets is to train data-constrained recurrent neural networks (dRNNs). Performing this training in real-time could open doors for research techniques and medical applications to model and control interventions at single-cell resolution and drive desired forms of animal behavior. However, existing training algorithms for dRNNs are inefficient and have limited scalability, making it a challenge to analyze large neural recordings even in offline scenarios. To address these issues, we introduce a training method termed Convex Optimization of Recurrent Neural Networks (CORNN). In studies of simulated recordings, CORNN attained training speeds $\sim$100-fold faster than traditional optimization approaches while maintaining or enhancing modeling accuracy. We further validated CORNN on simulations with thousands of cells that performed simple computations such as those of a 3-bit flip-flop or the execution of a timed response. Finally, we showed that CORNN can robustly reproduce network dynamics and underlying attractor structures despite mismatches between generator and inference models, severe subsampling of observed neurons, or mismatches in neural time-scales. Overall, by training dRNNs with millions of parameters in subminute processing times on a standard computer, CORNN constitutes a first step towards real-time network reproduction constrained on large-scale neural recordings and a powerful computational tool for advancing the understanding of neural computation.

Modern generative models exhibit unprecedented capabilities to generate extremely realistic data. However, given the inherent compositionality of the real world, reliable use of these models in practical applications requires that they exhibit the capability to compose a novel set of concepts to generate outputs not seen in the training data set. Prior work demonstrates that recent diffusion models do exhibit intriguing compositional generalization abilities, but also fail unpredictably. Motivated by this, we perform a controlled study for understanding compositional generalization in conditional diffusion models in a synthetic setting, varying different attributes of the training data and measuring the model's ability to generate samples out-of-distribution. Our results show: (i) the order in which the ability to generate samples from a concept and compose them emerges is governed by the structure of the underlying data-generating process; (ii) performance on compositional tasks exhibits a sudden "emergence" due to multiplicative reliance on the performance of constituent tasks, partially explaining emergent phenomena seen in generative models; and (iii) composing concepts with lower frequency in the training data to generate out-of-distribution samples requires considerably more optimization steps compared to generating in-distribution samples. Overall, our study lays a foundation for understanding emergent capabilities and compositionality in generative models from a data-centric perspective.

Animals display characteristic behavioural patterns when performing a task, such as the spiraling of a soaring bird or the surge-and-cast of a male moth searching for a female. Identifying such recurring sequences occurring rarely in noisy behavioural data is key to understanding the behavioural response to a distributed stimulus in unrestrained animals. Existing models seek to describe the dynamics of behaviour or segment individual locomotor episodes rather than to identify the rare and transient sequences of locomotor episodes that make up the behavioural response. To fill this gap, we develop a lexical, hierarchical model of behaviour. We designed an unsupervised algorithm called "BASS" to efficiently identify and segment recurring behavioural action sequences transiently occurring in long behavioural recordings. When applied to navigating larval zebrafish, BASS extracts a dictionary of remarkably long, non-Markovian sequences consisting of repeats and mixtures of slow forward and turn bouts. Applied to a novel chemotaxis assay, BASS uncovers chemotactic strategies deployed by zebrafish to avoid aversive cues consisting of sequences of fast large-angle turns and burst swims. In a simulated dataset of soaring gliders climbing thermals, BASS finds the spiraling patterns characteristic of soaring behaviour. In both cases, BASS succeeds in identifying rare action sequences in the behaviour deployed by freely moving animals. BASS can be easily incorporated into the pipelines of existing behavioural analyses across diverse species, and even more broadly used as a generic algorithm for pattern recognition in low-dimensional sequential data.

Inspired by BatchNorm, there has been an explosion of normalization layers in deep learning. Recent works have identified a multitude of beneficial properties in BatchNorm to explain its success. However, given the pursuit of alternative normalization layers, these properties need to be generalized so that any given layer's success/failure can be accurately predicted. In this work, we take a first step towards this goal by extending known properties of BatchNorm in randomly initialized deep neural networks (DNNs) to several recently proposed normalization layers. Our primary findings follow: (i) similar to BatchNorm, activations-based normalization layers can prevent exponential growth of activations in ResNets, but parametric techniques require explicit remedies; (ii) use of GroupNorm can ensure an informative forward propagation, with different samples being assigned dissimilar activations, but increasing group size results in increasingly indistinguishable activations for different samples, explaining slow convergence speed in models with LayerNorm; and (iii) small group sizes result in large gradient norm in earlier layers, hence explaining training instability issues in Instance Normalization and illustrating a speed-stability tradeoff in GroupNorm. Overall, our analysis reveals a unified set of mechanisms that underpin the success of normalization methods in deep learning, providing us with a compass to systematically explore the vast design space of DNN normalization layers.

In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle to efficiently capture regularities in the world, but the role of symmetry breaking is not well understood. Here, we develop a theoretical framework to study the "geometry of learning dynamics" in neural networks, and reveal a key mechanism of explicit symmetry breaking behind the efficiency and stability of modern neural networks. To build this understanding, we model the discrete learning dynamics of gradient descent using a continuous-time Lagrangian formulation, in which the learning rule corresponds to the kinetic energy and the loss function corresponds to the potential energy. Then, we identify "kinetic symmetry breaking" (KSB), the condition when the kinetic energy explicitly breaks the symmetry of the potential function. We generalize Noether’s theorem known in physics to take into account KSB and derive the resulting motion of the Noether charge: "Noether's Learning Dynamics" (NLD). Finally, we apply NLD to neural networks with normalization layers and reveal how KSB introduces a mechanism of implicit adaptive optimization, establishing an analogy between learning dynamics induced by normalization layers and RMSProp. Overall, through the lens of Lagrangian mechanics, we have established a theoretical foundation to discover geometric design principles for the learning dynamics of neural networks.

Despite the growing constellation of genetic loci linked to common traits, these loci have yet to account for most heritable variation, and most act through poorly understood mechanisms. Recent machine learning (ML) systems have used hierarchical biological knowledge to associate genetic mutations with phenotypic outcomes, yielding substantial predictive power and mechanistic insight. Here, we use an ontology-guided ML system to map single nucleotide variants (SNVs) focusing on 6 classic phenotypic traits in natural yeast populations. The 29 identified loci are largely novel and account for ~17% of the phenotypic variance, versus <3% for standard genetic analysis. Representative results show that sensitivity to hydroxyurea is linked to SNVs in two alternative purine biosynthesis pathways, and that sensitivity to copper arises through failure to detoxify reactive oxygen species in fatty acid metabolism. This work demonstrates a knowledge-based approach to amplifying and interpreting signals in population genetic studies.

Pruning the parameters of deep neural networks has generated intense interest due to potential savings in time, memory and energy both during training and at test time. Recent works have identified, through an expensive sequence of training and pruning cycles, the existence of winning lottery tickets or sparse trainable subnetworks at initialization. This raises a foundational question: can we identify highly sparse trainable subnetworks at initialization, without ever training, or indeed without ever looking at the data? We provide an affirmative answer to this question through theory driven algorithm design. We first mathematically formulate and experimentally verify a conservation law that explains why existing gradient-based pruning algorithms at initialization suffer from layer-collapse, the premature pruning of an entire layer rendering a network untrainable. This theory also elucidates how layer-collapse can be entirely avoided, motivating a novel pruning algorithm Iterative Synaptic Flow Pruning (SynFlow). This algorithm can be interpreted as preserving the total flow of synaptic strengths through the network at initialization subject to a sparsity constraint. Notably, this algorithm makes no reference to the training data and consistently competes with or outperforms existing state-of-the-art pruning algorithms at initialization over a range of models (VGG and ResNet), datasets (CIFAR-10/100 and Tiny ImageNet), and sparsity constraints (up to 99.99 percent). Thus our data-agnostic pruning algorithm challenges the existing paradigm that, at initialization, data must be used to quantify which synapses are important.

Recently, deep feedforward neural networks have achieved considerable success in modeling biological sensory processing, in terms of reproducing the input-output map of sensory neurons. However, such models raise profound questions about the very nature of explanation in neuroscience. Are we simply replacing one complex system (a biological circuit) with another (a deep network), without understanding either? Moreover, beyond neural representations, are the deep network's computational mechanisms for generating neural responses the same as those in the brain? Without a systematic approach to extracting and understanding computational mechanisms from deep neural network models, it can be difficult both to assess the degree of utility of deep learning approaches in neuroscience, and to extract experimentally testable hypotheses from deep networks. We develop such a systematic approach by combining dimensionality reduction and modern attribution methods for determining the relative importance of interneurons for specific visual computations. We apply this approach to deep network models of the retina, revealing a conceptual understanding of how the retina acts as a predictive feature extractor that signals deviations from expectations for diverse spatiotemporal stimuli. For each stimulus, our extracted computational mechanisms are consistent with prior scientific literature, and in one case yields a new mechanistic hypothesis. Thus overall, this work not only yields insights into the computational mechanisms underlying the striking predictive capabilities of the retina, but also places the framework of deep networks as neuroscientific models on firmer theoretical foundations, by providing a new roadmap to go beyond comparing neural representations to extracting and understand computational mechanisms.

We propose an online anomal movement detection method using incremental unsupervised learning. As the feature for discrimination, we extract the principal component of the spatio-temporal feature by incremental PCA. We then detect anomal movements by an incremental 1-class SVM. In order to use principal component as the feature for discrimination while supporting incrementation of the subspace, we modify the SVM kernel function to take account of the difference in distance scale between the principal component feature vectors and that of the feature vectors after the subspace is incremented. This allows us to efficiently conduct the relearning process even though the dimension of the original input spatio-temporal feature is high. Experiments show that anomal scenes can be detected without the cost of preparing a lot of labeled data for preliminary learning.

Proposes a new estimation method of 3D shape of an object and the illuminant direction from a single image using the zero crossings under the assumption that the illuminant direction and strength, and the object surface albado are unknown. In most practical cases the illuminant direction is unknown. For these cases, a new theory was proposed by M.J. Brooks and B.K.P. Horn (1985) where the illuminant direction and 3D shape are simultaneously estimated from a single image. This theory, however, can not be applied to an object whose surface is not convex. The authors propose a new theory which has no such drawback.>