325 research outputs found
A probabilistic successor representation for context-dependent learning
Two of the main impediments to learning complex tasks are that relationships between different stimuli, including rewards, can be uncertain and context-dependent. Reinforcement learning (RL) provides a framework for learning, by predicting total future reward directly (model-free RL), or via predictions of future states (model-based RL). Within this framework, "successor representation" (SR) predicts total future occupancy of all states. A recent theoretical proposal suggests that the hippocampus encodes the SR in order to facilitate prediction of future reward. However, this proposal does not take into account how learning should adapt under uncertainty and switches of context. Here, we introduce a theory of learning SRs using prediction errors which includes optimally balancing uncertainty in new observations versus existing knowledge. We then generalize that approach to a multicontext setting, allowing the model to learn and maintain multiple task-specific SRs and infer which one to use at any moment based on the accuracy of its predictions. Thus, the context used for predictions can be determined by both the contents of the states themselves and the distribution of transitions between them. This probabilistic SR model captures animal behavior in tasks which require contextual memory and generalization, and unifies previous SR theory with hippocampal-dependent contextual decision-making. (PsycInfo Database Record (c) 2023 APA, all rights reserved)
Overshoots in stress strain curves: Colloid experiments and schematic mode coupling theory
The stress versus strain curves in dense colloidal dispersions under start-up
shear flow are investigated combining experiments on model core-shell
microgels, computer simulations of hard disk mixtures, and mode coupling
theory. In dense fluid and glassy states, the transient stresses exhibit first
a linear increase with the accumulated strain, then a maximum ('stress
overshoot') for strain values around 5%, before finally approaching the
stationary value, which makes up the flow curve. These phenomena arise in
well-equilibrated systems and for homogeneous flows, indicating that they are
generic phenomena of the shear-driven transient structural relaxation.
Microscopic mode coupling theory (generalized to flowing states by integration
through the transients) derives them from the transient stress correlations,
which first exhibit a plateau (corresponding to the solid-like elastic shear
modulus) at intermediate times, and then negative stress correlations during
the final decay. We introduce and validate a schematic model within mode
coupling theory which captures all of these phenomena and handily can be used
to jointly analyse linear and large-amplitude moduli, flow curves, and
stress-strain curves. This is done by introducing a new strain- and
time-dependent vertex into the relation between the the generalized shear
modulus and the transient density correlator.Comment: 21 pages, 13 figure
Efficient Benchmarking of Algorithm Configuration Procedures via Model-Based Surrogates
The optimization of algorithm (hyper-)parameters is crucial for achieving
peak performance across a wide range of domains, ranging from deep neural
networks to solvers for hard combinatorial problems. The resulting algorithm
configuration (AC) problem has attracted much attention from the machine
learning community. However, the proper evaluation of new AC procedures is
hindered by two key hurdles. First, AC benchmarks are hard to set up. Second
and even more significantly, they are computationally expensive: a single run
of an AC procedure involves many costly runs of the target algorithm whose
performance is to be optimized in a given AC benchmark scenario. One common
workaround is to optimize cheap-to-evaluate artificial benchmark functions
(e.g., Branin) instead of actual algorithms; however, these have different
properties than realistic AC problems. Here, we propose an alternative
benchmarking approach that is similarly cheap to evaluate but much closer to
the original AC problem: replacing expensive benchmarks by surrogate benchmarks
constructed from AC benchmarks. These surrogate benchmarks approximate the
response surface corresponding to true target algorithm performance using a
regression model, and the original and surrogate benchmark share the same
(hyper-)parameter space. In our experiments, we construct and evaluate
surrogate benchmarks for hyperparameter optimization as well as for AC problems
that involve performance optimization of solvers for hard combinatorial
problems, drawing training data from the runs of existing AC procedures. We
show that our surrogate benchmarks capture overall important characteristics of
the AC scenarios, such as high- and low-performing regions, from which they
were derived, while being much easier to use and orders of magnitude cheaper to
evaluate
The relation of phase noise and luminance contrast to overt attention in complex visual stimuli
Models of attention are typically based on difference maps in low-level features but neglect higher order stimulus structure. To what extent does higher order statistics affect human attention in natural stimuli? We recorded eye movements while observers viewed unmodified and modified images of natural scenes. Modifications included contrast modulations (resulting in changes to first- and second-order statistics), as well as the addition of noise to the Fourier phase (resulting in changes to higher order statistics). We have the following findings: (1) Subjects' interpretation of a stimulus as a ânaturalâ depiction of an outdoor scene depends on higher order statistics in a highly nonlinear, categorical fashion. (2) Confirming previous findings, contrast is elevated at fixated locations for a variety of stimulus categories. In addition, we find that the size of this elevation depends on higher order statistics and reduces with increasing phase noise. (3) Global modulations of contrast bias eye position toward high contrasts, consistent with a linear effect of contrast on fixation probability. This bias is independent of phase noise. (4) Small patches of locally decreased contrast repel eye position less than large patches of the same aggregate area, irrespective of phase noise. Our findings provide evidence that deviations from surrounding statistics, rather than contrast per se, underlie the well-established relation of contrast to fixation
Information-Theoretic Characterization of the Generalization Error for Iterative Semi-Supervised Learning
Using information-theoretic principles, we consider the generalization error
(gen-error) of iterative semi-supervised learning (SSL) algorithms that
iteratively generate pseudo-labels for a large amount of unlabelled data to
progressively refine the model parameters. In contrast to most previous works
that {\em bound} the gen-error, we provide an {\em exact} expression for the
gen-error and particularize it to the binary Gaussian mixture model. Our
theoretical results suggest that when the class conditional variances are not
too large, the gen-error decreases with the number of iterations, but quickly
saturates. On the flip side, if the class conditional variances (and so amount
of overlap between the classes) are large, the gen-error increases with the
number of iterations. To mitigate this undesirable effect, we show that
regularization can reduce the gen-error. The theoretical results are
corroborated by extensive experiments on the MNIST and CIFAR datasets in which
we notice that for easy-to-distinguish classes, the gen-error improves after
several pseudo-labelling iterations, but saturates afterwards, and for more
difficult-to-distinguish classes, regularization improves the generalization
performance.Comment: 52 pages, 17 figure
Toward Understanding Generative Data Augmentation
Generative data augmentation, which scales datasets by obtaining fake labeled
examples from a trained conditional generative model, boosts classification
performance in various learning tasks including (semi-)supervised learning,
few-shot learning, and adversarially robust learning. However, little work has
theoretically investigated the effect of generative data augmentation. To fill
this gap, we establish a general stability bound in this not independently and
identically distributed (non-i.i.d.) setting, where the learned distribution is
dependent on the original train set and generally not the same as the true
distribution. Our theoretical result includes the divergence between the
learned distribution and the true distribution. It shows that generative data
augmentation can enjoy a faster learning rate when the order of divergence term
is , where is the train
set size and is the corresponding stability constant. We further
specify the learning setup to the Gaussian mixture model and generative
adversarial nets. We prove that in both cases, though generative data
augmentation does not enjoy a faster learning rate, it can improve the learning
guarantees at a constant level when the train set is small, which is
significant when the awful overfitting occurs. Simulation results on the
Gaussian mixture model and empirical results on generative adversarial nets
support our theoretical conclusions. Our code is available at
https://github.com/ML-GSAI/Understanding-GDA.Comment: 39 page
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