12,442 research outputs found
Beyond Sparsity: Tree Regularization of Deep Models for Interpretability
The lack of interpretability remains a key barrier to the adoption of deep
models in many applications. In this work, we explicitly regularize deep models
so human users might step through the process behind their predictions in
little time. Specifically, we train deep time-series models so their
class-probability predictions have high accuracy while being closely modeled by
decision trees with few nodes. Using intuitive toy examples as well as medical
tasks for treating sepsis and HIV, we demonstrate that this new tree
regularization yields models that are easier for humans to simulate than
simpler L1 or L2 penalties without sacrificing predictive power.Comment: To appear in AAAI 2018. Contains 9-page main paper and appendix with
supplementary materia
Multivariate Differential Association Analysis
Identifying how dependence relationships vary across different conditions
plays a significant role in many scientific investigations. For example, it is
important for the comparison of biological systems to see if relationships
between genomic features differ between cases and controls. In this paper, we
seek to evaluate whether the relationships between two sets of variables is
different across two conditions. Specifically, we assess: do two sets of
high-dimensional variables have similar dependence relationships across two
conditions?. We propose a new kernel-based test to capture the differential
dependence. Specifically, the new test determines whether two measures that
detect dependence relationships are similar or not under two conditions. We
introduce the asymptotic permutation null distribution of the test statistic
and it is shown to work well under finite samples such that the test is
computationally efficient, making it easily applicable to analyze large data
sets. We demonstrate through numerical studies that our proposed test has high
power for detecting differential linear and non-linear relationships. The
proposed method is implemented in an R package kerDAA
Dynamics of Neural Networks with Continuous Attractors
We investigate the dynamics of continuous attractor neural networks (CANNs).
Due to the translational invariance of their neuronal interactions, CANNs can
hold a continuous family of stationary states. We systematically explore how
their neutral stability facilitates the tracking performance of a CANN, which
is believed to have wide applications in brain functions. We develop a
perturbative approach that utilizes the dominant movement of the network
stationary states in the state space. We quantify the distortions of the bump
shape during tracking, and study their effects on the tracking performance.
Results are obtained on the maximum speed for a moving stimulus to be
trackable, and the reaction time to catch up an abrupt change in stimulus.Comment: 6 pages, 7 figures with 4 caption
Dynamical Synapses Enhance Neural Information Processing: Gracefulness, Accuracy and Mobility
Experimental data have revealed that neuronal connection efficacy exhibits
two forms of short-term plasticity, namely, short-term depression (STD) and
short-term facilitation (STF). They have time constants residing between fast
neural signaling and rapid learning, and may serve as substrates for neural
systems manipulating temporal information on relevant time scales. The present
study investigates the impact of STD and STF on the dynamics of continuous
attractor neural networks (CANNs) and their potential roles in neural
information processing. We find that STD endows the network with slow-decaying
plateau behaviors-the network that is initially being stimulated to an active
state decays to a silent state very slowly on the time scale of STD rather than
on the time scale of neural signaling. This provides a mechanism for neural
systems to hold sensory memory easily and shut off persistent activities
gracefully. With STF, we find that the network can hold a memory trace of
external inputs in the facilitated neuronal interactions, which provides a way
to stabilize the network response to noisy inputs, leading to improved accuracy
in population decoding. Furthermore, we find that STD increases the mobility of
the network states. The increased mobility enhances the tracking performance of
the network in response to time-varying stimuli, leading to anticipative neural
responses. In general, we find that STD and STP tend to have opposite effects
on network dynamics and complementary computational advantages, suggesting that
the brain may employ a strategy of weighting them differentially depending on
the computational purpose.Comment: 40 pages, 17 figure
A Moving Bump in a Continuous Manifold: A Comprehensive Study of the Tracking Dynamics of Continuous Attractor Neural Networks
Understanding how the dynamics of a neural network is shaped by the network
structure, and consequently how the network structure facilitates the functions
implemented by the neural system, is at the core of using mathematical models
to elucidate brain functions. This study investigates the tracking dynamics of
continuous attractor neural networks (CANNs). Due to the translational
invariance of neuronal recurrent interactions, CANNs can hold a continuous
family of stationary states. They form a continuous manifold in which the
neural system is neutrally stable. We systematically explore how this property
facilitates the tracking performance of a CANN, which is believed to have clear
correspondence with brain functions. By using the wave functions of the quantum
harmonic oscillator as the basis, we demonstrate how the dynamics of a CANN is
decomposed into different motion modes, corresponding to distortions in the
amplitude, position, width or skewness of the network state. We then develop a
perturbative approach that utilizes the dominating movement of the network's
stationary states in the state space. This method allows us to approximate the
network dynamics up to an arbitrary accuracy depending on the order of
perturbation used. We quantify the distortions of a Gaussian bump during
tracking, and study their effects on the tracking performance. Results are
obtained on the maximum speed for a moving stimulus to be trackable and the
reaction time for the network to catch up with an abrupt change in the
stimulus.Comment: 43 pages, 10 figure
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