72 research outputs found
Symmetry Analysis and Exact Solutions to the Space-Dependent Coefficient PDEs in Finance
The variable-coefficients partial differential equations (vc-PDEs) in finance are investigated by Lie symmetry analysis and the generalized power series method. All of the geometric vector fields of the equations are obtained; the symmetry reductions and exact solutions to the equations are presented, including the exponentiated solutions and the similarity solutions. Furthermore, the exact analytic solutions are provided by the transformation technique and generalized power series method, which has shown that the combination of Lie symmetry analysis and the generalized power series method is a feasible approach to dealing with exact solutions to the variable-coefficients PDEs
Disentangled Generative Causal Representation Learning
This paper proposes a Disentangled gEnerative cAusal Representation (DEAR)
learning method. Unlike existing disentanglement methods that enforce
independence of the latent variables, we consider the general case where the
underlying factors of interests can be causally correlated. We show that
previous methods with independent priors fail to disentangle causally
correlated factors. Motivated by this finding, we propose a new disentangled
learning method called DEAR that enables causal controllable generation and
causal representation learning. The key ingredient of this new formulation is
to use a structural causal model (SCM) as the prior for a bidirectional
generative model. The prior is then trained jointly with a generator and an
encoder using a suitable GAN loss incorporated with supervision. We provide
theoretical justification on the identifiability and asymptotic consistency of
the proposed method, which guarantees disentangled causal representation
learning under appropriate conditions. We conduct extensive experiments on both
synthesized and real data sets to demonstrate the effectiveness of DEAR in
causal controllable generation, and the benefits of the learned representations
for downstream tasks in terms of sample efficiency and distributional
robustness
Mitigating the Alignment Tax of RLHF
LLMs acquire a wide range of abilities during pre-training, but aligning LLMs
under Reinforcement Learning with Human Feedback (RLHF) can lead to forgetting,
which is also known as the alignment tax. To empirically verify this
hypothesis, we conducted experiments with existing RLHF algorithms using
OpenLLaMA-3B, which revealed a pronounced alignment tax in NLP tasks. On the
other hand, despite various techniques to mitigate forgetting, they are often
at odds with the RLHF performance, leading to a trade-off between reward
maximization and forgetting mitigation.
In light of the above pressing issue in aligning LLMs, in this paper we
explore model averaging, which interpolates between pre and post RLHF model
weights, to achieve a more efficient reward-tax Pareto front. To understand its
effectiveness, We offer theoretical insights into model averaging, revealing
that it enhances performance Pareto front by increasing feature diversity on
the layers where tasks share overlapped feature spaces. Empirical evidence
corroborates our analysis by showing the benefits of averaging low-level
transformer layers. Building on the analysis and the observation that averaging
different layers of the transformer leads to significantly different reward-tax
trade-offs, we propose Adaptive Model Averaging (AMA) to adaptively find
various combination ratios of model layers. AMA seeks to maximize the alignment
reward while incurring minimal alignment tax. Moreover, we validate AMA's
performance across a range of RLHF algorithms over OpenLLaMA-3B and further
extend our findings to Mistral-7B.Comment: 28 Page
Spin torque resonant vortex core expulsion for an efficient radio-frequency detection scheme
Spin-polarised radio-frequency currents, whose frequency is equal to that of
the gyrotropic mode, will cause an excitation of the core of a magnetic vortex
confined in a magnetic tunnel junction. When the excitation radius of the
vortex core is greater than that of the junction radius, vortex core expulsion
is observed, leading to a large change in resistance, as the layer enters a
predominantly uniform magnetisation state. Unlike the conventional spin-torque
diode effect, this highly tunable resonant effect will generate a voltage which
does not decrease as a function of rf power, and has the potential to form the
basis of a new generation of tunable nanoscale radio-frequency detectors
Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficients
The nonlinear Schrödinger (NLS) types of equations play a key role in quantum mechanics, Quantum communication and physical applications. However, how to deal with explicit solutions and other properties of the NLS equations, especially for the variable-coefficient NLS (vc-NLS) types of equations is a difficult problem. In this paper, we construct the form-preserving equivalent transformations (ETs) to transform the vc-NLS systems into constant-coefficient NLS (cc-NLS) systems, and the form-preserving ETs are given explicitly. Then, based on the equivalent transformation method, we deal with the integrability of the NLS equations, and the Lax pairs (LPs) are provided as verification of the integrability
Improving web search personalization using Luhn-Inspired vector re-weighting
Web search personalization has been studied as a way to tailor Web search results to individual users based on their interests and preferences. Commonly, document and personalization profile features are stored in vector space models using measures such as term frequency (TF) and term frequency-inverse document frequency (TF*IDF). Inspired by Luhn's model of term importance, a novel approach is proposed in this thesis to identify and re-weight significant terms in the vector-based personalization models. Evaluations with a set of ambiguous queries illustrate that the order of the search results using this approach is superior to the TF approach and comparable to the TF*IDF approach. However, it is based only on the information stored in the personalization profiles, rather than requiring access to the distribution of each term across the document collection. As such, it can be applied more broadly when only limited information regarding the collection being searched is available
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