Freie Universität Berlin
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FELRec: Efficient Handling of Item Cold-Start With Dynamic Representation Learning in Recommender Systems
No full textRecommender systems suffer from the cold-start problem whenever a new user joins the platform or a new item is added to the catalog. To address item cold-start, we propose to replace the embedding layer in sequential recommenders with a dynamic storage that has no learnable weights and can keep an arbitrary number of representations. In this paper, we present FELRec, a large embedding network that refines the existing representations of users and items in a recursive manner, as new information becomes available. In contrast to similar approaches, our model represents new users and items without side information and time-consuming finetuning, instead it runs a single forward pass over a sequence of existing representations. During item cold-start, our method outperforms similar method by 29.50–47.45%. Further, our proposed model generalizes well to previously unseen datasets in zero-shot settings. The source code is publicly available
Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity II: close to H1 initial data
No full textIn this paper, we consider the initial-boundary value problem to the three-dimensional primitive equations for the oceanic and atmospheric dynamics with only horizontal eddy viscosities in the horizontal momentum equations and only vertical diffusivity in the temperature equation in the domain Ω=M×(−h,h), with M=(0,1)×(0,1). Global well-posedness of strong solutions is established, for any initial data (v0,T0)∈H1(Ω)∩L∞(Ω) with (∂zv0,∇HT0)∈Lq(Ω) and v0∈L1z(B1q,2(M)), for some q∈(2,∞), by using delicate energy estimates and maximal regularity estimate in the anisotropic setting
Dynamical Measure Transport and Neural PDE Solvers for Sampling
No full textThe task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using deterministic or stochastic evolutions described by partial differential equations (PDEs). This framework incorporates prior trajectory-based sampling methods, such as diffusion models or Schrödinger bridges, without relying on the concept of time-reversals. Moreover, it allows us to propose novel numerical methods for solving the transport task and thus sampling from complicated targets without the need for the normalization constant or data samples. We employ physics-informed neural networks (PINNs) to approximate the respective PDE solutions, implying both conceptional and computational advantages. In particular, PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently, leading to significantly better mode coverage in the sampling task compared to alternative methods. Moreover, they can readily be fine-tuned with Gauss-Newton methods to achieve high accuracy in sampling
Bridging discrete and continuous state spaces: Exploring the Ehrenfest process in time-continuous diffusion models
No full textGenerative modeling via stochastic processes has led to remarkable empirical results as well as to recent advances in their theoretical understanding. In principle, both space and time of the processes can be discrete or continuous. In this work, we study time-continuous Markov jump processes on discrete state spaces and investigate their correspondence to state-continuous diffusion processes given by SDEs. In particular, we revisit the Ehrenfest process, which converges to an Ornstein-Uhlenbeck process in the infinite state space limit. Likewise, we can show that the time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process. This observation bridges discrete and continuous state spaces and allows to carry over methods from one to the respective other setting. Additionally, we suggest an algorithm for training the time-reversal of Markov jump processes which relies on conditional expectations and can thus be directly related to denoising score matching. We demonstrate our methods in multiple convincing numerical experiments
Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN
No full textThe dominant eigenfunctions of the Koopman operator characterize the metastabilities and slow-timescale dynamics of stochastic diffusion processes. In the context of molecular dynamics and Markov state modeling, they allow for a description of the location and frequencies of rare transitions, which are hard to obtain by direct simulation alone. In this article, we reformulate the eigenproblem in terms of the ISOKANN framework, an iterative algorithm that learns the eigenfunctions by alternating between short burst simulations and a mixture of machine learning and classical numerics, which naturally leads to a proof of convergence. We furthermore show how the intermediate iterates can be used to reduce the sampling variance by importance sampling and optimal control (enhanced sampling), as well as to select locations for further training (adaptive sampling). We demonstrate the usage of our proposed method in experiments, increasing the approximation accuracy by several orders of magnitude
Derivation of a generalized Langevin equation from a generic time-dependent Hamiltonian
No full textThe traditional Mori–Zwanzig formalism yields equations of motion, so-called generalized Langevin equations (GLEs), for phase-space observables of interest from the microscopic dynamics of a many-body system governed by a time-independent Hamiltonian using projection techniques. By using time-ordered propagators and time-independent projection operators, we derive the GLE for a scalar observable from a generic time-dependent Hamiltonian. The only restriction in our derivation is that the time-dependent part of the Hamiltonian and the observable of interest depend on spatial phase-space variables only. If the observable obeys Gaussian statistics and the time-dependent part of the Hamiltonian can be expressed as an odd power of the observable, the friction memory kernel in the GLE becomes proportional to the second moment of the complementary force, as is the case for a time-independent Hamiltonian in the Mori–Zwanzig formalism
CuttleFlow: Infrastructure-Specific Workflow Adaption for Improved Reusability
No full textScientific workflows have gained popularity for large-scale data analysis due to their potential to improve the reproducibility, scalability and documentation of complex multistep scientific analysis pipelines. However, their reusability is currently limited in practice, as a workflow is typically developed for a specific infrastructure. This is reflected in the choice of tools (e.g. less/more memory requirements), their configuration (e.g. number of threads) and the workflow topology (e.g. data parallel scatter/gather). Re-running such a workflow requires access to the same, or at least a highly similar, computing environment, effectively reducing its use by other groups. To address this challenge, we present CuttleFlow, a novel method for adapting and rewriting scientific workflows given a description of an infrastructure and its inputs. CuttleFlow starts from an abstract workflow description and compiles it into an infrastructure-specific logical workflow using three types of rewriting operations, namely tool replacement, tool reconfiguration, and data scattering/gathering for task parallelization. We implement a prototype based on NextFlow and evaluate it for two important bioinformatics data analysis problems, namely RNAseq and metagenomics, on a distributed infrastructure. We demonstrate the large impact that the rewriting of CuttleFlow can have on runtime, achieving a reduction in makespan of up to 71%. We also demonstrate a significant reduction in resource usage through our rewriting approach
Hierarchical Interleaved Bloom Filter: enabling ultrafast, approximate sequence queries
No full textWe present a novel data structure for searching sequences in large databases: the Hierarchical Interleaved Bloom Filter (HIBF). It is extremely fast and space efficient, yet so general that it could serve as the underlying engine for many applications. We show that the HIBF is superior in build time, index size, and search time while achieving a comparable or better accuracy compared to other state-of-the-art tools. The HIBF builds an index up to 211 times faster, using up to 14 times less space, and can answer approximate membership queries faster by a factor of up to 129.
We show that the HIBF is superior in build time, index size and search time while achieving a comparable or better accuracy compared to other state-of-the art tools (Mantis and Bifrost). The HIBF builds an index up to 211 times faster, using up to 14 times less space and can answer approximate membership queries faster by a factor of up to 129. This can be considered a quantum leap that opens the door to indexing complete sequence archives like the European Nucleotide Archive or even larger metagenomics data sets
Noise-induced instabilities in a stochastic Brusselator
No full textWe consider a stochastic version of the so-called Brusselator - a mathematical model for a two-dimensional chemical reaction network - in which one of its parameters is assumed to vary randomly. It has been suggested via numerical explorations that the system exhibits noise-induced synchronization when time goes to infinity. Complementing this perspective, in this work we explore some of its finite-time features from a random dynamical systems perspective. In particular, we focus on the deviations that orbits of neighboring initial conditions exhibit under the influence of the same noise realization. For this, we explore its local instabilities via finite-time Lyapunov exponents. Furthermore, we present the stochastic Brusselator as a fast-slow system in the case that one of the parameters is much larger than the other one. In this framework, an apparent mechanism for generating the stochastic instabilities is revealed, being associated to the transition between the slow and fast regimes
Canards in modified equations for Euler discretizations
No full textCanards are a well-studied phenomenon in fast-slow ordinary differential equations implying the delayed loss of stability after the slow passage through a singularity. Recent studies have shown that the corresponding maps stemming from explicit Runge-Kutta discretizations, in particular the forward Euler scheme, exhibit significant distinctions to the continuous-time behavior: for folds, the delay in loss of stability is typically shortened whereas, for transcritical singularities, it is arbitrarily prolonged. We employ the method of modified equations, which correspond with the fixed discretization schemes up to higher order, to understand and quantify these effects directly from a fast-slow ODE, yielding consistent results with the discrete-time behavior and opening a new perspective on the wide range of (de-)stabilization phenomena along canards