597 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
The coherent measurement cost of coherence distillation
Quantum coherence is an indispensable resource for quantum technological
applications. It is known to be distillable from a noisy form using operations
that cannot create coherence. However, distillation exacts a hidden coherent
measurement cost, whose extent has not previously been estimated. Here we show
that this cost (quantified by an equivalent number of Hadamard measurements) is
related to what we call the irretrievable coherence: the difference between the
coherence of formation and the distillable coherence. We conjecture (and make
partial progress towards proving) that when distilling from many copies of a
given noisy coherent state, the coherent measurement cost scales extensively in
the number of copies, at an asymptotic rate exactly equalling the input's
irretrievable coherence. This cost applies to any application whereof coherence
distillation is an incidental outcome (e.g. incoherent randomness extraction),
but the implications are more dramatic if pure coherence is the only desired
outcome: the measurement cost may often be higher than the distilled yield, in
which case coherence should rather be prepared afresh than distilled from a
noisy input.Comment: 24+5 pages, 1 figur
Generalising weighted model counting
Given a formula in propositional or (finite-domain) first-order logic and some non-negative weights, weighted model counting (WMC) is a function problem that asks to compute the sum of the weights of the models of the formula. Originally used as a flexible way of performing probabilistic inference on graphical models, WMC has found many applications across artificial intelligence (AI), machine learning, and other domains. Areas of AI that rely on WMC include explainable AI, neural-symbolic AI, probabilistic programming, and statistical relational AI. WMC also has applications in bioinformatics, data mining, natural language processing, prognostics, and robotics.
In this work, we are interested in revisiting the foundations of WMC and considering generalisations of some of the key definitions in the interest of conceptual clarity and practical efficiency. We begin by developing a measure-theoretic perspective on WMC, which suggests a new and more general way of defining the weights of an instance. This new representation can be as succinct as standard WMC but can also expand as needed to represent less-structured probability distributions. We demonstrate the performance benefits of the new format by developing a novel WMC encoding for Bayesian networks. We then show how existing WMC encodings for Bayesian networks can be transformed into this more general format and what conditions ensure that the transformation is correct (i.e., preserves the answer). Combining the strengths of the more flexible representation with the tricks used in existing encodings yields further efficiency improvements in Bayesian network probabilistic inference.
Next, we turn our attention to the first-order setting. Here, we argue that the capabilities of practical model counting algorithms are severely limited by their inability to perform arbitrary recursive computations. To enable arbitrary recursion, we relax the restrictions that typically accompany domain recursion and generalise circuits (used to express a solution to a model counting problem) to graphs that are allowed to have cycles. These improvements enable us to find efficient solutions to counting fundamental structures such as injections and bijections that were previously unsolvable by any available algorithm.
The second strand of this work is concerned with synthetic data generation. Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithmâs superiority over another. However, benchmarks are often limited and fail to reveal differences among the algorithms. First, we show how random instances of probabilistic logic programs (that typically use WMC algorithms for inference) can be generated using constraint programming. We also introduce a new constraint to control the independence structure of the underlying probability distribution and provide a combinatorial argument for the correctness of the constraint model. This model allows us to, for the first time, experimentally investigate inference algorithms on more than just a handful of instances. Second, we introduce a random model for WMC instances with a parameter that influences primal treewidthâthe parameter most commonly used to characterise the difficulty of an instance. We show that the easy-hard-easy pattern with respect to clause density is different for algorithms based on dynamic programming and algebraic decision diagrams than for all other solvers. We also demonstrate that all WMC algorithms scale exponentially with respect to primal treewidth, although at differing rates
Stable frames and weights
Was paper 839 in the author's list until winter 2023 when it was divided into
three.
Part I: We would like to generalize imaginary elements, weight of
ortp-weight, -simple types, etc. from
[She90, Ch. III,V,\S4] to the context of good frames. This requires allowing
the vocabulary to have predicates and function symbols of infinite arity, but
it seemed that we do not suffer any real loss.
Part II: Good frames were suggested in [She09d] as the (bare bones) right
parallel among a.e.c. to superstable (among elementary classes). Here we
consider -frames as candidates for being the right
parallel to the class of -saturated models of a stable theory (among
elementary classes). A loss as compared to the superstable case is that going
up by induction on cardinals is problematic (for cardinals of small
cofinality). But this arises only when we try to lift. For this context we
investigate the dimension.
Part III: In the context of Part II, we consider the main gap problem for the
parallel of somewhat saturated model; showing we are not worse than in the
first order case
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Locally Stationary Graph Processes
Stationary graph process models are commonly used in the analysis and
inference of data sets collected on irregular network topologies. While most of
the existing methods represent graph signals with a single stationary process
model that is globally valid on the entire graph, in many practical problems,
the characteristics of the process may be subject to local variations in
different regions of the graph. In this work, we propose a locally stationary
graph process (LSGP) model that aims to extend the classical concept of local
stationarity to irregular graph domains. We characterize local stationarity by
expressing the overall process as the combination of a set of component
processes such that the extent to which the process adheres to each component
varies smoothly over the graph. We propose an algorithm for computing LSGP
models from realizations of the process, and also study the approximation of
LSGPs locally with WSS processes. Experiments on signal interpolation problems
show that the proposed process model provides accurate signal representations
competitive with the state of the art
Decidability of Querying First-Order Theories via Countermodels of Finite Width
We propose a generic framework for establishing the decidability of a wide
range of logical entailment problems (briefly called querying), based on the
existence of countermodels that are structurally simple, gauged by certain
types of width measures (with treewidth and cliquewidth as popular examples).
As an important special case of our framework, we identify logics exhibiting
width-finite finitely universal model sets, warranting decidable entailment for
a wide range of homomorphism-closed queries, subsuming a diverse set of
practically relevant query languages. As a particularly powerful width measure,
we propose Blumensath's partitionwidth, which subsumes various other commonly
considered width measures and exhibits highly favorable computational and
structural properties. Focusing on the formalism of existential rules as a
popular showcase, we explain how finite partitionwidth sets of rules subsume
other known abstract decidable classes but -- leveraging existing notions of
stratification -- also cover a wide range of new rulesets. We expose natural
limitations for fitting the class of finite unification sets into our picture
and provide several options for remedy
Deployment of Deep Neural Networks on Dedicated Hardware Accelerators
Deep Neural Networks (DNNs) have established themselves as powerful tools for
a wide range of complex tasks, for example computer vision or natural language
processing. DNNs are notoriously demanding on compute resources and as a
result, dedicated hardware accelerators for all use cases are developed. Different
accelerators provide solutions from hyper scaling cloud environments for the
training of DNNs to inference devices in embedded systems. They implement
intrinsics for complex operations directly in hardware. A common example
are intrinsics for matrix multiplication. However, there exists a gap between
the ecosystems of applications for deep learning practitioners and hardware
accelerators. HowDNNs can efficiently utilize the specialized hardware intrinsics
is still mainly defined by human hardware and software experts.
Methods to automatically utilize hardware intrinsics in DNN operators are a
subject of active research. Existing literature often works with transformationdriven
approaches, which aim to establish a sequence of program rewrites and
data-layout transformations such that the hardware intrinsic can be used to
compute the operator. However, the complexity this of task has not yet been
explored, especially for less frequently used operators like Capsule Routing. And
not only the implementation of DNN operators with intrinsics is challenging,
also their optimization on the target device is difficult. Hardware-in-the-loop
tools are often used for this problem. They use latency measurements of implementations
candidates to find the fastest one. However, specialized accelerators
can have memory and programming limitations, so that not every arithmetically
correct implementation is a valid program for the accelerator. These invalid
implementations can lead to unnecessary long the optimization time.
This work investigates the complexity of transformation-driven processes to
automatically embed hardware intrinsics into DNN operators. It is explored
with a custom, graph-based intermediate representation (IR). While operators
like Fully Connected Layers can be handled with reasonable effort, increasing
operator complexity or advanced data-layout transformation can lead to scaling issues.
Building on these insights, this work proposes a novel method to embed
hardware intrinsics into DNN operators. It is based on a dataflow analysis.
The dataflow embedding method allows the exploration of how intrinsics and
operators match without explicit transformations. From the results it can derive
the data layout and program structure necessary to compute the operator with
the intrinsic. A prototype implementation for a dedicated hardware accelerator
demonstrates state-of-the art performance for a wide range of convolutions, while
being agnostic to the data layout. For some operators in the benchmark, the
presented method can also generate alternative implementation strategies to
improve hardware utilization, resulting in a geo-mean speed-up of Ă2.813 while
reducing the memory footprint. Lastly, by curating the initial set of possible
implementations for the hardware-in-the-loop optimization, the median timeto-
solution is reduced by a factor of Ă2.40. At the same time, the possibility to
have prolonged searches due a bad initial set of implementations is reduced,
improving the optimizationâs robustness by Ă2.35
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