We provide a novel approach to achieving a desired outcome in a coordination game: the original 2x2 game is embedded in a 2x3 game where one of the players may use a third action. For a large set of payoff values only one of the Nash equilibria of the original 2x2 game is stable under replicator dynamics. We show that this Nash equilibrium is the {\omega}-limit of all initial conditions in the interior of the state space for the modified 2x3 game. Thus, the existence of a third action for one of the players, although not used, allows both players to coordinate on one Nash equilibrium. This Nash equilibrium is the one preferred by, at least, the player with access to the new action. This approach deals with both coordination failure (players choose the payoff-dominant Nash equilibrium, if such a Nash equilibrium exists) and miscoordination (players do not use mixed strategies).
相關內容
Running quantum algorithms protected by quantum error correction requires a real time, classical decoder. To prevent the accumulation of a backlog, this decoder must process syndromes from the quantum device at a faster rate than they are generated. Most prior work on real time decoding has focused on an isolated logical qubit encoded in the surface code. However, for surface code, quantum programs of utility will require multi-qubit interactions performed via lattice surgery. A large merged patch can arise during lattice surgery -- possibly as large as the entire device. This puts a significant strain on a real time decoder, which must decode errors on this merged patch and maintain the level of fault-tolerance that it achieves on isolated logical qubits. These requirements are relaxed by using spatially parallel decoding, which can be accomplished by dividing the physical qubits on the device into multiple overlapping groups and assigning a decoder module to each. We refer to this approach as spatially parallel windows. While previous work has explored similar ideas, none have addressed system-specific considerations pertinent to the task or the constraints from using hardware accelerators. In this work, we demonstrate how to configure spatially parallel windows, so that the scheme (1) is compatible with hardware accelerators, (2) supports general lattice surgery operations, (3) maintains the fidelity of the logical qubits, and (4) meets the throughput requirement for real time decoding. Furthermore, our results reveal the importance of optimally choosing the buffer width to achieve a balance between accuracy and throughput -- a decision that should be influenced by the device's physical noise.
Motivated by the problem of compressing point sets into as few bits as possible while maintaining information about approximate distances between points, we construct random nonlinear maps $\varphi_\ell$ that compress point sets in the following way. For a point set $S$, the map $\varphi_\ell:\mathbb{R}^d \to N^{-1/2}\{-1,1\}^N$ has the property that storing $\varphi_\ell(S)$ (a \emph{sketch} of $S$) allows one to report pairwise squared distances between points in $S$ up to some multiplicative $(1\pm \epsilon)$ error with high probability as long as the minimum distance is not too small compared to $\epsilon$. The maps $\varphi_\ell$ are the $\ell$-fold composition of a certain type of random feature mapping. Moreover, we determine how large $N$ needs to be as a function of $\epsilon$ and other parameters of the point set. Compared to existing techniques, our maps offer several advantages. The standard method for compressing point sets by random mappings relies on the Johnson-Lindenstrauss lemma which implies that if a set of $n$ points is mapped by a Gaussian random matrix to $\mathbb{R}^k$ with $k =\Theta(\epsilon^{-2}\log n)$, then pairwise distances between points are preserved up to a multiplicative $(1\pm \epsilon)$ error with high probability. The main advantage of our maps $\varphi_\ell$ over random linear maps is that ours map point sets directly into the discrete cube $N^{-1/2}\{-1,1\}^N$ and so there is no additional step needed to convert the sketch to bits. For some range of parameters, our maps $\varphi_\ell$ produce sketches which require fewer bits of storage space.
Constructing a timeline requires identifying the chronological order of events in an article. In prior timeline construction datasets, temporal orders are typically annotated by either event-to-time anchoring or event-to-event pairwise ordering, both of which suffer from missing temporal information. To mitigate the issue, we develop a new evaluation dataset, TimeSET, consisting of single-document timelines with document-level order annotation. TimeSET features saliency-based event selection and partial ordering, which enable a practical annotation workload. Aiming to build better automatic timeline construction systems, we propose a novel evaluation framework to compare multiple task formulations with TimeSET by prompting open LLMs, i.e., Llama 2 and Flan-T5. Considering that identifying temporal orders of events is a core subtask in timeline construction, we further benchmark open LLMs on existing event temporal ordering datasets to gain a robust understanding of their capabilities. Our experiments show that (1) NLI formulation with Flan-T5 demonstrates a strong performance among others, while (2) timeline construction and event temporal ordering are still challenging tasks for few-shot LLMs. Our code and data are available at //github.com/kimihiroh/timeset.
Simpson's paradox is an obstacle to establishing a probabilistic association between two events $a_1$ and $a_2$, given the third (lurking) random variable $B$. We focus on scenarios when the random variables $A$ (which combines $a_1$, $a_2$, and their complements) and $B$ have a common cause $C$ that need not be observed. Alternatively, we can assume that $C$ screens out $A$ from $B$. For such cases, the correct association between $a_1$ and $a_2$ is to be defined via conditioning over $C$. This set-up generalizes the original Simpson's paradox. Now its two contradicting options simply refer to two particular and different causes $C$. We show that if $B$ and $C$ are binary and $A$ is quaternary (the minimal and the most widespread situation for valid Simpson's paradox), the conditioning over any binary common cause $C$ establishes the same direction of the association between $a_1$ and $a_2$ as the conditioning over $B$ in the original formulation of the paradox. Thus, for the minimal common cause, one should choose the option of Simpson's paradox that assumes conditioning over $B$ and not its marginalization. For tertiary (unobserved) common causes $C$ all three options of Simpson's paradox become possible (i.e. marginalized, conditional, and none of them), and one needs prior information on $C$ to choose the right option.
The deconfounder was proposed as a method for estimating causal parameters in a context with multiple causes and unobserved confounding. It is based on recovery of a latent variable from the observed causes. We disentangle the causal interpretation from the statistical estimation problem and show that the deconfounder in general estimates adjusted regression target parameters. It does so by outcome regression adjusted for the recovered latent variable termed the substitute. We refer to the general algorithm, stripped of causal assumptions, as substitute adjustment. We give theoretical results to support that substitute adjustment estimates adjusted regression parameters when the regressors are conditionally independent given the latent variable. We also introduce a variant of our substitute adjustment algorithm that estimates an assumption-lean target parameter with minimal model assumptions. We then give finite sample bounds and asymptotic results supporting substitute adjustment estimation in the case where the latent variable takes values in a finite set. A simulation study illustrates finite sample properties of substitute adjustment. Our results support that when the latent variable model of the regressors hold, substitute adjustment is a viable method for adjusted regression.
Quantum entanglement is a fundamental property of quantum mechanics and plays a crucial role in quantum computation and information. We study entanglement via the lens of computational complexity by considering quantum generalizations of the class NP with multiple unentangled quantum proofs, the so-called QMA(2) and its variants. The complexity of QMA(2) is a longstanding open problem, and only the trivial bounds QMA $\subseteq$ QMA(2) $\subseteq$ NEXP are known. In this work, we study the power of unentangled quantum proofs with non-negative amplitudes, a class which we denote $\text{QMA}^+(2)$. In this setting, we are able to design proof verification protocols for problems both using logarithmic size quantum proofs and having a constant probability gap in distinguishing yes from no instances. In particular, we design global protocols for small set expansion, unique games, and PCP verification. As a consequence, we obtain NP $\subseteq \text{QMA}^+_{\log}(2)$ with a constant gap. By virtue of the new constant gap, we are able to ``scale up'' this result to $\text{QMA}^+(2)$, obtaining the full characterization $\text{QMA}^+(2)$=NEXP by establishing stronger explicitness properties of the PCP for NEXP. One key novelty of these protocols is the manipulation of quantum proofs in a global and coherent way yielding constant gaps. Previous protocols (only available for general amplitudes) are either local having vanishingly small gaps or treat the quantum proofs as classical probability distributions requiring polynomially many proofs thereby not implying non-trivial bounds on QMA(2). Finally, we show that QMA(2) is equal to $\text{QMA}^+(2)$ provided the gap of the latter is a sufficiently large constant. In particular, if $\text{QMA}^+(2)$ admits gap amplification, then QMA(2)=NEXP.
Separating signals from an additive mixture may be an unnecessarily hard problem when one is only interested in specific properties of a given signal. In this work, we tackle simpler "statistical component separation" problems that focus on recovering a predefined set of statistical descriptors of a target signal from a noisy mixture. Assuming access to samples of the noise process, we investigate a method devised to match the statistics of the solution candidate corrupted by noise samples with those of the observed mixture. We first analyze the behavior of this method using simple examples with analytically tractable calculations. Then, we apply it in an image denoising context employing 1) wavelet-based descriptors, 2) ConvNet-based descriptors on astrophysics and ImageNet data. In the case of 1), we show that our method better recovers the descriptors of the target data than a standard denoising method in most situations. Additionally, despite not constructed for this purpose, it performs surprisingly well in terms of peak signal-to-noise ratio on full signal reconstruction. In comparison, representation 2) appears less suitable for image denoising. Finally, we extend this method by introducing a diffusive stepwise algorithm which gives a new perspective to the initial method and leads to promising results for image denoising under specific circumstances.
Tactile sensing in mobile robots remains under-explored, mainly due to challenges related to sensor integration and the complexities of distributed sensing. In this work, we present a tactile sensing architecture for mobile robots based on wheel-mounted acoustic waveguides. Our sensor architecture enables tactile sensing along the entire circumference of a wheel with a single active component: an off-the-shelf acoustic rangefinder. We present findings showing that our sensor, mounted on the wheel of a mobile robot, is capable of discriminating between different terrains, detecting and classifying obstacles with different geometries, and performing collision detection via contact localization. We also present a comparison between our sensor and sensors traditionally used in mobile robots, and point to the potential for sensor fusion approaches that leverage the unique capabilities of our tactile sensing architecture. Our findings demonstrate that autonomous mobile robots can further leverage our sensor architecture for diverse mapping tasks requiring knowledge of terrain material, surface topology, and underlying structure.
Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.
We propose a novel two-layered attention network based on Bidirectional Long Short-Term Memory for sentiment analysis. The novel two-layered attention network takes advantage of the external knowledge bases to improve the sentiment prediction. It uses the Knowledge Graph Embedding generated using the WordNet. We build our model by combining the two-layered attention network with the supervised model based on Support Vector Regression using a Multilayer Perceptron network for sentiment analysis. We evaluate our model on the benchmark dataset of SemEval 2017 Task 5. Experimental results show that the proposed model surpasses the top system of SemEval 2017 Task 5. The model performs significantly better by improving the state-of-the-art system at SemEval 2017 Task 5 by 1.7 and 3.7 points for sub-tracks 1 and 2 respectively.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191