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Extended resolution shows that auxiliary variables are very powerful in theory. However, attempts to exploit this potential in practice have had limited success. One reasonably effective method in this regard is bounded variable addition (BVA), which automatically reencodes formulas by introducing new variables and eliminating clauses, often significantly reducing formula size. We find motivating examples suggesting that the performance improvement caused by BVA stems not only from this size reduction but also from the introduction of effective auxiliary variables. Analyzing specific packing-coloring instances, we discover that BVA is fragile with respect to formula randomization, relying on variable order to break ties. With this understanding, we augment BVA with a heuristic for breaking ties in a structured way. We evaluate our new preprocessing technique, Structured BVA (SBVA), on more than 29,000 formulas from previous SAT competitions and show that it is robust to randomization. In a simulated competition setting, our implementation outperforms BVA on both randomized and original formulas, and appears to be well-suited for certain families of formulas.

In this paper, we first introduce the multilayer random dot product graph (MRDPG) model, which can be seen as an extension of the random dot product graph model to multilayer networks. The MRDPG model is convenient for incorporating nodes' latent positions when understanding connectivity. By modelling a multilayer network as an MRDPG, we further deploy a tensor-based method and demonstrate its superiority over the state-of-the-art methods. We then move from a static to a dynamic MRDPG and are concerned with online change point detection problems. At every time point, we observe a realisation from an $L$-layered MRDPG. Across layers, we assume shared common node sets and latent positions, but allow for different connectivity matrices. In this paper we unfold a comprehensive picture concerning a range of problems. For both fixed and random latent position cases, we propose efficient online change point detection algorithms, minimising the delay in detection while controlling the false alarms. Notably, in the random latent position case, we devise a novel nonparametric change point detection algorithm with a kernel estimator in its core, allowing for the case when the density does not exist, accommodating stochastic block models as special cases. Our theoretical findings are supported by extensive numerical experiments, with the code available online //github.com/MountLee/MRDPG.

Computer simulations, especially of complex phenomena, can be expensive, requiring high-performance computing resources. Often, to understand a phenomenon, multiple simulations are run, each with a different set of simulation input parameters. These data are then used to create an interpolant, or surrogate, relating the simulation outputs to the corresponding inputs. When the inputs and outputs are scalars, a simple machine learning model can suffice. However, when the simulation outputs are vector valued, available at locations in two or three spatial dimensions, often with a temporal component, creating a surrogate is more challenging. In this report, we use a two-dimensional problem of a jet interacting with high explosives to understand how we can build high-quality surrogates. The characteristics of our data set are unique - the vector-valued outputs from each simulation are available at over two million spatial locations; each simulation is run for a relatively small number of time steps; the size of the computational domain varies with each simulation; and resource constraints limit the number of simulations we can run. We show how we analyze these extremely large data-sets, set the parameters for the algorithms used in the analysis, and use simple ways to improve the accuracy of the spatio-temporal surrogates without substantially increasing the number of simulations required.

Although Large Language Models (LLMs) have shown great potential in Natural Language Generation, it is still challenging to characterize the uncertainty of model generations, i.e., when users could trust model outputs. Our research is derived from the heuristic facts that tokens are created unequally in reflecting the meaning of generations by auto-regressive LLMs, i.e., some tokens are more relevant (or representative) than others, yet all the tokens are equally valued when estimating uncertainty. It is because of the linguistic redundancy where mostly a few keywords are sufficient to convey the meaning of a long sentence. We name these inequalities as generative inequalities and investigate how they affect uncertainty estimation. Our results reveal that considerable tokens and sentences containing limited semantics are weighted equally or even heavily when estimating uncertainty. To tackle these biases posed by generative inequalities, we propose to jointly Shifting Attention to more Relevant (SAR) components from both the token level and the sentence level while estimating uncertainty. We conduct experiments over popular "off-the-shelf" LLMs (e.g., OPT, LLaMA) with model sizes up to 30B and powerful commercial LLMs (e.g., Davinci from OpenAI), across various free-form question-answering tasks. Experimental results and detailed demographic analysis indicate the superior performance of SAR. Code is available at //github.com/jinhaoduan/shifting-attention-to-relevance.

Artificial intelligence (AI) systems are increasingly used for providing advice to facilitate human decision making in a wide range of domains, such as healthcare, criminal justice, and finance. Motivated by limitations of the current practice where algorithmic advice is provided to human users as a constant element in the decision-making pipeline, in this paper we raise the question of when should algorithms provide advice? We propose a novel design of AI systems in which the algorithm interacts with the human user in a two-sided manner and aims to provide advice only when it is likely to be beneficial for the user in making their decision. The results of a large-scale experiment show that our advising approach manages to provide advice at times of need and to significantly improve human decision making compared to fixed, non-interactive, advising approaches. This approach has additional advantages in facilitating human learning, preserving complementary strengths of human decision makers, and leading to more positive responsiveness to the advice.

We present an end-to-end procedure for embodied exploration based on two biologically inspired computations: predictive coding and uncertainty minimization. The procedure can be applied to any exploration setting in a task-independent and intrinsically driven manner. We first demonstrate our approach in a maze navigation task and show that our model is capable of discovering the underlying transition distribution and reconstructing the spatial features of the environment. Second, we apply our model to the more complex task of active vision, where an agent must actively sample its visual environment to gather information. We show that our model is able to build unsupervised representations that allow it to actively sample and efficiently categorize sensory scenes. We further show that using these representations as input for downstream classification leads to superior data efficiency and learning speed compared to other baselines, while also maintaining lower parameter complexity. Finally, the modularity of our model allows us to analyze its internal mechanisms and to draw insight into the interactions between perception and action during exploratory behavior.

Multi-flagellated bacteria utilize the hydrodynamic interaction between their filamentary tails, known as flagella, to swim and change their swimming direction in low Reynolds number flow. This interaction, referred to as bundling and tumbling, is often overlooked in simplified hydrodynamic models such as Resistive Force Theories (RFT). However, for the development of efficient and steerable robots inspired by bacteria, it becomes crucial to exploit this interaction. In this paper, we present the construction of a macroscopic bio-inspired robot featuring two rigid flagella arranged as right-handed helices, along with a cylindrical head. By rotating the flagella in opposite directions, the robot's body can reorient itself through repeatable and controllable tumbling. To accurately model this bi-flagellated mechanism in low Reynolds flow, we employ a coupling of rigid body dynamics and the method of Regularized Stokeslet Segments (RSS). Unlike RFT, RSS takes into account the hydrodynamic interaction between distant filamentary structures. Furthermore, we delve into the exploration of the parameter space to optimize the propulsion and torque of the system. To achieve the desired reorientation of the robot, we propose a tumble control scheme that involves modulating the rotation direction and speed of the two flagella. By implementing this scheme, the robot can effectively reorient itself to attain the desired attitude. Notably, the overall scheme boasts a simplified design and control as it only requires two control inputs. With our macroscopic framework serving as a foundation, we envision the eventual miniaturization of this technology to construct mobile and controllable micro-scale bacterial robots.

The Q-learning algorithm is known to be affected by the maximization bias, i.e. the systematic overestimation of action values, an important issue that has recently received renewed attention. Double Q-learning has been proposed as an efficient algorithm to mitigate this bias. However, this comes at the price of an underestimation of action values, in addition to increased memory requirements and a slower convergence. In this paper, we introduce a new way to address the maximization bias in the form of a "self-correcting algorithm" for approximating the maximum of an expected value. Our method balances the overestimation of the single estimator used in conventional Q-learning and the underestimation of the double estimator used in Double Q-learning. Applying this strategy to Q-learning results in Self-correcting Q-learning. We show theoretically that this new algorithm enjoys the same convergence guarantees as Q-learning while being more accurate. Empirically, it performs better than Double Q-learning in domains with rewards of high variance, and it even attains faster convergence than Q-learning in domains with rewards of zero or low variance. These advantages transfer to a Deep Q Network implementation that we call Self-correcting DQN and which outperforms regular DQN and Double DQN on several tasks in the Atari 2600 domain.

Recently pre-trained language representation models such as BERT have shown great success when fine-tuned on downstream tasks including information retrieval (IR). However, pre-training objectives tailored for ad-hoc retrieval have not been well explored. In this paper, we propose Pre-training with Representative wOrds Prediction (PROP) for ad-hoc retrieval. PROP is inspired by the classical statistical language model for IR, specifically the query likelihood model, which assumes that the query is generated as the piece of text representative of the "ideal" document. Based on this idea, we construct the representative words prediction (ROP) task for pre-training. Given an input document, we sample a pair of word sets according to the document language model, where the set with higher likelihood is deemed as more representative of the document. We then pre-train the Transformer model to predict the pairwise preference between the two word sets, jointly with the Masked Language Model (MLM) objective. By further fine-tuning on a variety of representative downstream ad-hoc retrieval tasks, PROP achieves significant improvements over baselines without pre-training or with other pre-training methods. We also show that PROP can achieve exciting performance under both the zero- and low-resource IR settings. The code and pre-trained models are available at //github.com/Albert-Ma/PROP.