Recurrent neural networks (RNNs) have achieved state-of-the-art performances in many natural language processing tasks, such as language modeling and machine translation. However, when the vocabulary is large, the RNN model will become very big (e.g., possibly beyond the memory capacity of a GPU device) and its training will become very inefficient. In this work, we propose a novel technique to tackle this challenge. The key idea is to use 2-Component (2C) shared embedding for word representations. We allocate every word in the vocabulary into a table, each row of which is associated with a vector, and each column associated with another vector.

Recurrent neural networks (RNNs) have achieved state-of-the-art performances in many natural language processing tasks, such as language modeling and machine translation. However, when the vocabulary is large, the RNN model will become very big (e.g., possibly beyond the memory capacity of a GPU device) and its training will become very inefficient. In this work, we propose a novel technique to tackle this challenge. The key idea is to use 2-Component (2C) shared embedding for word representations. We allocate every word in the vocabulary into a table, each row of which is associated with a vector, and each column associated with another vector.

Throughout this section, we will assume the same variables as in Eq.1-5 and Section 3 by default, We omit the soft constraints in original objective. "draw the optimal point back" from too far, and thus we can ignore the points outside the When we consider the effect of violating constraints, we only consider non-degraded activated cone, i.e.,, for an activated cone in a Thus it is straightforward to apply our proofs to the general form of Eq.5. A.2 Lemma 7 In order to prove Theorem 2, we give a crucial lemma. Since K is non-degraded, we have r + q n . With equations in Eq. 17, we get See Theorem 3 for the meaning of union.

In this study, we approach morphological productivity from two perspectives: a cognitive-computational perspective, and a diachronic perspective zooming in on an actual speaker, Thomas Mann. For developing the first perspective, we make use of a cognitive computational model of the mental lexicon, the discriminative lexicon model. For computational mappings between form and meaning to be productive, in the sense that novel, previously unencountered words, can be understood and produced, there must be systematicities between the form space and the semantic space. If the relation between form and meaning would be truly arbitrary, a model could memorize form and meaning pairings, but there is no way in which the model would be able to generalize to novel test data. For Finnish nominal inflection, Malay derivation, and English compounding, we explore, using the Discriminative Lexicon Model as a computational tool, to trace differences in the degree to which inflectional and word formation patterns are productive. We show that the DLM tends to associate affix-like sublexical units with the centroids of the embeddings of the words with a given affix. For developing the second perspective, we study how the intake and output of one prolific writer, Thomas Mann, changes over time. We show by means of an examination of what Thomas Mann is likely to have read, and what he wrote, that the rate at which Mann produces novel derived words is extremely low. There are far more novel words in his input than in his output. We show that Thomas Mann is less likely to produce a novel derived word with a given suffix the greater the average distance is of the embeddings of all derived words to the corresponding centroid, and discuss the challenges of using speaker-specific embeddings for low-frequency and novel words.

Rapid search and rescue is critical to maximizing survival rates following natural disasters. However, these efforts are challenged by the need to search large disaster zones, lack of reliability in the communications infrastructure, and a priori unknown numbers of objects of interest (OOIs), such as injured survivors. Aerial robots are increasingly being deployed for search and rescue due to their high mobility, but there remains a gap in deploying multi-robot autonomous aerial systems for methodical search of large environments. Prior works have relied on preprogrammed paths from human operators or are evaluated only in simulation. We bridge these gaps in the state of the art by developing and demonstrating a decentralized active search system, which biases its trajectories to take additional views of uncertain OOIs. The methodology leverages stochasticity for rapid coverage in communication denied scenarios. When communications are available, robots share poses, goals, and OOI information to accelerate the rate of search. Extensive simulations and hardware experiments in Bloomingdale, OH, are conducted to validate the approach. The results demonstrate the active search approach outperforms greedy coverage-based planning in communication-denied scenarios while maintaining comparable performance in communication-enabled scenarios.

Large Language Models (LLMs) have demonstrated great potential as generalist assistants, showcasing powerful task understanding and problem-solving capabilities. To deploy LLMs as AI assistants, it is crucial that these models exhibit desirable behavioral traits, such as non-toxicity and resilience against jailbreak attempts. Current methods for detoxification or preventing jailbreaking usually involve Supervised Fine-Tuning (SFT) or Reinforcement Learning from Human Feedback (RLHF), which requires finetuning billions of parameters through gradient descent with substantial computation cost. Furthermore, models modified through SFT and RLHF may deviate from the pretrained models, potentially leading to a degradation in foundational LLM capabilities. In this paper, we observe that surprisingly, directly editing a small subset of parameters can effectively modulate specific behaviors of LLMs, such as detoxification and resistance to jailbreaking. Specifically, for a behavior that we aim to avoid, we employ a linear classifier, which we term the behavior probe, to classify binary behavior labels within the hidden state space of the LLM. Using this probe, we introduce an algorithm to identify a critical subset of LLM parameters that significantly influence this targeted behavior. Then we directly edit these selected parameters by shifting them towards the behavior probe. Such a direct parameter editing method necessitates only inference-level computational resources. Experiments demonstrate that in the representative detoxification task, our approach achieves reductions of up to 90.0\% in toxicity on the RealToxicityPrompts dataset and 49.2\% on ToxiGen, while maintaining the LLM's general capabilities in areas such as common sense, question answering, and mathematics. Our code is available at https://github.com/lucywang720/model-surgery.

Matrix sketching, aimed at approximating a matrix $\boldsymbol{A} \in \mathbb{R}^{N\times d}$ consisting of vector streams of length $N$ with a smaller sketching matrix $\boldsymbol{B} \in \mathbb{R}^{\ell\times d}, \ell \ll N$, has garnered increasing attention in fields such as large-scale data analytics and machine learning. A well-known deterministic matrix sketching method is the Frequent Directions algorithm, which achieves the optimal $O\left(\frac{d}{\varepsilon}\right)$ space bound and provides a covariance error guarantee of $\varepsilon = \lVert \boldsymbol{A}^\top \boldsymbol{A} - \boldsymbol{B}^\top \boldsymbol{B} \rVert_2/\lVert \boldsymbol{A} \rVert_F^2$. The matrix sketching problem becomes particularly interesting in the context of sliding windows, where the goal is to approximate the matrix $\boldsymbol{A}_W$, formed by input vectors over the most recent $N$ time units. However, despite recent efforts, whether achieving the optimal $O\left(\frac{d}{\varepsilon}\right)$ space bound on sliding windows is possible has remained an open question. In this paper, we introduce the DS-FD algorithm, which achieves the optimal $O\left(\frac{d}{\varepsilon}\right)$ space bound for matrix sketching over row-normalized, sequence-based sliding windows. We also present matching upper and lower space bounds for time-based and unnormalized sliding windows, demonstrating the generality and optimality of \dsfd across various sliding window models. This conclusively answers the open question regarding the optimal space bound for matrix sketching over sliding windows. Furthermore, we conduct extensive experiments with both synthetic and real-world datasets, validating our theoretical claims and thus confirming the correctness and effectiveness of our algorithm, both theoretically and empirically.

We investigate the emergence of periodic behavior in opinion dynamics and its underlying geometry. For this, we use a bounded-confidence model with contrarian agents in a convolution social network. This means that agents adapt their opinions by interacting with their neighbors in a time-varying social network. Being contrarian, the agents are kept from reaching consensus. This is the key feature that allows the emergence of cyclical trends. We show that the systems either converge to nonconsensual equilibrium or are attracted to periodic or quasi-periodic orbits. We bound the dimension of the attractors and the period of cyclical trends. We exhibit instances where each orbit is dense and uniformly distributed within its attractor. We also investigate the case of randomly changing social networks.

It has been over six years since the Transformer architecture was put forward. Surprisingly, the vanilla Transformer architecture is still widely used today. One reason is that the lack of deep understanding and comprehensive interpretation of the Transformer architecture makes it more challenging to improve the Transformer architecture. In this paper, we first interpret the Transformer architecture comprehensively in plain words based on our understanding and experiences. The interpretations are further proved and verified. These interpretations also cover the Extractor, a family of drop-in replacements for the multi-head self-attention in the Transformer architecture. Then, we propose an improvement on a type of the Extractor that outperforms the self-attention, without introducing additional trainable parameters. Experimental results demonstrate that the improved Extractor performs even better, showing a way to improve the Transformer architecture.