Category Archives: Cognitive Sciences

Equivalence between Transformers and SVMs

September 12, 2024 11:16 ,

Davoud Ataee Tarzanagh, Yingcong Li, Christos Thrampoulidis, Samet Oymak, Transformers as Support Vector Machines, arXiv:2308.16898 [cs.LG], https://arxiv.org/abs/2308.16898.

Since its inception in “Attention Is All You Need”, transformer architecture has led to revolutionary advancements in NLP. The attention layer within the transformer admits a sequence of input tokens X and makes them interact through pairwise similarities computed as softmax(XQK⊤X⊤), where (K,Q) are the trainable key-query parameters. In this work, we establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem that separates optimal input tokens from non-optimal tokens using linear constraints on the outer-products of token pairs. This formalism allows us to characterize the implicit bias of 1-layer transformers optimized with gradient descent: (1) Optimizing the attention layer with vanishing regularization, parameterized by (K,Q), converges in direction to an SVM solution minimizing the nuclear norm of the combined parameter W=KQ⊤. Instead, directly parameterizing by W minimizes a Frobenius norm objective. We characterize this convergence, highlighting that it can occur toward locally-optimal directions rather than global ones. (2) Complementing this, we prove the local/global directional convergence of gradient descent under suitable geometric conditions. Importantly, we show that over-parameterization catalyzes global convergence by ensuring the feasibility of the SVM problem and by guaranteeing a benign optimization landscape devoid of stationary points. (3) While our theory applies primarily to linear prediction heads, we propose a more general SVM equivalence that predicts the implicit bias with nonlinear heads. Our findings are applicable to arbitrary datasets and their validity is verified via experiments. We also introduce several open problems and research directions. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.

Posted in: Artificial Intelligence , Tagged: , , ,

A novel way of addressing the maximization bias in RL

September 12, 2024 08:34 ,

Martin Waltz, Ostap Okhrin, Addressing maximization bias in reinforcement learning with two-sample testing, Artificial Intelligence, Volume 336, 2024, DOI: 10.1016/j.artint.2024.104204.

Value-based reinforcement-learning algorithms have shown strong results in games, robotics, and other real-world applications. Overestimation bias is a known threat to those algorithms and can sometimes lead to dramatic performance decreases or even complete algorithmic failure. We frame the bias problem statistically and consider it an instance of estimating the maximum expected value (MEV) of a set of random variables. We propose the T-Estimator (TE) based on two-sample testing for the mean, that flexibly interpolates between over- and underestimation by adjusting the significance level of the underlying hypothesis tests. We also introduce a generalization, termed K-Estimator (KE), that obeys the same bias and variance bounds as the TE and relies on a nearly arbitrary kernel function. We introduce modifications of Q-Learning and the Bootstrapped Deep Q-Network (BDQN) using the TE and the KE, and prove convergence in the tabular setting. Furthermore, we propose an adaptive variant of the TE-based BDQN that dynamically adjusts the significance level to minimize the absolute estimation bias. All proposed estimators and algorithms are thoroughly tested and validated on diverse tasks and environments, illustrating the bias control and performance potential of the TE and KE.

Posted in: Reinforcement learning in AI , Tagged:

It seems that vectors can help in the path toward symbols for ANNs

September 6, 2024 09:30 ,

Steven T. Piantadosi, Dyana C.Y. Muller, Joshua S. Rule, Karthikeya Kaushik, Mark Gorenstein, Elena R. Leib, Emily Sanford, Why concepts are (probably) vectors, Trends in Cognitive Sciences, Volume 28, Issue 9, 2024, Pages 844-856 DOI: 10.1016/j.tics.2024.06.011.

For decades, cognitive scientists have debated what kind of representation might characterize human concepts. Whatever the format of the representation, it must allow for the computation of varied properties, including similarities, features, categories, definitions, and relations. It must also support the development of theories, ad hoc categories, and knowledge of procedures. Here, we discuss why vector-based representations provide a compelling account that can meet all these needs while being plausibly encoded into neural architectures. This view has become especially promising with recent advances in both large language models and vector symbolic architectures. These innovations show how vectors can handle many properties traditionally thought to be out of reach for neural models, including compositionality, definitions, structures, and symbolic computational processes.

Posted in: Psycho-physiological bases of engineering , Tagged: ,

Cognitive evidences of the need of abstraction (==”modularity”) in achieving AI

September 6, 2024 08:52 ,

Schilling, M., Hammer, B., Ohl, F.W. et al. Modularity in Nervous Systems—a Key to Efficient Adaptivity for Deep Reinforcement Learning, Cogn Comput 16, 2358–2373 (2024) DOI: 10.1007/s12559-022-10080-w.

Modularity as observed in biological systems has proven valuable for guiding classical motor theories towards good answers about action selection and execution. New challenges arise when we turn to learning: Trying to scale current computational models, such as deep reinforcement learning (DRL), to action spaces, input dimensions, and time horizons seen in biological systems still faces severe obstacles unless vast amounts of training data are available. This leads to the question: does biological modularity also hold an important key for better answers to obtain efficient adaptivity for deep reinforcement learning? We review biological experimental work on modularity in biological motor control and link this with current examples of (deep) RL approaches. Analyzing outcomes of simulation studies, we show that these approaches benefit from forms of modularization as found in biological systems. We identify three different strands of modularity exhibited in biological control systems. Two of them—modularity in state (i) and in action (ii) spaces—appear as a consequence of local interconnectivity (as in reflexes) and are often modulated by higher levels in a control hierarchy. A third strand arises from chunking of action elements along a (iii) temporal dimension. Usually interacting in an overarching spatio-temporal hierarchy of the overall system, the three strands offer major “factors” decomposing the entire modularity structure. We conclude that modularity with its above strands can provide an effective prior for DRL approaches to speed up learning considerably and making learned controllers more robust and adaptive.

Posted in: Psycho-physiological bases of engineering , Tagged:

Reducing dimensionality of brain-body state dynamics

September 6, 2024 08:10 ,

Daniel S. Kluger, Micah G. Allen, Joachim Gross, Brain–body states embody complex temporal dynamics, Trends in Cognitive Sciences, Volume 28, Issue 8, 2024, Pages 695-698 DOI: 10.1016/j.tics.2024.05.003.

We propose a computational framework for high-dimensional brain–body states as transient embodiments of nested internal and external dynamics governed by interoception. Unifying recent theoretical work, we suggest ways to reduce arbitrary state complexity to an observable number of features in order to accurately predict and intervene in pathological trajectories.

Posted in: Psycho-physiological bases of engineering , Tagged:

RL in periodic scenarios

July 18, 2024 12:42 ,

A. Aniket and A. Chattopadhyay, Online Reinforcement Learning in Periodic MDP, IEEE Transactions on Artificial Intelligence, vol. 5, no. 7, pp. 3624-3637, July 2024 DOI: 10.1109/TAI.2024.3375258.

We study learning in periodic Markov decision process (MDP), a special type of nonstationary MDP where both the state transition probabilities and reward functions vary periodically, under the average reward maximization setting. We formulate the problem as a stationary MDP by augmenting the state space with the period index and propose a periodic upper confidence bound reinforcement learning-2 (PUCRL2) algorithm. We show that the regret of PUCRL2 varies linearly with the period N and as O(TlogT−−−−−√) with the horizon length T . Utilizing the information about the sparsity of transition matrix of augmented MDP, we propose another algorithm [periodic upper confidence reinforcement learning with Bernstein bounds (PUCRLB) which enhances upon PUCRL2, both in terms of regret ( O(N−−√) dependency on period] and empirical performance. Finally, we propose two other algorithms U-PUCRL2 and U-PUCRLB for extended uncertainty in the environment in which the period is unknown but a set of candidate periods are known. Numerical results demonstrate the efficacy of all the algorithms.

Posted in: Reinforcement learning in AI , Tagged:

Setting up goals, even unproductive or unuseful ones, can help in building cognition

July 5, 2024 07:51 ,

Junyi Chu, Joshua B. Tenenbaum, Laura E. Schulz, In praise of folly: flexible goals and human cognition, Trends in Cognitive Sciences, Volume 28, Issue 7, 2024, Pages 628-642 DOI: 10.1016/j.tics.2024.03.006.

Humans often pursue idiosyncratic goals that appear remote from functional ends, including information gain. We suggest that this is valuable because goals (even prima facie foolish or unachievable ones) contain structured information that scaffolds thinking and planning. By evaluating hypotheses and plans with respect to their goals, humans can discover new ideas that go beyond prior knowledge and observable evidence. These hypotheses and plans can be transmitted independently of their original motivations, adapted across generations, and serve as an engine of cultural evolution. Here, we review recent empirical and computational research underlying goal generation and planning and discuss the ways that the flexibility of our motivational system supports cognitive gains for both individuals and societies.

Posted in: Psycho-physiological bases of engineering , Tagged: ,

Review of the current methologies for achieving continuous learning, and its biological bases

June 28, 2024 08:32 ,

Buddhi Wickramasinghe, Gobinda Saha , and Kaushik Roy, Continual Learning: A Review of Techniques, Challenges, and Future Directions, IEEE TRANSACTIONS ON ARTIFICIAL INTELLIGENCE, VOL. 5, NO. 6, JUNE 2024 DOI: 10.1109/TAI.2023.3339091.

Continual learning (CL), or the ability to acquire, process, and learn from new information without forgetting acquired knowledge, is a fundamental quality of an intelligent agent. The human brain has evolved into gracefully dealing with ever-changing circumstances and learning from experience with the help of complex neurophysiological mechanisms. Even though artificial intelligence takes after human intelligence, traditional neural networks do not possess the ability to adapt to dynamic environments. When presented with new information, an artificial neural network (ANN) often completely forgets its prior knowledge, a phenomenon called catastrophic forgetting or catastrophic interference. Incorporating CL capabilities into ANNs is an active field of research and is integral to achieving artificial general intelligence. In this review, we revisit CL approaches and critically examine their strengths and limitations. We conclude that CL approaches should look beyond mitigating catastrophic forgetting and strive for systems that can learn, store, recall, and transfer knowledge, much like the human brain. To this end, we highlight the importance of adopting alternative brain-inspired data representations and learning algorithms and provide our perspective on promising new directions where CL could play an instrumental role.

See also: doi: 10.1109/TAI.2024.3355879

Posted in: Artificial Intelligence, Psycho-physiological bases of engineering , Tagged:

Thermodynamics as a way of identifying hierarchies

June 7, 2024 11:26 ,

Morten L. Kringelbach, Yonatan Sanz Perl, Gustavo Deco, The Thermodynamics of Mind, Trends in Cognitive Sciences, Volume 28, Issue 6, 2024, Pages 568-581 DOI: 10.1016/j.tics.2024.03.009.

To not only survive, but also thrive, the brain must efficiently orchestrate distributed computation across space and time. This requires hierarchical organisation facilitating fast information transfer and processing at the lowest possible metabolic cost. Quantifying brain hierarchy is difficult but can be estimated from the asymmetry of information flow. Thermodynamics has successfully characterised hierarchy in many other complex systems. Here, we propose the ‘Thermodynamics of Mind’ framework as a natural way to quantify hierarchical brain orchestration and its underlying mechanisms. This has already provided novel insights into the orchestration of hierarchy in brain states including movie watching, where the hierarchy of the brain is flatter than during rest. Overall, this framework holds great promise for revealing the orchestration of cognition.

Posted in: Psycho-physiological bases of engineering , Tagged: ,

Reducing discovered skills in DRL to the essential ones, modelling skills with SMDP Q-learning

June 7, 2024 10:38 ,

Shuai Qing, Fei Zhu, Refine to the essence: Less-redundant skill learning via diversity clustering, Engineering Applications of Artificial Intelligence, Volume 133, Part A, 2024 DOI: 10.1016/j.engappai.2024.107981.

In reinforcement learning, skill is a potentially conditional policy that solves tasks in a hierarchically controlled manner. Progress on skill discovery helps agents learn a set of diverse and useful skills without external supervision to tackle complex tasks with sparse rewards. Although most of the studies have aimed to maximize the diversity of skills discovered, the distinguishability between skills diminishes as the number of skills increases, leading to a subset of similar and redundant skills. To tackle this problem, a method called Refine to the Essence of Skills (RE-Skill) is proposed, which aims at learning skills with less redundancy. RE-Skill integrates the concepts of cluster analysis and policy distillation, clustering similar skills together based on their unique features, learning the most optimal performance within each cluster, and filtering out similar skills that involve excessive and intricate actions, thereby reducing redundancy among skills. By refining clusters of similar skills into less-redundant independent skills, RE-Skill demonstrates superior performance compared to other skill discovery algorithms and shows how these less-redundant skills effectively address downstream tasks, indicating that RE-Skill is able to extend its efficacy to engineering applications in robot control and obstacle training tasks within complex environments.

Posted in: Reinforcement learning in AI , Tagged: , , ,