Christos H. Papadimitriou

Xi Chen, Christos Papadimitriou, Binghui Peng

Continual learning, or lifelong learning, is a formidable current challenge to machine learning. It requires the learner to solve a sequence of $k$ different learning tasks, one after the other, while retaining its aptitude for earlier tasks; the continual learner should scale better than the obvious solution of developing and maintaining a separate learner for each of the $k$ tasks. We embark on a complexity-theoretic study of continual learning in the PAC framework. We make novel uses of communication complexity to establish that any continual learner, even an improper one, needs memory that grows linearly with $k$, strongly suggesting that the problem is intractable. When logarithmically many passes over the learning tasks are allowed, we provide an algorithm based on multiplicative weights update whose memory requirement scales well; we also establish that improper learning is necessary for such performance. We conjecture that these results may lead to new promising approaches to continual learning.

Rashida Hakim, Ana-Andreea Stoica, Christos H. Papadimitriou et al.

Fairness in clustering has been considered extensively in the past; however, the trade-off between the two objectives -- e.g., can we sacrifice just a little in the quality of the clustering to significantly increase fairness, or vice-versa? -- has rarely been addressed. We introduce novel algorithms for tracing the complete trade-off curve, or Pareto front, between quality and fairness in clustering problems; that is, computing all clusterings that are not dominated in both objectives by other clusterings. Unlike previous work that deals with specific objectives for quality and fairness, we deal with all objectives for fairness and quality in two general classes encompassing most of the special cases addressed in previous work. Our algorithm must take exponential time in the worst case as the Pareto front itself can be exponential. Even when the Pareto front is polynomial, our algorithm may take exponential time, and we prove that this is inevitable unless P = NP. However, we also present a new polynomial-time algorithm for computing the entire Pareto front when the cluster centers are fixed, and for perhaps the most natural fairness objective: minimizing the sum, over all clusters, of the imbalance between the two groups in each cluster.

Max Dabagia, Christos H. Papadimitriou, Santosh S. Vempala

Even as machine learning exceeds human-level performance on many applications, the generality, robustness, and rapidity of the brain's learning capabilities remain unmatched. How cognition arises from neural activity is a central open question in neuroscience, inextricable from the study of intelligence itself. A simple formal model of neural activity was proposed in Papadimitriou [2020] and has been subsequently shown, through both mathematical proofs and simulations, to be capable of implementing certain simple cognitive operations via the creation and manipulation of assemblies of neurons. However, many intelligent behaviors rely on the ability to recognize, store, and manipulate temporal sequences of stimuli (planning, language, navigation, to list a few). Here we show that, in the same model, time can be captured naturally as precedence through synaptic weights and plasticity, and, as a result, a range of computations on sequences of assemblies can be carried out. In particular, repeated presentation of a sequence of stimuli leads to the memorization of the sequence through corresponding neural assemblies: upon future presentation of any stimulus in the sequence, the corresponding assembly and its subsequent ones will be activated, one after the other, until the end of the sequence. Finally, we show that any finite state machine can be learned in a similar way, through the presentation of appropriate patterns of sequences. Through an extension of this mechanism, the model can be shown to be capable of universal computation. We support our analysis with a number of experiments to probe the limits of learning in this model in key ways. Taken together, these results provide a concrete hypothesis for the basis of the brain's remarkable abilities to compute and learn, with sequences playing a vital role.

Christos Papadimitriou, Binghui Peng

The problem of continual learning in the domain of reinforcement learning, often called non-stationary reinforcement learning, has been identified as an important challenge to the application of reinforcement learning. We prove a worst-case complexity result, which we believe captures this challenge: Modifying the probabilities or the reward of a single state-action pair in a reinforcement learning problem requires an amount of time almost as large as the number of states in order to keep the value function up to date, unless the strong exponential time hypothesis (SETH) is false; SETH is a widely accepted strengthening of the P $\neq$ NP conjecture. Recall that the number of states in current applications of reinforcement learning is typically astronomical. In contrast, we show that just $\textit{adding}$ a new state-action pair is considerably easier to implement.

Daniel Mitropolsky, Christos H. Papadimitriou

We present a simulated biologically plausible language organ, made up of stylized but realistic neurons, synapses, brain areas, plasticity, and a simplified model of sensory perception. We show through experiments that this model succeeds in an important early step in language acquisition: the learning of nouns, verbs, and their meanings, from the grounded input of only a modest number of sentences. Learning in this system is achieved through Hebbian plasticity, and without backpropagation. Our model goes beyond a parser previously designed in a similar environment, with the critical addition of a biologically plausible account for how language can be acquired in the infant's brain, not just processed by a mature brain.

Christos Papadimitriou, Giorgos Filandrianos, Maria Lymperaiou et al.

Story Visualization (SV) is a challenging generative vision task, that requires both visual quality and consistency between different frames in generated image sequences. Previous approaches either employ some kind of memory mechanism to maintain context throughout an auto-regressive generation of the image sequence, or model the generation of the characters and their background separately, to improve the rendering of characters. On the contrary, we embrace a completely parallel transformer-based approach, exclusively relying on Cross-Attention with past and future captions to achieve consistency. Additionally, we propose a Character Guidance technique to focus on the generation of characters in an implicit manner, by forming a combination of text-conditional and character-conditional logits in the logit space. We also employ a caption-augmentation technique, carried out by a Large Language Model (LLM), to enhance the robustness of our approach. The combination of these methods culminates into state-of-the-art (SOTA) results over various metrics in the most prominent SV benchmark (Pororo-SV), attained with constraint resources while achieving superior computational complexity compared to previous arts. The validity of our quantitative results is supported by a human survey.

Daniel Mitropolsky, Michael J. Collins, Christos H. Papadimitriou

We describe a parser of English effectuated by biologically plausible neurons and synapses, and implemented through the Assembly Calculus, a recently proposed computational framework for cognitive function. We demonstrate that this device is capable of correctly parsing reasonably nontrivial sentences. While our experiments entail rather simple sentences in English, our results suggest that the parser can be extended beyond what we have implemented, to several directions encompassing much of language. For example, we present a simple Russian version of the parser, and discuss how to handle recursion, embedding, and polysemy.

Polina Golland, Jack Gallant, Greg Hager et al.

The history of computer science and brain sciences are intertwined. In his unfinished manuscript "The Computer and the Brain," von Neumann debates whether or not the brain can be thought of as a computing machine and identifies some of the similarities and differences between natural and artificial computation. Turing, in his 1950 article in Mind, argues that computing devices could ultimately emulate intelligence, leading to his proposed Turing test. Herbert Simon predicted in 1957 that most psychological theories would take the form of a computer program. In 1976, David Marr proposed that the function of the visual system could be abstracted and studied at computational and algorithmic levels that did not depend on the underlying physical substrate. In December 2014, a two-day workshop supported by the Computing Community Consortium (CCC) and the National Science Foundation's Computer and Information Science and Engineering Directorate (NSF CISE) was convened in Washington, DC, with the goal of bringing together computer scientists and brain researchers to explore these new opportunities and connections, and develop a new, modern dialogue between the two research communities. Specifically, our objectives were: 1. To articulate a conceptual framework for research at the interface of brain sciences and computing and to identify key problems in this interface, presented in a way that will attract both CISE and brain researchers into this space. 2. To inform and excite researchers within the CISE research community about brain research opportunities and to identify and explain strategic roles they can play in advancing this initiative. 3. To develop new connections, conversations and collaborations between brain sciences and CISE researchers that will lead to highly relevant and competitive proposals, high-impact research, and influential publications.

Moritz Hardt, Nimrod Megiddo, Christos Papadimitriou et al.

Machine learning relies on the assumption that unseen test instances of a classification problem follow the same distribution as observed training data. However, this principle can break down when machine learning is used to make important decisions about the welfare (employment, education, health) of strategic individuals. Knowing information about the classifier, such individuals may manipulate their attributes in order to obtain a better classification outcome. As a result of this behavior---often referred to as gaming---the performance of the classifier may deteriorate sharply. Indeed, gaming is a well-known obstacle for using machine learning methods in practice; in financial policy-making, the problem is widely known as Goodhart's law. In this paper, we formalize the problem, and pursue algorithms for learning classifiers that are robust to gaming. We model classification as a sequential game between a player named "Jury" and a player named "Contestant." Jury designs a classifier, and Contestant receives an input to the classifier, which he may change at some cost. Jury's goal is to achieve high classification accuracy with respect to Contestant's original input and some underlying target classification function. Contestant's goal is to achieve a favorable classification outcome while taking into account the cost of achieving it. For a natural class of cost functions, we obtain computationally efficient learning algorithms which are near-optimal. Surprisingly, our algorithms are efficient even on concept classes that are computationally hard to learn. For general cost functions, designing an approximately optimal strategy-proof classifier, for inverse-polynomial approximation, is NP-hard.

Yang Cai, Constantinos Daskalakis, Christos H. Papadimitriou

We propose an optimum mechanism for providing monetary incentives to the data sources of a statistical estimator such as linear regression, so that high quality data is provided at low cost, in the sense that the sum of payments and estimation error is minimized. The mechanism applies to a broad range of estimators, including linear and polynomial regression, kernel regression, and, under some additional assumptions, ridge regression. It also generalizes to several objectives, including minimizing estimation error subject to budget constraints. Besides our concrete results for regression problems, we contribute a mechanism design framework through which to design and analyze statistical estimators whose examples are supplied by workers with cost for labeling said examples.