Alessandro Achille

Luca Zancato, Arjun Seshadri, Yonatan Dukler et al.

We describe a family of architectures to support transductive inference by allowing memory to grow to a finite but a-priori unknown bound while making efficient use of finite resources for inference. Current architectures use such resources to represent data either eidetically over a finite span ("context" in Transformers), or fading over an infinite span (in State Space Models, or SSMs). Recent hybrid architectures have combined eidetic and fading memory, but with limitations that do not allow the designer or the learning process to seamlessly modulate the two, nor to extend the eidetic memory span. We leverage ideas from Stochastic Realization Theory to develop a class of models called B'MOJO to seamlessly combine eidetic and fading memory within an elementary composable module. The overall architecture can be used to implement models that can access short-term eidetic memory "in-context," permanent structural memory "in-weights," fading memory "in-state," and long-term eidetic memory "in-storage" by natively incorporating retrieval from an asynchronously updated memory. We show that Transformers, existing SSMs such as Mamba, and hybrid architectures such as Jamba are special cases of B'MOJO and describe a basic implementation, to be open sourced, that can be stacked and scaled efficiently in hardware. We test B'MOJO on transductive inference tasks, such as associative recall, where it outperforms existing SSMs and Hybrid models; as a baseline, we test ordinary language modeling where B'MOJO achieves perplexity comparable to similarly-sized Transformers and SSMs up to 1.4B parameters, while being up to 10% faster to train. Finally, we show that B'MOJO's ability to modulate eidetic and fading memory results in better inference on longer sequences tested up to 32K tokens, four-fold the length of the longest sequences seen during training.

Tian Yu Liu, Matthew Trager, Alessandro Achille et al.

We propose to extract meaning representations from autoregressive language models by considering the distribution of all possible trajectories extending an input text. This strategy is prompt-free, does not require fine-tuning, and is applicable to any pre-trained autoregressive model. Moreover, unlike vector-based representations, distribution-based representations can also model asymmetric relations (e.g., direction of logical entailment, hypernym/hyponym relations) by using algebraic operations between likelihood functions. These ideas are grounded in distributional perspectives on semantics and are connected to standard constructions in automata theory, but to our knowledge they have not been applied to modern language models. We empirically show that the representations obtained from large models align well with human annotations, outperform other zero-shot and prompt-free methods on semantic similarity tasks, and can be used to solve more complex entailment and containment tasks that standard embeddings cannot handle. Finally, we extend our method to represent data from different modalities (e.g., image and text) using multimodal autoregressive models. Our code is available at: https://github.com/tianyu139/meaning-as-trajectories

Aditya Golatkar, Alessandro Achille, Yu-Xiang Wang et al.

We introduce AdaMix, an adaptive differentially private algorithm for training deep neural network classifiers using both private and public image data. While pre-training language models on large public datasets has enabled strong differential privacy (DP) guarantees with minor loss of accuracy, a similar practice yields punishing trade-offs in vision tasks. A few-shot or even zero-shot learning baseline that ignores private data can outperform fine-tuning on a large private dataset. AdaMix incorporates few-shot training, or cross-modal zero-shot learning, on public data prior to private fine-tuning, to improve the trade-off. AdaMix reduces the error increase from the non-private upper bound from the 167-311\% of the baseline, on average across 6 datasets, to 68-92\% depending on the desired privacy level selected by the user. AdaMix tackles the trade-off arising in visual classification, whereby the most privacy sensitive data, corresponding to isolated points in representation space, are also critical for high classification accuracy. In addition, AdaMix comes with strong theoretical privacy guarantees and convergence analysis.

Marco Fumero, Florian Wenzel, Luca Zancato et al.

Recovering the latent factors of variation of high dimensional data has so far focused on simple synthetic settings. Mostly building on unsupervised and weakly-supervised objectives, prior work missed out on the positive implications for representation learning on real world data. In this work, we propose to leverage knowledge extracted from a diversified set of supervised tasks to learn a common disentangled representation. Assuming each supervised task only depends on an unknown subset of the factors of variation, we disentangle the feature space of a supervised multi-task model, with features activating sparsely across different tasks and information being shared as appropriate. Importantly, we never directly observe the factors of variations but establish that access to multiple tasks is sufficient for identifiability under sufficiency and minimality assumptions. We validate our approach on six real world distribution shift benchmarks, and different data modalities (images, text), demonstrating how disentangled representations can be transferred to real settings.

Benjamin Bowman, Alessandro Achille, Luca Zancato et al. · amazon-science

We introduce À-la-carte Prompt Tuning (APT), a transformer-based scheme to tune prompts on distinct data so that they can be arbitrarily composed at inference time. The individual prompts can be trained in isolation, possibly on different devices, at different times, and on different distributions or domains. Furthermore each prompt only contains information about the subset of data it was exposed to during training. During inference, models can be assembled based on arbitrary selections of data sources, which we call "à-la-carte learning". À-la-carte learning enables constructing bespoke models specific to each user's individual access rights and preferences. We can add or remove information from the model by simply adding or removing the corresponding prompts without retraining from scratch. We demonstrate that à-la-carte built models achieve accuracy within $5\%$ of models trained on the union of the respective sources, with comparable cost in terms of training and inference time. For the continual learning benchmarks Split CIFAR-100 and CORe50, we achieve state-of-the-art performance.

Michael Kleinman, Alessandro Achille, Stefano Soatto et al.

We propose a notion of common information that allows one to quantify and separate the information that is shared between two random variables from the information that is unique to each. Our notion of common information is defined by an optimization problem over a family of functions and recovers the Gács-Körner common information as a special case. Importantly, our notion can be approximated empirically using samples from the underlying data distribution. We then provide a method to partition and quantify the common and unique information using a simple modification of a traditional variational auto-encoder. Empirically, we demonstrate that our formulation allows us to learn semantically meaningful common and unique factors of variation even on high-dimensional data such as images and videos. Moreover, on datasets where ground-truth latent factors are known, we show that we can accurately quantify the common information between the random variables.

Achin Jain, Gurumurthy Swaminathan, Paolo Favaro et al.

We propose an approach to estimate the number of samples required for a model to reach a target performance. We find that the power law, the de facto principle to estimate model performance, leads to large error when using a small dataset (e.g., 5 samples per class) for extrapolation. This is because the log-performance error against the log-dataset size follows a nonlinear progression in the few-shot regime followed by a linear progression in the high-shot regime. We introduce a novel piecewise power law (PPL) that handles the two data regimes differently. To estimate the parameters of the PPL, we introduce a random forest regressor trained via meta learning that generalizes across classification/detection tasks, ResNet/ViT based architectures, and random/pre-trained initializations. The PPL improves the performance estimation on average by 37% across 16 classification and 33% across 10 detection datasets, compared to the power law. We further extend the PPL to provide a confidence bound and use it to limit the prediction horizon that reduces over-estimation of data by 76% on classification and 91% on detection datasets.

Matthew Trager, Pramuditha Perera, Luca Zancato et al.

We investigate compositional structures in data embeddings from pre-trained vision-language models (VLMs). Traditionally, compositionality has been associated with algebraic operations on embeddings of words from a pre-existing vocabulary. In contrast, we seek to approximate representations from an encoder as combinations of a smaller set of vectors in the embedding space. These vectors can be seen as "ideal words" for generating concepts directly within the embedding space of the model. We first present a framework for understanding compositional structures from a geometric perspective. We then explain what these compositional structures entail probabilistically in the case of VLM embeddings, providing intuitions for why they arise in practice. Finally, we empirically explore these structures in CLIP's embeddings and we evaluate their usefulness for solving different vision-language tasks such as classification, debiasing, and retrieval. Our results show that simple linear algebraic operations on embedding vectors can be used as compositional and interpretable methods for regulating the behavior of VLMs.

Mohamad Rida Rammal, Alessandro Achille, Aditya Golatkar et al.

We derive information theoretic generalization bounds for supervised learning algorithms based on a new measure of leave-one-out conditional mutual information (loo-CMI). Contrary to other CMI bounds, which are black-box bounds that do not exploit the structure of the problem and may be hard to evaluate in practice, our loo-CMI bounds can be computed easily and can be interpreted in connection to other notions such as classical leave-one-out cross-validation, stability of the optimization algorithm, and the geometry of the loss-landscape. It applies both to the output of training algorithms as well as their predictions. We empirically validate the quality of the bound by evaluating its predicted generalization gap in scenarios for deep learning. In particular, our bounds are non-vacuous on large-scale image-classification tasks.

Alessandro Achille, Michael Kearns, Carson Klingenberg et al.

Responsible use of data is an indispensable part of any machine learning (ML) implementation. ML developers must carefully collect and curate their datasets, and document their provenance. They must also make sure to respect intellectual property rights, preserve individual privacy, and use data in an ethical way. Over the past few years, ML models have significantly increased in size and complexity. These models require a very large amount of data and compute capacity to train, to the extent that any defects in the training corpus cannot be trivially remedied by retraining the model from scratch. Despite sophisticated controls on training data and a significant amount of effort dedicated to ensuring that training corpora are properly composed, the sheer volume of data required for the models makes it challenging to manually inspect each datum comprising a training corpus. One potential fix for training corpus data defects is model disgorgement -- the elimination of not just the improperly used data, but also the effects of improperly used data on any component of an ML model. Model disgorgement techniques can be used to address a wide range of issues, such as reducing bias or toxicity, increasing fidelity, and ensuring responsible usage of intellectual property. In this paper, we introduce a taxonomy of possible disgorgement methods that are applicable to modern ML systems. In particular, we investigate the meaning of "removing the effects" of data in the trained model in a way that does not require retraining from scratch.

Kaiwen Gui, Alexander M. Dalzell, Alessandro Achille et al.

We propose a novel deterministic method for preparing arbitrary quantum states. When our protocol is compiled into CNOT and arbitrary single-qubit gates, it prepares an $N$-dimensional state in depth $O(\log(N))$ and spacetime allocation (a metric that accounts for the fact that oftentimes some ancilla qubits need not be active for the entire circuit) $O(N)$, which are both optimal. When compiled into the $\{\mathrm{H,S,T,CNOT}\}$ gate set, we show that it requires asymptotically fewer quantum resources than previous methods. Specifically, it prepares an arbitrary state up to error $ε$ with optimal depth of $O(\log(N) + \log (1/ε))$ and spacetime allocation $O(N\log(\log(N)/ε))$, improving over $O(\log(N)\log(\log (N)/ε))$ and $O(N\log(N/ε))$, respectively. We illustrate how the reduced spacetime allocation of our protocol enables rapid preparation of many disjoint states with only constant-factor ancilla overhead -- $O(N)$ ancilla qubits are reused efficiently to prepare a product state of $w$ $N$-dimensional states in depth $O(w + \log(N))$ rather than $O(w\log(N))$, achieving effectively constant depth per state. We highlight several applications where this ability would be useful, including quantum machine learning, Hamiltonian simulation, and solving linear systems of equations. We provide quantum circuit descriptions of our protocol, detailed pseudocode, and gate-level implementation examples using Braket.

Yonatan Dukler, Benjamin Bowman, Alessandro Achille et al.

We present Synergy Aware Forgetting Ensemble (SAFE), a method to adapt large models on a diverse collection of data while minimizing the expected cost to remove the influence of training samples from the trained model. This process, also known as selective forgetting or unlearning, is often conducted by partitioning a dataset into shards, training fully independent models on each, then ensembling the resulting models. Increasing the number of shards reduces the expected cost to forget but at the same time it increases inference cost and reduces the final accuracy of the model since synergistic information between samples is lost during the independent model training. Rather than treating each shard as independent, SAFE introduces the notion of a shard graph, which allows incorporating limited information from other shards during training, trading off a modest increase in expected forgetting cost with a significant increase in accuracy, all while still attaining complete removal of residual influence after forgetting. SAFE uses a lightweight system of adapters which can be trained while reusing most of the computations. This allows SAFE to be trained on shards an order-of-magnitude smaller than current state-of-the-art methods (thus reducing the forgetting costs) while also maintaining high accuracy, as we demonstrate empirically on fine-grained computer vision datasets.

Yonatan Dukler, Alessandro Achille, Hao Yang et al.

We propose InCA, a lightweight method for transfer learning that cross-attends to any activation layer of a pre-trained model. During training, InCA uses a single forward pass to extract multiple activations, which are passed to external cross-attention adapters, trained anew and combined or selected for downstream tasks. We show that, even when selecting a single top-scoring adapter, InCA achieves performance comparable to full fine-tuning, at a cost comparable to fine-tuning just the last layer. For example, with a cross-attention probe 1.3% the size of a pre-trained ViT-L/16 model, we achieve performance within 0.2% of the full fine-tuning paragon at a computational training cost of 51% of the baseline, on average across 11 downstream classification. Unlike other forms of efficient adaptation, InCA does not require backpropagating through the pre-trained model, thus leaving its execution unaltered at both training and inference. The versatility of InCA is best illustrated in fine-grained tasks, which may require accessing information absent in the last layer but accessible in intermediate layer activations. Since the backbone is fixed, InCA allows parallel ensembling as well as parallel execution of multiple tasks. InCA achieves state-of-the-art performance in the ImageNet-to-Sketch multi-task benchmark.

Michael Kleinman, Alessandro Achille, Stefano Soatto

We show that the ability of a neural network to integrate information from diverse sources hinges critically on being exposed to properly correlated signals during the early phases of training. Interfering with the learning process during this initial stage can permanently impair the development of a skill, both in artificial and biological systems where the phenomenon is known as a critical learning period. We show that critical periods arise from the complex and unstable early transient dynamics, which are decisive of final performance of the trained system and their learned representations. This evidence challenges the view, engendered by analysis of wide and shallow networks, that early learning dynamics of neural networks are simple, akin to those of a linear model. Indeed, we show that even deep linear networks exhibit critical learning periods for multi-source integration, while shallow networks do not. To better understand how the internal representations change according to disturbances or sensory deficits, we introduce a new measure of source sensitivity, which allows us to track the inhibition and integration of sources during training. Our analysis of inhibition suggests cross-source reconstruction as a natural auxiliary training objective, and indeed we show that architectures trained with cross-sensor reconstruction objectives are remarkably more resilient to critical periods. Our findings suggest that the recent success in self-supervised multi-modal training compared to previous supervised efforts may be in part due to more robust learning dynamics and not solely due to better architectures and/or more data.

Aditya Golatkar, Alessandro Achille, Ashwin Swaminathan et al.

We introduce Compartmentalized Diffusion Models (CDM), a method to train different diffusion models (or prompts) on distinct data sources and arbitrarily compose them at inference time. The individual models can be trained in isolation, at different times, and on different distributions and domains and can be later composed to achieve performance comparable to a paragon model trained on all data simultaneously. Furthermore, each model only contains information about the subset of the data it was exposed to during training, enabling several forms of training data protection. In particular, CDMs enable perfect selective forgetting and continual learning for large-scale diffusion models, allow serving customized models based on the user's access rights. Empirically the quality (FID) of the class-conditional CDMs (8-splits) is within 10% (on fine-grained vision datasets) of a monolithic model (no splits), and allows (8x) faster forgetting compared monolithic model with a maximum FID increase of 1%. When applied to text-to-image generation, CDMs improve alignment (TIFA) by 14.33% over a monolithic model trained on MSCOCO. CDMs also allow determining the importance of a subset of the data (attribution) in generating particular samples, and reduce memorization.

Luca Zancato, Alessandro Achille, Tian Yu Liu et al.

We introduce Train/Test-Time Adaptation with Retrieval (${\rm T^3AR}$), a method to adapt models both at train and test time by means of a retrieval module and a searchable pool of external samples. Before inference, ${\rm T^3AR}$ adapts a given model to the downstream task using refined pseudo-labels and a self-supervised contrastive objective function whose noise distribution leverages retrieved real samples to improve feature adaptation on the target data manifold. The retrieval of real images is key to ${\rm T^3AR}$ since it does not rely solely on synthetic data augmentations to compensate for the lack of adaptation data, as typically done by other adaptation algorithms. Furthermore, thanks to the retrieval module, our method gives the user or service provider the possibility to improve model adaptation on the downstream task by incorporating further relevant data or to fully remove samples that may no longer be available due to changes in user preference after deployment. First, we show that ${\rm T^3AR}$ can be used at training time to improve downstream fine-grained classification over standard fine-tuning baselines, and the fewer the adaptation data the higher the relative improvement (up to 13%). Second, we apply ${\rm T^3AR}$ for test-time adaptation and show that exploiting a pool of external images at test-time leads to more robust representations over existing methods on DomainNet-126 and VISDA-C, especially when few adaptation data are available (up to 8%).

Michael Kleinman, Alessandro Achille, Stefano Soatto

Critical learning periods are periods early in development where temporary sensory deficits can have a permanent effect on behavior and learned representations. Despite the radical differences between biological and artificial networks, critical learning periods have been empirically observed in both systems. This suggests that critical periods may be fundamental to learning and not an accident of biology. Yet, why exactly critical periods emerge in deep networks is still an open question, and in particular it is unclear whether the critical periods observed in both systems depend on particular architectural or optimization details. To isolate the key underlying factors, we focus on deep linear network models, and show that, surprisingly, such networks also display much of the behavior seen in biology and artificial networks, while being amenable to analytical treatment. We show that critical periods depend on the depth of the model and structure of the data distribution. We also show analytically and in simulations that the learning of features is tied to competition between sources. Finally, we extend our analysis to multi-task learning to show that pre-training on certain tasks can damage the transfer performance on new tasks, and show how this depends on the relationship between tasks and the duration of the pre-training stage. To the best of our knowledge, our work provides the first analytically tractable model that sheds light into why critical learning periods emerge in biological and artificial networks.

Pramuditha Perera, Matthew Trager, Luca Zancato et al.

We investigate whether prompts learned independently for different tasks can be later combined through prompt algebra to obtain a model that supports composition of tasks. We consider Visual Language Models (VLM) with prompt tuning as our base classifier and formally define the notion of prompt algebra. We propose constrained prompt tuning to improve performance of the composite classifier. In the proposed scheme, prompts are constrained to appear in the lower dimensional subspace spanned by the basis vectors of the pre-trained vocabulary. Further regularization is added to ensure that the learned prompt is grounded correctly to the existing pre-trained vocabulary. We demonstrate the effectiveness of our method on object classification and object-attribute classification datasets. On average, our composite model obtains classification accuracy within 2.5% of the best base model. On UTZappos it improves classification accuracy over the best base model by 8.45% on average.

Alessandro Achille, Stefano Soatto

We revisit the classic signal-to-symbol barrier in light of the remarkable ability of deep neural networks to generate realistic synthetic data. DeepFakes and spoofing highlight the feebleness of the link between physical reality and its abstract representation, whether learned by a digital computer or a biological agent. Starting from a widely applicable definition of abstract concept, we show that standard feed-forward architectures cannot capture but trivial concepts, regardless of the number of weights and the amount of training data, despite being extremely effective classifiers. On the other hand, architectures that incorporate recursion can represent a significantly larger class of concepts, but may still be unable to learn them from a finite dataset. We qualitatively describe the class of concepts that can be "understood" by modern architectures trained with variants of stochastic gradient descent, using a (free energy) Lagrangian to measure information complexity. Even if a concept has been understood, however, a network has no means of communicating its understanding to an external agent, except through continuous interaction and validation. We then characterize physical objects as abstract concepts and use the previous analysis to show that physical objects can be encoded by finite architectures. However, to understand physical concepts, sensors must provide persistently exciting observations, for which the ability to control the data acquisition process is essential (active perception). The importance of control depends on the modality, benefiting visual more than acoustic or chemical perception. Finally, we conclude that binding physical entities to digital identities is possible in finite time with finite resources, solving in principle the signal-to-symbol barrier problem, but we highlight the need for continuous validation.

Chethan Parameshwara, Alessandro Achille, Matthew Trager et al.

We describe a first step towards learning general-purpose visual representations of physical scenes using only image prediction as a training criterion. To do so, we first define "physical scene" and show that, even though different agents may maintain different representations of the same scene, the underlying physical scene that can be inferred is unique. Then, we show that NeRFs cannot represent the physical scene, as they lack extrapolation mechanisms. Those, however, could be provided by Diffusion Models, at least in theory. To test this hypothesis empirically, NeRFs can be combined with Diffusion Models, a process we refer to as NeRF Diffusion, used as unsupervised representations of the physical scene. Our analysis is limited to visual data, without external grounding mechanisms that can be provided by independent sensory modalities.

Tian Yu Liu, Aditya Golatkar, Stefano Soatto et al.

We propose a lightweight continual learning method which incorporates information from specialized datasets incrementally, by integrating it along the vector field of "generalist" models. The tangent plane to the specialist model acts as a generalist guide and avoids the kind of over-fitting that leads to catastrophic forgetting, while exploiting the convexity of the optimization landscape in the tangent plane. It maintains a small fixed-size memory buffer, as low as 0.4% of the source datasets, which is updated by simple resampling. Our method achieves strong performance across various buffer sizes for different datasets. Specifically, in the class-incremental setting we outperform the existing methods that do not require distillation by an average of 18.77% and 28.48%, for Seq-CIFAR-10 and Seq-TinyImageNet respectively. Our method can easily be used in conjunction with existing replay-based continual learning methods. When memory buffer constraints are relaxed to allow storage of metadata such as logits, we attain an error reduction of 17.84% towards the paragon performance on Seq-CIFAR-10.

Vijay Lingam, Aditya Golatkar, Anwesan Pal et al.

For large language models deployed through black-box APIs, recurring inference costs often exceed one-time training costs. This motivates composed agentic systems that amortize expensive reasoning into reusable intermediate representations. We study a broad class of such systems, termed Guide-Core Policies (GCoP), in which a guide model generates a structured strategy that is executed by a black-box core model. This abstraction subsumes base, supervised, and advisor-style approaches, which differ primarily in how the guide is trained. We formalize GCoP under a cost-sensitive utility objective and show that end-to-end performance is governed by guide-averaged executability: the probability that a strategy generated by the guide can be faithfully executed by the core. Our analysis shows that existing GCoP instantiations often fail to optimize executability under deployment constraints, resulting in brittle strategies and inefficient computation. Motivated by these insights, we propose ExecTune, a principled training recipe that combines teacher-guided acceptance sampling, supervised fine-tuning, and structure-aware reinforcement learning to directly optimize syntactic validity, execution success, and cost efficiency. Across mathematical reasoning and code-generation benchmarks, GCoP with ExecTune improves accuracy by up to 9.2% over prior state-of-the-art baselines while reducing inference cost by up to 22.4%. It enables Claude Haiku 3.5 to outperform Sonnet 3.5 on both math and code tasks, and to come within 1.7% absolute accuracy of Sonnet 4 at 38% lower cost. Beyond efficiency, GCoP also supports modular adaptation by updating the guide without retraining the core.

Michael Kleinman, Matthew Trager, Alessandro Achille et al.

Increasing the thinking budget of AI models can significantly improve accuracy, but not all questions warrant the same amount of reasoning. Users may prefer to allocate different amounts of reasoning effort depending on how they value output quality versus latency and cost. To leverage this tradeoff effectively, users need fine-grained control over the amount of thinking used for a particular query, but few approaches enable such control. Existing methods require users to specify the absolute number of desired tokens, but this requires knowing the difficulty of the problem beforehand to appropriately set the token budget for a query. To address these issues, we propose Adaptive Effort Control, a self-adaptive reinforcement learning method that trains models to use a user-specified fraction of tokens relative to the current average chain-of-thought length for each query. This approach eliminates dataset- and phase-specific tuning while producing better cost-accuracy tradeoff curves compared to standard methods. Users can dynamically adjust the cost-accuracy trade-off through a continuous effort parameter specified at inference time. We observe that the model automatically learns to allocate resources proportionally to the task difficulty and, across model scales ranging from 1.5B to 32B parameters, our approach enables a 2-3x reduction in chain-of-thought length while maintaining or improving performance relative to the base model used for RL training.

Matthew Trager, Alessandro Achille, Pramuditha Perera et al.

We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework aims to shed light on the emergence of structural patterns in data representations, a phenomenon widely acknowledged but arguably still lacking a solid formal grounding. Specifically, we introduce a characterization of compositional structures in terms of "interaction decompositions," and we establish necessary and sufficient conditions for the presence of such structures within the representations of a model.

Renos Zabounidis, Aditya Golatkar, Michael Kleinman et al.

We propose Re-FORC, an adaptive reward prediction method that, given a context, enables prediction of the expected future rewards as a function of the number of future thinking tokens. Re-FORC trains a lightweight adapter on reasoning models, demonstrating improved prediction with longer reasoning and larger models. Re-FORC enables: 1) early stopping of unpromising reasoning chains, reducing compute by 26% while maintaining accuracy, 2) optimized model and thinking length selection that achieves 4% higher accuracy at equal compute and 55% less compute at equal accuracy compared to the largest model, 3) adaptive test-time scaling, which increases accuracy by 11% in high compute regime, and 7% in low compute regime. Re-FORC allows dynamic reasoning with length control via cost-per-token thresholds while estimating computation time upfront.

Alessandro Favero, Luca Zancato, Matthew Trager et al. · cambridge

Generative Vision-Language Models (VLMs) are prone to generate plausible-sounding textual answers that, however, are not always grounded in the input image. We investigate this phenomenon, usually referred to as "hallucination" and show that it stems from an excessive reliance on the language prior. In particular, we show that as more tokens are generated, the reliance on the visual prompt decreases, and this behavior strongly correlates with the emergence of hallucinations. To reduce hallucinations, we introduce Multi-Modal Mutual-Information Decoding (M3ID), a new sampling method for prompt amplification. M3ID amplifies the influence of the reference image over the language prior, hence favoring the generation of tokens with higher mutual information with the visual prompt. M3ID can be applied to any pre-trained autoregressive VLM at inference time without necessitating further training and with minimal computational overhead. If training is an option, we show that M3ID can be paired with Direct Preference Optimization (DPO) to improve the model's reliance on the prompt image without requiring any labels. Our empirical findings show that our algorithms maintain the fluency and linguistic capabilities of pre-trained VLMs while reducing hallucinations by mitigating visually ungrounded answers. Specifically, for the LLaVA 13B model, M3ID and M3ID+DPO reduce the percentage of hallucinated objects in captioning tasks by 25% and 28%, respectively, and improve the accuracy on VQA benchmarks such as POPE by 21% and 24%.

Aditya Golatkar, Alessandro Achille, Luca Zancato et al.

Retrieval Augmented Generation (RAG) is emerging as a flexible and robust technique to adapt models to private users data without training, to handle credit attribution, and to allow efficient machine unlearning at scale. However, RAG techniques for image generation may lead to parts of the retrieved samples being copied in the model's output. To reduce risks of leaking private information contained in the retrieved set, we introduce Copy-Protected generation with Retrieval (CPR), a new method for RAG with strong copyright protection guarantees in a mixed-private setting for diffusion models.CPR allows to condition the output of diffusion models on a set of retrieved images, while also guaranteeing that unique identifiable information about those example is not exposed in the generated outputs. In particular, it does so by sampling from a mixture of public (safe) distribution and private (user) distribution by merging their diffusion scores at inference. We prove that CPR satisfies Near Access Freeness (NAF) which bounds the amount of information an attacker may be able to extract from the generated images. We provide two algorithms for copyright protection, CPR-KL and CPR-Choose. Unlike previously proposed rejection-sampling-based NAF methods, our methods enable efficient copyright-protected sampling with a single run of backward diffusion. We show that our method can be applied to any pre-trained conditional diffusion model, such as Stable Diffusion or unCLIP. In particular, we empirically show that applying CPR on top of unCLIP improves quality and text-to-image alignment of the generated results (81.4 to 83.17 on TIFA benchmark), while enabling credit attribution, copy-right protection, and deterministic, constant time, unlearning.

Benet Oriol Sabat, Alessandro Achille, Matthew Trager et al.

We propose NeRF-Insert, a NeRF editing framework that allows users to make high-quality local edits with a flexible level of control. Unlike previous work that relied on image-to-image models, we cast scene editing as an in-painting problem, which encourages the global structure of the scene to be preserved. Moreover, while most existing methods use only textual prompts to condition edits, our framework accepts a combination of inputs of different modalities as reference. More precisely, a user may provide a combination of textual and visual inputs including images, CAD models, and binary image masks for specifying a 3D region. We use generic image generation models to in-paint the scene from multiple viewpoints, and lift the local edits to a 3D-consistent NeRF edit. Compared to previous methods, our results show better visual quality and also maintain stronger consistency with the original NeRF.

Alessandro Achille, Greg Ver Steeg, Tian Yu Liu et al.

Quantifying the degree of similarity between images is a key copyright issue for image-based machine learning. In legal doctrine however, determining the degree of similarity between works requires subjective analysis, and fact-finders (judges and juries) can demonstrate considerable variability in these subjective judgement calls. Images that are structurally similar can be deemed dissimilar, whereas images of completely different scenes can be deemed similar enough to support a claim of copying. We seek to define and compute a notion of "conceptual similarity" among images that captures high-level relations even among images that do not share repeated elements or visually similar components. The idea is to use a base multi-modal model to generate "explanations" (captions) of visual data at increasing levels of complexity. Then, similarity can be measured by the length of the caption needed to discriminate between the two images: Two highly dissimilar images can be discriminated early in their description, whereas conceptually dissimilar ones will need more detail to be distinguished. We operationalize this definition and show that it correlates with subjective (averaged human evaluation) assessment, and beats existing baselines on both image-to-image and text-to-text similarity benchmarks. Beyond just providing a number, our method also offers interpretability by pointing to the specific level of granularity of the description where the source data are differentiated.

Alessandro Achille, Stefano Soatto

AI reasoning agents are already able to solve a variety of tasks by deploying tools, simulating outcomes of multiple hypotheses and reflecting on them. In doing so, they perform computation, although not in the classical sense -- there is no program being executed. Still, if they perform computation, can AI agents be universal? Can chain-of-thought reasoning solve any computable task? How does an AI Agent learn to reason? Is it a matter of model size? Or training dataset size? In this work, we reinterpret the role of learning in the context of AI Agents, viewing them as compute-capable stochastic dynamical systems, and highlight the role of time in a foundational principle for learning to reason. In doing so, we propose a shift from classical inductive learning to transductive learning -- where the objective is not to approximate the distribution of past data, but to capture their algorithmic structure to reduce the time needed to find solutions to new tasks. Transductive learning suggests that, counter to Shannon's theory, a key role of information in learning is about reduction of time rather than reconstruction error. In particular, we show that the optimal speed-up that a universal solver can achieve using past data is tightly related to their algorithmic information. Using this, we show a theoretical derivation for the observed power-law scaling of inference time versus training time. We then show that scaling model size can lead to behaviors that, while improving accuracy on benchmarks, fail any reasonable test of intelligence, let alone super-intelligence: In the limit of infinite space and time, large models can behave as savants, able to brute-force through any task without any insight. Instead, we argue that the key quantity to optimize when scaling reasoning models is time, whose critical role in learning has so far only been indirectly considered.

Yingheng Wang, Zichen Wang, Gil Sadeh et al.

Self-supervised training of language models (LMs) has seen great success for protein sequences in learning meaningful representations and for generative drug design. Most protein LMs are based on the Transformer architecture trained on individual proteins with short context lengths. Such protein LMs cannot extrapolate to longer proteins and protein complexes well. They also fail to account for the underlying biological mechanisms carried out by biomolecular interactions and dynamics i.e., proteins often interact with other proteins, molecules, and pathways in complex biological systems. In this work, we propose LC-PLM based on an alternative protein LM architecture, BiMamba-S, built upon selective structured state-space models, to learn high-quality universal protein representations at the amino acid token level using masked language modeling. We also introduce its graph-contextual variant, LC-PLM, which contextualizes protein-protein interaction (PPI) graphs for a second stage of training. LC-PLM demonstrates favorable neural scaling laws, better length extrapolation capability, and up to 30% and 16% improvements on protein downstream tasks compared to Transformer-based ESM-2 when trained with 100B and 1T tokens, respectively. LC-PLM-G further trained within the context of PPI graphs shows promising results on protein structure and function prediction tasks. Our study demonstrates the benefit of increasing the context size with computationally efficient LM architecture (e.g., structured state space models) in learning universal protein representations and incorporating molecular interaction contexts contained in biological graphs.

Tian Yu Liu, Alessandro Achille, Matthew Trager et al.

Providing Large Language Models with relevant contextual knowledge at inference time has been shown to greatly improve the quality of their generations. This is often achieved by prepending informative passages of text, or 'contexts', retrieved from external knowledge bases to their input. However, processing additional contexts online incurs significant computation costs that scale with their length. State Space Models (SSMs) offer a promising solution by allowing a database of contexts to be mapped onto fixed-dimensional states from which to start the generation. A key challenge arises when attempting to leverage information present across multiple contexts, since there is no straightforward way to condition generation on multiple independent states in existing SSMs. To address this, we leverage a simple mathematical relation derived from SSM dynamics to compose multiple states into one that efficiently approximates the effect of concatenating raw context tokens. Since the temporal ordering of contexts can often be uninformative, we enforce permutation-invariance by efficiently averaging states obtained via our composition algorithm across all possible context orderings. We evaluate our resulting method on WikiText and MSMARCO in both zero-shot and fine-tuned settings, and show that we can match the strongest performing baseline while enjoying on average 5.4x speedup.

Pramuditha Perera, Matthew Trager, Luca Zancato et al.

This paper explores the possibility of learning custom tokens for representing new concepts in Vision-Language Models (VLMs). Our aim is to learn tokens that can be effective for both discriminative and generative tasks while composing well with words to form new input queries. The targeted concept is specified in terms of a small set of images and a parent concept described using text. We operate on CLIP text features and propose to use a combination of a textual inversion loss and a classification loss to ensure that text features of the learned token are aligned with image features of the concept in the CLIP embedding space. We restrict the learned token to a low-dimensional subspace spanned by tokens for attributes that are appropriate for the given super-class. These modifications improve the quality of compositions of the learned token with natural language for generating new scenes. Further, we show that learned custom tokens can be used to form queries for text-to-image retrieval task, and also have the important benefit that composite queries can be visualized to ensure that the desired concept is faithfully encoded. Based on this, we introduce the method of Generation Aided Image Retrieval, where the query is modified at inference time to better suit the search intent. On the DeepFashion2 dataset, our method improves Mean Reciprocal Retrieval (MRR) over relevant baselines by 7%.

Benjamin Biggs, Arjun Seshadri, Yang Zou et al.

We present Diffusion Soup, a compartmentalization method for Text-to-Image Generation that averages the weights of diffusion models trained on sharded data. By construction, our approach enables training-free continual learning and unlearning with no additional memory or inference costs, since models corresponding to data shards can be added or removed by re-averaging. We show that Diffusion Soup samples from a point in weight space that approximates the geometric mean of the distributions of constituent datasets, which offers anti-memorization guarantees and enables zero-shot style mixing. Empirically, Diffusion Soup outperforms a paragon model trained on the union of all data shards and achieves a 30% improvement in Image Reward (.34 $\to$ .44) on domain sharded data, and a 59% improvement in IR (.37 $\to$ .59) on aesthetic data. In both cases, souping also prevails in TIFA score (respectively, 85.5 $\to$ 86.5 and 85.6 $\to$ 86.8). We demonstrate robust unlearning -- removing any individual domain shard only lowers performance by 1% in IR (.45 $\to$ .44) -- and validate our theoretical insights on anti-memorization using real data. Finally, we showcase Diffusion Soup's ability to blend the distinct styles of models finetuned on different shards, resulting in the zero-shot generation of hybrid styles.

Xiang Xu, Tianchen Zhao, Zheng Zhang et al.

Protecting digital identities of human face from various attack vectors is paramount, and face anti-spoofing plays a crucial role in this endeavor. Current approaches primarily focus on detecting spoofing attempts within individual frames to detect presentation attacks. However, the emergence of hyper-realistic generative models capable of real-time operation has heightened the risk of digitally generated attacks. In light of these evolving threats, this paper aims to address two key aspects. First, it sheds light on the vulnerabilities of state-of-the-art face anti-spoofing methods against digital attacks. Second, it presents a comprehensive taxonomy of common threats encountered in face anti-spoofing systems. Through a series of experiments, we demonstrate the limitations of current face anti-spoofing detection techniques and their failure to generalize to novel digital attack scenarios. Notably, the existing models struggle with digital injection attacks including adversarial noise, realistic deepfake attacks, and digital replay attacks. To aid in the design and implementation of robust face anti-spoofing systems resilient to these emerging vulnerabilities, the paper proposes key design principles from model accuracy and robustness to pipeline robustness and even platform robustness. Especially, we suggest to implement the proactive face anti-spoofing system using active sensors to significant reduce the risks for unseen attack vectors and improve the user experience.

Matthew Wallingford, Hao Li, Alessandro Achille et al.

Adapting pre-trained models with broad capabilities has become standard practice for learning a wide range of downstream tasks. The typical approach of fine-tuning different models for each task is performant, but incurs a substantial memory cost. To efficiently learn multiple downstream tasks we introduce Task Adaptive Parameter Sharing (TAPS), a general method for tuning a base model to a new task by adaptively modifying a small, task-specific subset of layers. This enables multi-task learning while minimizing resources used and competition between tasks. TAPS solves a joint optimization problem which determines which layers to share with the base model and the value of the task-specific weights. Further, a sparsity penalty on the number of active layers encourages weight sharing with the base model. Compared to other methods, TAPS retains high accuracy on downstream tasks while introducing few task-specific parameters. Moreover, TAPS is agnostic to the model architecture and requires only minor changes to the training scheme. We evaluate our method on a suite of fine-tuning tasks and architectures (ResNet, DenseNet, ViT) and show that it achieves state-of-the-art performance while being simple to implement.

Simone Bombari, Alessandro Achille, Zijian Wang et al.

Memorization of the relation between entities in a dataset can lead to privacy issues when using a trained model for question answering. We introduce Relational Memorization (RM) to understand, quantify and control this phenomenon. While bounding general memorization can have detrimental effects on the performance of a trained model, bounding RM does not prevent effective learning. The difference is most pronounced when the data distribution is long-tailed, with many queries having only few training examples: Impeding general memorization prevents effective learning, while impeding only relational memorization still allows learning general properties of the underlying concepts. We formalize the notion of Relational Privacy (RP) and, inspired by Differential Privacy (DP), we provide a possible definition of Differential Relational Privacy (DrP). These notions can be used to describe and compute bounds on the amount of RM in a trained model. We illustrate Relational Privacy concepts in experiments with large-scale models for Question Answering.

Yonatan Dukler, Alessandro Achille, Giovanni Paolini et al.

We present a method to compute the derivative of a learning task with respect to a dataset. A learning task is a function from a training set to the validation error, which can be represented by a trained deep neural network (DNN). The "dataset derivative" is a linear operator, computed around the trained model, that informs how perturbations of the weight of each training sample affect the validation error, usually computed on a separate validation dataset. Our method, DIVA (Differentiable Validation) hinges on a closed-form differentiable expression of the leave-one-out cross-validation error around a pre-trained DNN. Such expression constitutes the dataset derivative. DIVA could be used for dataset auto-curation, for example removing samples with faulty annotations, augmenting a dataset with additional relevant samples, or rebalancing. More generally, DIVA can be used to optimize the dataset, along with the parameters of the model, as part of the training process without the need for a separate validation dataset, unlike bi-level optimization methods customary in AutoML. To illustrate the flexibility of DIVA, we report experiments on sample auto-curation tasks such as outlier rejection, dataset extension, and automatic aggregation of multi-modal data.

Aditya Deshpande, Alessandro Achille, Avinash Ravichandran et al.

Fine-tuning from a collection of models pre-trained on different domains (a "model zoo") is emerging as a technique to improve test accuracy in the low-data regime. However, model selection, i.e. how to pre-select the right model to fine-tune from a model zoo without performing any training, remains an open topic. We use a linearized framework to approximate fine-tuning, and introduce two new baselines for model selection -- Label-Gradient and Label-Feature Correlation. Since all model selection algorithms in the literature have been tested on different use-cases and never compared directly, we introduce a new comprehensive benchmark for model selection comprising of: i) A model zoo of single and multi-domain models, and ii) Many target tasks. Our benchmark highlights accuracy gain with model zoo compared to fine-tuning Imagenet models. We show our model selection baseline can select optimal models to fine-tune in few selections and has the highest ranking correlation to fine-tuning accuracy compared to existing algorithms.

Orchid Majumder, Avinash Ravichandran, Subhransu Maji et al.

Few-shot learning aims to transfer information from one task to enable generalization on novel tasks given a few examples. This information is present both in the domain and the class labels. In this work we investigate the complementary roles of these two sources of information by combining instance-discriminative contrastive learning and supervised learning in a single framework called Supervised Momentum Contrastive learning (SUPMOCO). Our approach avoids a problem observed in supervised learning where information in images not relevant to the task is discarded, which hampers their generalization to novel tasks. We show that (self-supervised) contrastive learning and supervised learning are mutually beneficial, leading to a new state-of-the-art on the META-DATASET - a recently introduced benchmark for few-shot learning. Our method is based on a simple modification of MOCO and scales better than prior work on combining supervised and self-supervised learning. This allows us to easily combine data from multiple domains leading to further improvements.

Hrayr Harutyunyan, Alessandro Achille, Giovanni Paolini et al.

We define a notion of information that an individual sample provides to the training of a neural network, and we specialize it to measure both how much a sample informs the final weights and how much it informs the function computed by the weights. Though related, we show that these quantities have a qualitatively different behavior. We give efficient approximations of these quantities using a linearized network and demonstrate empirically that the approximation is accurate for real-world architectures, such as pre-trained ResNets. We apply these measures to several problems, such as dataset summarization, analysis of under-sampled classes, comparison of informativeness of different data sources, and detection of adversarial and corrupted examples. Our work generalizes existing frameworks but enjoys better computational properties for heavily over-parametrized models, which makes it possible to apply it to real-world networks.

Giovanni Paolini, Ben Athiwaratkun, Jason Krone et al.

We propose a new framework, Translation between Augmented Natural Languages (TANL), to solve many structured prediction language tasks including joint entity and relation extraction, nested named entity recognition, relation classification, semantic role labeling, event extraction, coreference resolution, and dialogue state tracking. Instead of tackling the problem by training task-specific discriminative classifiers, we frame it as a translation task between augmented natural languages, from which the task-relevant information can be easily extracted. Our approach can match or outperform task-specific models on all tasks, and in particular, achieves new state-of-the-art results on joint entity and relation extraction (CoNLL04, ADE, NYT, and ACE2005 datasets), relation classification (FewRel and TACRED), and semantic role labeling (CoNLL-2005 and CoNLL-2012). We accomplish this while using the same architecture and hyperparameters for all tasks and even when training a single model to solve all tasks at the same time (multi-task learning). Finally, we show that our framework can also significantly improve the performance in a low-resource regime, thanks to better use of label semantics.

Aditya Golatkar, Alessandro Achille, Avinash Ravichandran et al.

We show that the influence of a subset of the training samples can be removed -- or "forgotten" -- from the weights of a network trained on large-scale image classification tasks, and we provide strong computable bounds on the amount of remaining information after forgetting. Inspired by real-world applications of forgetting techniques, we introduce a novel notion of forgetting in mixed-privacy setting, where we know that a "core" subset of the training samples does not need to be forgotten. While this variation of the problem is conceptually simple, we show that working in this setting significantly improves the accuracy and guarantees of forgetting methods applied to vision classification tasks. Moreover, our method allows efficient removal of all information contained in non-core data by simply setting to zero a subset of the weights with minimal loss in performance. We achieve these results by replacing a standard deep network with a suitable linear approximation. With opportune changes to the network architecture and training procedure, we show that such linear approximation achieves comparable performance to the original network and that the forgetting problem becomes quadratic and can be solved efficiently even for large models. Unlike previous forgetting methods on deep networks, ours can achieve close to the state-of-the-art accuracy on large scale vision tasks. In particular, we show that our method allows forgetting without having to trade off the model accuracy.

Alessandro Achille, Aditya Golatkar, Avinash Ravichandran et al.

Classifiers that are linear in their parameters, and trained by optimizing a convex loss function, have predictable behavior with respect to changes in the training data, initial conditions, and optimization. Such desirable properties are absent in deep neural networks (DNNs), typically trained by non-linear fine-tuning of a pre-trained model. Previous attempts to linearize DNNs have led to interesting theoretical insights, but have not impacted the practice due to the substantial performance gap compared to standard non-linear optimization. We present the first method for linearizing a pre-trained model that achieves comparable performance to non-linear fine-tuning on most of real-world image classification tasks tested, thus enjoying the interpretability of linear models without incurring punishing losses in performance. LQF consists of simple modifications to the architecture, loss function and optimization typically used for classification: Leaky-ReLU instead of ReLU, mean squared loss instead of cross-entropy, and pre-conditioning using Kronecker factorization. None of these changes in isolation is sufficient to approach the performance of non-linear fine-tuning. When used in combination, they allow us to reach comparable performance, and even superior in the low-data regime, while enjoying the simplicity, robustness and interpretability of linear-quadratic optimization.

Michael Kleinman, Alessandro Achille, Daksh Idnani et al.

We introduce a notion of usable information contained in the representation learned by a deep network, and use it to study how optimal representations for the task emerge during training. We show that the implicit regularization coming from training with Stochastic Gradient Descent with a high learning-rate and small batch size plays an important role in learning minimal sufficient representations for the task. In the process of arriving at a minimal sufficient representation, we find that the content of the representation changes dynamically during training. In particular, we find that semantically meaningful but ultimately irrelevant information is encoded in the early transient dynamics of training, before being later discarded. In addition, we evaluate how perturbing the initial part of training impacts the learning dynamics and the resulting representations. We show these effects on both perceptual decision-making tasks inspired by neuroscience literature, as well as on standard image classification tasks.

Luca Zancato, Alessandro Achille, Avinash Ravichandran et al.

We tackle the problem of predicting the number of optimization steps that a pre-trained deep network needs to converge to a given value of the loss function. To do so, we leverage the fact that the training dynamics of a deep network during fine-tuning are well approximated by those of a linearized model. This allows us to approximate the training loss and accuracy at any point during training by solving a low-dimensional Stochastic Differential Equation (SDE) in function space. Using this result, we are able to predict the time it takes for Stochastic Gradient Descent (SGD) to fine-tune a model to a given loss without having to perform any training. In our experiments, we are able to predict training time of a ResNet within a 20% error margin on a variety of datasets and hyper-parameters, at a 30 to 45-fold reduction in cost compared to actual training. We also discuss how to further reduce the computational and memory cost of our method, and in particular we show that by exploiting the spectral properties of the gradients' matrix it is possible predict training time on a large dataset while processing only a subset of the samples.

Matteo Terzi, Alessandro Achille, Marco Maggipinto et al.

Recent results show that features of adversarially trained networks for classification, in addition to being robust, enable desirable properties such as invertibility. The latter property may seem counter-intuitive as it is widely accepted by the community that classification models should only capture the minimal information (features) required for the task. Motivated by this discrepancy, we investigate the dual relationship between Adversarial Training and Information Theory. We show that the Adversarial Training can improve linear transferability to new tasks, from which arises a new trade-off between transferability of representations and accuracy on the source task. We validate our results employing robust networks trained on CIFAR-10, CIFAR-100 and ImageNet on several datasets. Moreover, we show that Adversarial Training reduces Fisher information of representations about the input and of the weights about the task, and we provide a theoretical argument which explains the invertibility of deterministic networks without violating the principle of minimality. Finally, we leverage our theoretical insights to remarkably improve the quality of reconstructed images through inversion.

Kamal Gupta, Justin Lazarow, Alessandro Achille et al.

We address the problem of scene layout generation for diverse domains such as images, mobile applications, documents, and 3D objects. Most complex scenes, natural or human-designed, can be expressed as a meaningful arrangement of simpler compositional graphical primitives. Generating a new layout or extending an existing layout requires understanding the relationships between these primitives. To do this, we propose LayoutTransformer, a novel framework that leverages self-attention to learn contextual relationships between layout elements and generate novel layouts in a given domain. Our framework allows us to generate a new layout either from an empty set or from an initial seed set of primitives, and can easily scale to support an arbitrary of primitives per layout. Furthermore, our analyses show that the model is able to automatically capture the semantic properties of the primitives. We propose simple improvements in both representation of layout primitives, as well as training methods to demonstrate competitive performance in very diverse data domains such as object bounding boxes in natural images(COCO bounding box), documents (PubLayNet), mobile applications (RICO dataset) as well as 3D shapes (Part-Net). Code and other materials will be made available at https://kampta.github.io/layout.

Aditya Golatkar, Alessandro Achille, Stefano Soatto

We describe a procedure for removing dependency on a cohort of training data from a trained deep network that improves upon and generalizes previous methods to different readout functions and can be extended to ensure forgetting in the activations of the network. We introduce a new bound on how much information can be extracted per query about the forgotten cohort from a black-box network for which only the input-output behavior is observed. The proposed forgetting procedure has a deterministic part derived from the differential equations of a linearized version of the model, and a stochastic part that ensures information destruction by adding noise tailored to the geometry of the loss landscape. We exploit the connections between the activation and weight dynamics of a DNN inspired by Neural Tangent Kernels to compute the information in the activations.

Qing Liu, Orchid Majumder, Alessandro Achille et al.

Majority of the modern meta-learning methods for few-shot classification tasks operate in two phases: a meta-training phase where the meta-learner learns a generic representation by solving multiple few-shot tasks sampled from a large dataset and a testing phase, where the meta-learner leverages its learnt internal representation for a specific few-shot task involving classes which were not seen during the meta-training phase. To the best of our knowledge, all such meta-learning methods use a single base dataset for meta-training to sample tasks from and do not adapt the algorithm after meta-training. This strategy may not scale to real-world use-cases where the meta-learner does not potentially have access to the full meta-training dataset from the very beginning and we need to update the meta-learner in an incremental fashion when additional training data becomes available. Through our experimental setup, we develop a notion of incremental learning during the meta-training phase of meta-learning and propose a method which can be used with multiple existing metric-based meta-learning algorithms. Experimental results on benchmark dataset show that our approach performs favorably at test time as compared to training a model with the full meta-training set and incurs negligible amount of catastrophic forgetting